**Preface to "Advanced Characterization and On-Line Process Monitoring of Additively Manufactured Materials and Components"**

Additive manufactured (AM) metallic materials are becoming more common in research and development. This is not completely true for AM components in the industry since they need to be screened for quality control and meet stringent requirements. The quality of AM components depends on the microstructure and internal stress resulting from the manufacturing process. Consequently, important aspects of quality control are not only defect analysis, microstructural investigations and determination of residual stress, but also online monitoring. This Special Issue is concerned with these aspects and the non-destructive testing techniques associated with the assessment of the AM part quality

**Giovanni Bruno and Christiane Maierhofer**

*Editors*

### *Editorial* **Advanced Characterization and On-Line Process Monitoring of Additively Manufactured Materials and Components**

**Giovanni Bruno \* and Christiane Maierhofer**

BAM, Bundesanstalt für Materialforschung und -Prüfung, Unter den Eichen 87, 122025 Berlin, Germany **\*** Correspondence: giovanni.bruno@bam.de

#### **1. Introduction**

Additive manufacturing (AM) techniques have risen to prominence in many industrial sectors. This rapid success of AM is due to the freeform design, which offers enormous possibilities to the engineer, and to the reduction of waste material, which has both environmental and economic advantages. Even safety-critical parts are now being produced using AM. This enthusiastic penetration of AM in our daily life is not yet paralleled by a thorough characterization and understanding of the microstructure of materials and of the internal stresses of parts. The same holds for the understanding of the formation of defects during manufacturing. While simulation efforts are sprouting and some experimental techniques for on-line monitoring are available, still little is known about the propagation of defects throughout the life of a component (from powder to operando/service conditions). This Issue was aimed at collecting contributions about the advanced characterization of AM materials and components (especially at large-scale experimental facilities such as Synchrotron and Neutron sources), as well as efforts to liaise on-line process monitoring to the final product, and even to the component during operation. The goal was to give an overview of advances in the understanding of the impacts of microstructure and defects on component performance and life at several length scales of both defects and parts.

#### **2. Characterization and Process Monitoring**

This Issue was born with a further precise scope: BAM funded in 2018 two large internal projects on characterization of materials and on-line process monitoring in additive manufacturing (AM) of metals (therefore including PBF, LMD and WAAM techniques). Therefore, we aimed to spark the debate on those two important aspects, starting from the output of such projects. In particular, we fostered a) the discussion about the influence of the microstructure and residual stress in AM of metals on the performance of materials and components and b) the investigation of possible ways to predict the appearance of defects in printed parts by on-line monitoring during manufacture. One particular aspect of point a) above was the use of advanced characterization techniques, especially based on large-scale facilities (synchrotron radiation and neutrons).

Indeed, many aspects of the generation, determination, and effects of residual stress (RS) in metallic AM materials and components are discussed in this Special Issue [1–3], whereby such stresses are determined by neutron or synchrotron X-ray diffraction. A review paper on the subject is also published in this Special Issue [4]. Moreover, advanced imaging techniques, in particular laboratory and synchrotron X-ray computed tomography, are used to disclose the defects generated by AM processes and some strategies for their mitigation [5–7].

Another axis of investigation in AM is the use of on-line monitoring techniques and their coupling with post-mortem microstructural analysis. This Special Issue contains a number of important contributions to the solution of the problems of how to extract defect distributions from temperature profiles in the manufactured parts during printing [8,9]. Not only are X-ray computed tomography data compared with infrared thermographic

**Citation:** Bruno, G.; Maierhofer, C. Advanced Characterization and On-Line Process Monitoring of Additively Manufactured Materials and Components. *Metals* **2022**, *12*, 1498. https://doi.org/10.3390/ met12091498

Received: 22 August 2022 Accepted: 6 September 2022 Published: 9 September 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

investigations, but also aspects of the calibration and registration of such techniques are thoroughly discussed [10,11].

Interestingly enough, authors contributed to demonstrating how more 'classic' nondestructive testing techniques can also well give invaluable insights into the problem of defect characterization [12], thereby complementing the high-end (but somehow expensive) characterization techniques.

Finally, the discussion is extended to component level, whereby defects [13] and residual stress [14] are determined in relevant industrial cases.

#### **3. Conclusions**

The Special Issue opens a few important points for discussion in the scientific community, such as the correlation between on-line measurements and defects in the final AM printed part, and the proper determination of residual stress in complex materials and components, such as additively manufactured metallic parts. It demonstrates that advanced and classic characterization techniques are both needed to solve the problems of defect and microstructure determination in the above-mentioned materials, together with on-line monitoring techniques and data fusion.

**Author Contributions:** G.B. conception and writing, C.M. conception. G.B. and C.M. funding and administration. All authors have read and agreed to the published version of the manuscript.

**Funding:** Part of this research received BAM internal funding in the frame of the BAM internal Projects ProMoAM and AGIL (see https://www.bam.de/Content/EN/Standard-Articles/Topics/ Materials/article-agil.html and https://www.bam.de/Content/EN/Press-Releases/2019/Materials/ 2019-03-27-detecting-defects-with-thermography.html, accessed on 5 September 2022).

**Acknowledgments:** Christiane Maierhofer passed away in June 2022. We all acknowledge her inspiring, leading and supportive role in designing the Issue, supervising her students, supporting her peers, and carrying out the role of editor. We wish she would still be with us to further help and inspire us.

**Conflicts of Interest:** The authors declare no conflict of interest. Moreover, the funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

#### **References**


### *Article* **On the Registration of Thermographic In Situ Monitoring Data and Computed Tomography Reference Data in the Scope of Defect Prediction in Laser Powder Bed Fusion**

**Simon Oster 1,\*, Tobias Fritsch 1, Alexander Ulbricht 1, Gunther Mohr 1, Giovanni Bruno 1,2, Christiane Maierhofer <sup>1</sup> and Simon J. Altenburg <sup>1</sup>**


**Abstract:** The detection of internal irregularities is crucial for quality assessment in metal-based additive manufacturing (AM) technologies such as laser powder bed fusion (L-PBF). The utilization of in-process thermography as an in situ monitoring tool in combination with post-process X-ray micro computed tomography (XCT) as a reference technique has shown great potential for this aim. Due to the small irregularity dimensions, a precise registration of the datasets is necessary as a requirement for correlation. In this study, the registration of thermography and XCT reference datasets of a cylindric specimen containing keyhole pores is carried out for the development of a porosity prediction model. The considered datasets show variations in shape, data type and dimensionality, especially due to shrinkage and material elevation effects present in the manufactured part. Since the resulting deformations are challenging for registration, a novel preprocessing methodology is introduced that involves an adaptive volume adjustment algorithm which is based on the porosity distribution in the specimen. Thus, the implementation of a simple three-dimensional image-to-image registration is enabled. The results demonstrate the influence of the part deformation on the resulting porosity location and the importance of registration in terms of irregularity prediction.

**Keywords:** selective laser melting (SLM); laser powder bed fusion (L-PBF); additive manufacturing (AM); process monitoring; infrared thermography; X-ray micro computed tomography (XCT); defect detection; image registration

#### **1. Introduction**

The industrial use of metal-based additive manufacturing (AM) processes has rapidly increased in recent years [1]. In comparison to traditional manufacturing, AM technologies such as laser powder bed fusion (L-PBF) offer the benefit of producing parts of highly complex geometry directly from the 3D CAD model while reducing the material waste [2]. L-PBF counts as one of the most established AM techniques and stands out due to its ability to produce features in high spatial resolution of tens of microns [3,4]. However, the occurrence of irregularities such as internal porosity, cracks, or surface roughness during manufacturing poses a risk to the final component quality [4,5]. Poor process parametrization (i.e., by scan velocity and laser power) was found to be an influential factor for the formation of irregularities [5]. Thermography as a radiometric nondestructive testing method has been utilized to monitor the part's local thermal history. This is performed by extracting thermal features from the spatial and temporal temperature distribution of the melt pool and part surface. From the obtained feature distribution, local areas of thermal

**Citation:** Oster, S.; Fritsch, T.; Ulbricht, A.; Mohr, G.; Bruno, G.; Maierhofer, C.; Altenburg, S.J. On the Registration of Thermographic In Situ Monitoring Data and Computed Tomography Reference Data in the Scope of Defect Prediction in Laser Powder Bed Fusion. *Metals* **2022**, *12*, 947. https://doi.org/10.3390/ met12060947

Academic Editor: Yongho Sohn

Received: 22 April 2022 Accepted: 25 May 2022 Published: 31 May 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

deviation can be identified in which porosity is likely to form [6]. As a reference technique for the determination of the spatial distribution of porosity, X-ray micro computed tomography (XCT) is widely applied [7]. The correlation of thermographic feature data and XCT reference data facilitates the prediction of porosity likelihood [6]. The in situ detection of porosity has received increasing attention in the scientific community in recent years which is evident from the rising number of publications [8].

An important aspect for the prediction of irregularities such as porosity is the registration of the in situ monitoring and the reference XCT data. Image registration can be understood as the spatial alignment of two or more images. This mainly includes the goal of finding a transformation that aligns the features of interest visible in the image data [9]. A registration function can be obtained by applying a spatial transformation on a moving image that is registered with a fixed image. Here, a similarity measure or a cost function between the two images is optimized typically in several iteration steps [10,11]. A common example of a registration function is the affine transformation model, which allows translation, rotation, scaling, and skew of the moving image. This high number of degrees of freedom with respect to image transformation is not always necessary. For many applications, it might be sufficient to utilize only a rigid model that allows translation and rotation [11]. The evaluation of the registration accuracy is challenging and often limited to a qualitative validation by the user [12].

In terms of predicting internal porosity from sensor data, methods of artificial intelligence such as machine learning (ML) algorithms can be applied [13]. A requirement for a successful prediction is the accurate spatial allocation between sensor signal and resulting porosity information. Otherwise, the model is trained on spatially mismatched data and basically learns irrelevant data patterns. In L-PBF, the occurring irregularities have small dimensions. For example, in a study by Sinclair et al. [14], keyhole pores with diameters in the range of 10–60 μm were quantified. From that, it can be concluded that for a prediction of single keyhole pores, even small allocation errors resulting from the registration may significantly reduce the performance of the prediction model.

Furthermore, the differences in data format and dimensionality resulting from the different measurement methods are challenging for registration. The layer-wise acquired thermograms from in situ thermography contain information about the thermal radiation from the different object surfaces visible in the field of view of the camera (i.e., melt pool, solidified material, unmolten powder, and machine surroundings) [15]. Due to the projection of the 3-dimensional (3D) scene to the 2-dimensional (2D) focal plane array of the camera sensor, the height information of the specimen surface is lost. Thermographic in situ monitoring in L-PBF will result in 4-dimensional (4D) data consisting of a time series of 2D thermograms for each manufactured layer. Here, the measurable signal is limited by the camera dynamics as well as the chosen spatial and temporal resolution. In contrast, XCT provides a spatially high resolved 3D object representation of the manufactured specimen. The 3D object reconstruction is created from 2D projection images captured by a flat panel X-ray detector. The projection images are reconstructed using algorithms such as the Feldkamp algorithm for cone beam geometry [16]. The reconstruction includes an interpolation process on the gray value voxel grid. Artifacts, such as scatter [17], cone beam [18], and beam hardening [19], may decrease the spatial resolution and the registration procedure. Furthermore, the XCT data contains all shape deformations of the part caused by the manufacturing process which remain in the part after removal from the dummy cylinder, such as shrinkage and warping [20].

In the literature [6,8,21–27], a range of methods is utilized to align thermographic in situ monitoring data and XCT reference data as a preparational step for irregularity prediction in the scope of L-PBF. Here, the insertion of artificial voids offers the advantage of predefined void location and shape. This benefits the identification of the defects in the determined in situ signal [8]. Mireles et al. [21] integrated artificial voids in the design of a metal part manufactured by electron beam melting. The correlation between reference XCT data and data obtained by an off-axis infrared (IR) camera was performed utilizing the known defect position within the part. Lough et al. [22] qualitatively compared single lateral slices in a cylindrical test specimen on the basis of voids that were produced by decreasing the laser power. In a study by Coeck et al. [23], the registration of IR data and XCT data was performed utilizing the large size of the present lack of fusion (LoF) voids in the observed specimen as reference object. Due to the low number of voids (45 voids in a 10 mm<sup>3</sup> volume) and their large dimensions, a straightforward spatial assignment between voids and melt pool monitoring data was feasible. The data time series derived from the off-axis photodiodes of the melt pool monitoring system were mapped to the 3D position of the laser scanner. Single data points from the obtained point cloud were allocated to a void event if the distance between the data point centroid and the void centroid was below 500 μm. Forien et al. [24] overlapped X-ray radiography scans of single tracks with coaxial pyrometry in situ monitoring data using a manual translation. Like [23], the time series data obtained by pyrometry was mapped to the 3D laser scanner position. Voids were segmented manually and correlated with the pyrometry signal in a radius of 65 μm around the void centroids.

Apart from manual mapping of signal and reference data, image registration algorithms can be utilized to automatically align multiple images for further analysis [9]. A 3D image registration was performed by Mohr et al. [25] to overlap optical tomography and XCT datasets. Here, the open-source software elastix 4.9 (University Medical Center Utrecht, Utrecht and contributors, The Netherlands) was utilized to apply an affine transformation. In a recently published study, Lough et al. [6] performed a voxel-based quantitative analysis using a layer-by-layer registration along the *z* axis of the specimen which included down-sampling of the XCT dataset. Here, the datasets were aligned manually along the *z* axis. Afterwards, an automated translation algorithm was applied. Taherkani et al. [26] registered XCT data according to the specimens CAD file using the 3D image analysis software Dragonfly Pro v4.0 (Object Research Systems Inc., Montreal, QC, Canada). As geometric reference, horizontal and vertical grooves were integrated into their specimen design. The alignment of the CT data with the melt pool monitoring data was carried out on the basis of artificial voids integrated in the specimen. Gobert et al. [27] utilized an affine mapping function to register CT data and powder bed image data acquired by a high resolution digital single-lens camera. The registration was based on minimization of the root mean square error between geometrical reference points in the datasets.

The literature [4,5] emphasizes that irregularity prediction in L-PBF is an important task to predict the service life of the produced part. The development of accurate prediction models requires a precise image registration of the acquired monitoring data and the reference data, especially due to the small dimensions of the occurring irregularities. To the authors' knowledge, few systematic investigations concerning registration methods in the scope of irregularity prediction in L-PBF have been performed. Some authors [21,22] rely on large artificial voids integrated in the specimen design to simplify their detection in the sensor data and in the ground truth data. If registration algorithms are applied, their accuracy is usually not further specified, even though it is essential information to evaluate the measurement uncertainty. Furthermore, the influence of occurring shape distortions such as warping or shrinkage in the datasets are usually not included in the registration approach.

This study focuses on the registration of feature datasets extracted from in situ thermography and an XCT dataset of a cylindric specimen that contained keyhole pores [28]. The registration is performed as a preliminary step to facilitate a highly accurate prediction of the present irregularities using ML methods (to be reported in a sister paper). The introduced registration methodology focuses on dataset preprocessing to enable the application of a simple 3D image-by-image registration. A systematic description of the singular data processing steps and the challenges arising from the different formats and dimensionalities of the datasets is given. In the context of the XCT dataset, especially the influence of the present shrinkage and material elevation on the registration accuracy is examined. Here, a novel method to adaptively adjust the part deformation is developed based on the pore

distribution in the specimen. The obtained registration accuracy is evaluated and future challenges in the context of irregularity prediction in L-PBF are derived.

#### **2. Materials and Experimental Procedures**

A cylindrical specimen was produced on a commercial L-PBF machine (SLM 280 HL, SLM Solutions Group AG, Lübeck, Germany) using AISI 316L stainless steel powder. The powder was specified as follows: apparent density of 4.58 g/cm3, Dmean = 34.69 μm, D10 = 18.22 μm, D50 = 30.5 μm, and D90 = 55.87 μm. The specimen design included a surrounding staircase structure as registration landmark (see Figure 1) inspired by a study by Gobert et al. [27]. The entire specimen was built upon the milled surface of a dummy cylinder to prevent cutting losses. The inner cylinder (diameter: 7 mm, height: 12 mm) consisted of six sections. The sections were manufactured with varying processing parameters to introduce keyhole porosity into the material. The parameter variation was performed by decreasing the scanning velocity. This resulted in increased volumetric energy densities (VED) [28], see Table 1. A hatch distance of 120 μm and a layer thickness of 50 μm were utilized. Furthermore, a cross and a letter landmark were added to the specimen's top surface as further geometric landmarks.

**Figure 1.** (**a**) Specimen design including staircase structure, top surface cross landmark, labeling letter landmark, dummy cylinder, and the introduced coordinate systems **S** and **S**- . The green areas mark sections that were manufactured using increased VED. In this view, section 1 is hidden behind the staircase which is indicated by the dashed line. (**b**) Manufactured specimen on dummy cylinder. Adapted from Ref. [28].

**Table 1.** Overview of the manufacturing conditions of the different cylinder sections (corresponding to specimen "B" in [28]). In the last column, the relative increase of the VED in comparison to sections 1, 3, and 5 is given by the percentage value in brackets.


The in situ monitoring setup consisted of three infrared cameras that were mounted off-axis outside of the machine, utilizing a custom-made optical entrance. The thermal radiation of the process was guided to the cameras by a system of gold-coated mirrors and beam splitters that were optically adapted to the spectral sensitivity of the respective camera system. For further details concerning the powder specifications, scanning strategy, and the machine setup, refer to a previously conducted study [28]. In this study, the in situ monitoring data of the deployed short-wave infrared camera (Goldeye CL-033 TEC1 from Allied Vision Technologies GmbH, Stadtroda, Germany) was utilized for the investigation.

From the short-wave infrared camera, a 4D dataset consisting of thermograms with the size of 90 pix2 (pixel scale of approximately 100 μm/pix) was obtained from 240 manufacturing layers during the process monitoring. The dataset size was 90 × 90 × nim,l × 240, where nim,l depicts the number of the image that was acquired during the exposure of a single layer l. nim,l could vary slightly for the different layers due to variations in the starting time of the recording and durations of the layer illumination. It was of the order of approximately 8000 images. All thermograms were temperature calibrated using a single point calibration method [29]. Ten different features were identified from the spatial and temporal temperature information present in the thermograms (Table 2). Detailed insights concerning the feature extraction can be found in [28]. A coordinate system **S** (Figure 1) was introduced to describe the respective 3D voxel position of each feature value in the specimen data. The features were distinguished into melt pool-based and time-dependent temperature features. Both feature classes differed in spatial information density. Melt pool-based features were extracted for each image and spatially assigned to the *x*-*y* position of the pixel with the highest temperature visible in the image. This pixel represented the position where the laser spot was located on the specimen surface. Due to the temporal and spatial resolution of the camera, the melt pool feature data were distributed sparsely in each respective layer. The sparsity was dependent on the scan velocity and resulted in data point distances along a single scan track ranging from approximately 110 μm (in section 6) to 200 μm (in sections 1, 3, and 5) with a hatch distance of 120 μm. The feature extraction resulted in 3D datasets **Fi** of the size 3 × nmp,l × 240. Here, the first dimension represented the individual feature value and its associated *x*-*y* position in the observed layer (in total 240 layers). The index i in **F<sup>i</sup>** corresponds to the observed melt pool feature and nmp,l corresponds to the number of melt pool images in the image series of the respective layer. The time-dependent features were calculated from the temporal temperature information of each image pixel from a single layer manufacturing. Hence, the spatial information density was limited only by the spatial resolution of the camera. As a result, 3D datasets **Fj** of the size 90 × <sup>90</sup> × 240 were generated for the respective time-dependent feature j. According to the spatial resolution of the camera and the nominal layer height, a voxel size of 100 × <sup>100</sup> × <sup>50</sup> <sup>μ</sup>m3 was present in all datasets.

**Table 2.** Extracted features from in-situ monitoring thermograms.


<sup>1</sup> Corresponding to the geometry and temperature distribution of the apparent melt pool blob visible in the thermogram data.

Subsequent to manufacturing, XCT was performed on the specimen and the surrounding staircase after separation from the base plate using the commercial CT-scanner GE v|tome|x 180/300 (GE Sensing and Inspection Technologies GmbH, Wunstorf, Germany) [28]. A voltage of 222 kV and a current of 45 μA were used to acquire 3000 projections

at an acquisition time of 2 s. To improve the signal-to-noise ratio of the projections, three images were taken at each of the 3000 angular positions, and their average was used for the 3D reconstruction. The reconstruction of the XCT projection data was performed by using the filtered back-projection algorithm [16], resulting in a raw dataset **V**raw with the spatial dimension of 2024 × <sup>2024</sup> × 2024 and a voxel size of 10 <sup>μ</sup>m3. The achieved voxel size enabled the quantitative analysis of features of a size above 20 μm3. A further coordinate system **S**- (Figure 1) given by the axis of the original XCT data was utilized to describe the XCT voxel positions. Subsequent to the reconstruction, a beam hardening correction [30] was performed. Furthermore, the cylinder axis was aligned parallel to the *z* axis. This was carried out using ImageJ Fiji [31] and MATLAB (MathWorks Inc., Natick, MA, USA). Here, contiguous *x*- -*y* slices were extracted from **V**raw and a circle fit [32] was applied to the circular shape visible in the slice. Afterwards, the circle fit centroids of all slices were calculated. From the calculated course of the centroids along the *z* axis, the angle of cylinder axis inclination was determined. The alignment was performed by manual rotation of the cylinder around the *x* and *y* axis. The resulting angle deviation after the axis alignment was calculated to approximately 0.005◦. This resulted in a maximum height deviation at the specimen surface of approximately 1 μm (regarding height and diameter of the CAD of the specimen). The image data were further processed by adjusting the brightness and the contrast. A 3D dataset **<sup>V</sup>**proc with the size of 711 × <sup>711</sup> × 1260 voxels was obtained containing the density information of inner cylinder and the landmark structures on the specimen top. In the following, a local thresholding algorithm introduced by Phansalker et al. [33] was applied to the data to distinguish between material and voids. The binarized dataset is denoted as **V**proc,bin. An overview of the datasets that are used in this study is given in Table 3.

**Table 3.** Overview of the obtained datasets from thermography and XCT. nmp,l corresponds to the number of images acquired during the manufacturing of a single layer and is in the order of approximately 8000 images.


#### **3. Registration Methodology and Results**

The aim of this study was the registration of the obtained thermogram feature datasets and the corresponding XCT dataset to produce an accurately aligned data basis for future irregularity prediction modeling. Preprocessing methods were used to adjust each dataset to match the original specimen geometry given by the CAD. Based on a sophisticated preprocessing workflow, the registration was simplified to a simple 3D image-to-image algorithm. In the following, the performed processing steps concerning thermogram feature data, the reference XCT data, and the image registration are described, and the obtained results are presented. A schematic overview of all performed steps is given in Figure 2.

**Figure 2.** Schematic overview the processing steps for the registration of thermographic and XCT datasets. The dashed lines indicate which steps correspond to the data preprocessing and which correspond to the registration. Datasets are indicated by bold frames.

#### *3.1. Preprocessing of Thermogram Feature Dataset*

A first evaluation of the obtained melt pool-based feature dataset **F**<sup>i</sup> and the timedependent feature dataset **F**<sup>j</sup> revealed three pre-registration challenges: First of all, due to the sparse nature of **F**<sup>i</sup> , a volume interpolation was necessary to perform an imageto-image registration [34]. Secondly, perspective distortion was found in both datasets resulting from the optical setup [28] used for the process monitoring. Such distortion led to inconsistent voxel scales in the *x* and *y* axis. Thirdly, the datasets were resampled to the voxel scale 10 μm3 of the XCT reference data to enable the precise spatial overlap of all datasets. One 3D linear interpolation algorithm was implemented to solve all three preregistration challenges. Thus, missing pixel values in the sparse melt pool-based features were interpolated (see Figure 3a), the present imaging error was rectified, and the voxel size was adjusted. The distorted image scales s*<sup>x</sup>* = 103.8 μm/pix and s*<sup>y</sup>* = 108.9 μm/pix were calculated from pre-manufacturing recordings of a calibration target (grid pattern), while the scale in the z direction s*<sup>z</sup>* was given by the layer thickness of 50 μm. The size of

the rectified target volume **A** (width wA, depth dA, and height hA) was derived from the former thermogram size 90 pix<sup>2</sup> and the overall layer count (240 layers):

$$\mathbf{w}\_{\mathbf{A}} = 90 \cdot \frac{\mathbf{s}\_{\mathbf{x'}}}{\mathbf{s}\_x} \tag{1}$$

$$\mathbf{d}\_{\Lambda} = 90 \cdot \frac{\mathbf{s}\_{y'}}{\mathbf{s}\_{y}} \tag{2}$$

$$\mathbf{h}\_{\rm A} = 240 \cdot \frac{\mathbf{s}\_{\rm z'}}{\mathbf{s}\_{\rm z}} \tag{3}$$

Here, s*x*- = 10 μm, s*y*- = 10 μm and s*z*- = 10 μm denote the voxel size of the XCT data. From the initial datasets **F**<sup>i</sup> and **F**<sup>j</sup> , k = i + j = 10 datasets **<sup>A</sup>**<sup>k</sup> with a size of <sup>935</sup> × <sup>980</sup> × <sup>1200</sup> voxels were interpolated. The results of the interpolation of melt pool-based feature data from a single layer are depicted in Figure 3b.

**Figure 3.** Preprocessing of thermogram feature data (here: melt pool blob size) of layer 59. (**a**) Incremental data points of melt pool blob size containing image distortion. (**b**) Rectified and resampled thermogram with an adjusted scale of 10 μm/pix.

#### *3.2. Preprocessing of XCT Dataset*

The XCT dataset contained the porosity information present in the specimen. The dimensions and the shape of the cylindric specimen in the XCT dataset deviated significantly from the shape of the original CAD. A first comparison of the specimen to the CAD model height showed a vertical shrinkage. Furthermore, the observation of the top surface revealed a severe shape deformation. The surface rim was elevated in comparison to its center. This resulted in significant height deviations (see Figure 4). The maximum height differences of approximately 400 μm between surface rim and center (which corresponds to 8 manufacturing layers) would produce major errors if a simple lateral slicing along the *x*- -*y* plane was performed for correlation with the monitoring data. Alongside this, the registration landmarks (letter and cross) that were later utilized to obtain a registration function were inspected since they can be clearly separated from the main cylindrical specimen. The bordering areas of the landmarks exhibited a local height increase. This represented a distortion of the original surface (see Figure 4). The surface deformation posed a major difficulty for the registration because it was unclear how the deformation was formed over the course of the manufacturing process.

**Figure 4.** Cross-sectional slice of XCT reference volume at a depth of *x*- = 3 mm. Gray value variations in the bulk material are image artifacts originated by the cone-beam reconstruction of strong absorbing material. Height elevations on the surface rim and lateral shrinkage in the section of increased VED are visible. The approximated top surface shape (continuous blue line) is repeated below (dashed blue line) for a better comparison with the pore distribution. In Detail A, the areas of local surface height increase close to the landmarks are marked by blue circles.

Ulbricht et al. [7] found a similar surface deformation in an equally designed specimen that was manufactured using the same material and machine. Furthermore, they found indications of a comparable surface deformation at multiple stages of the manufacturing process. These previous deformations were estimated from the observation of LoF voids at the transition from a void-free section and followed by a section with artificial voids (notches) within the specimen. The authors suggested that the deformation could have been present during the entire manufacturing process. In the current study, the observation of the pore distribution in the transition from section 5 to 6 indicated a similar effect (see Figure 4). Therefore, a method was developed to adjust the surface in the dataset based on the deformation information obtained from the pore distribution. The method assumed that all previous surface deformations that had formed during manufacturing had a qualitatively similar shape to the visible deformation of the specimen surface. Furthermore, it was assumed that the previous surface deformation can be reconstructed from the depth distribution of the lowest keyhole pores at the onset of a region with increased VED, i.e., section 6. Finally, the preprocessing method for the XCT dataset consisted of five steps (compare Figure 2):


#### 3.2.1. Preliminary Height Adjustment

Due to the height difference between the manufactured specimen represented in the XCT dataset and the original CAD, a preliminary height adjustment was performed. The shrinkage was estimated from the height of the staircase treads that were built as registration landmarks. The staircase was built upon the milled surface of the dummy structure and scanned by XCT along with the cylindric specimen. The stair treads were located at specific layer heights, starting at a height of 3 mm, and repeating every 1 mm. Even though the staircase was built without VED variation (utilization of standard VED of 65.45 J/mm3), it was found that the highest staircase tread had an approximately equal height to the rim of the top surface. Furthermore, it was found that section 1 exhibited a

height decrease of approximately 230 μm (7.66%) in comparison to the CAD model. This was probably caused by solidification shrinkage [25]. In the remaining sections 2 to 6, the height decrease was noticeably lower and amounted in total to approximately 60 μm (0.67%). A 3D linear interpolation to the original CAD height was utilized to perform the height adjustment. From the large difference in height decrease, it was decided to split the whole dataset into two subsets (the first subset containing section 1, and the second subset containing sections 2 to 6) and to perform separate height adjustments. Afterwards, the two subsets were vertically fused again.

The voxel size was effectively locally distorted by the performed height adjustment. In the case of a quantitative void volume analysis, this must be considered. For this study, this effect was of no further significance.

#### 3.2.2. Determination of the Surface Deformation

For the quantification of the surface deformation, the voxels representing the specimen surface were extracted in the first place. For further refinement of the surface information of **V**proc,bin, the extraction was performed on the adjusted intensities of **V**proc. Here, a customized thresholding algorithm was utilized. It is based on the ISO50% value TISO50% which was calculated as a global threshold from the intensity values of **V**proc. The ISO50% value represents the average between the highest peak of background voxels and the highest peak of material voxels in a histogram of all voxel gray values [35]. The surface height was calculated for every single *x*- -*y* position. To suppress errors arising from possible reconstruction artifacts located above the surface, the algorithm was extended by further thresholding conditions. A subset **V**proc,ROI was extracted from a region of interest (ROI) in **V**proc which included the entire surface information. I*x*- *,y*- *,z* corresponds to the respective gray value of a voxel in **V**proc,ROI where the indices *x*- , *y*- , and *z* correspond to the voxel position in the respective axis. A surface edge was determined if the following criteria were fulfilled:

$$\mathbf{T}\_{\mathbf{x}',\mathbf{y}',z'} \succeq \mathbf{T}\_{\mathbf{I}\mathbf{S}\mathbf{C}\mathbf{S}\mathbf{0}\mathbf{y}}\tag{4}$$

$$\mathcal{I}\_{\mathbf{x'},\mathbf{y'},z'+1} \prec \mathcal{T}\_{\text{ISO50\%}}\tag{5}$$

$$\sum\_{\mathbf{i}=1}^{\text{nvox}} \mathbf{I}\_{\mathbf{x}', \mathbf{y}', \mathbf{z}'-\mathbf{i}} \ge \mathbf{n}\_{\text{vox}} \cdot \mathbf{T}\_{\text{ISO50\%}}\tag{6}$$

nvox is the number of voxels below the observed edge voxel which were considered for the surface determination. The parameter was manually tuned to 10, which produced good results concerning the suppression of reconstruction artifacts. The 2D array of calculated surface data points (Figure 5a) were denoted as **H**surf. Subsequently, the cross landmark, the labeling letter, and their bordering areas were removed since the found local surface increase was obstructive for determination of the surface information. Here, arithmetic image multiplication with polygon masks was used to perform the removal of the cross landmark and the labeling letter. An interpolation algorithm [36] was used to reconstruct the missing surface parts. Additional smoothing was applied to remove local height deviations, i.e., spatter elements that were connected to the surface. The determination accuracy was quantified by a mean absolute error (MAE) of approximately 4 μm. The resulting surface reconstruction **H**surf,rec is depicted in Figure 5b.

**Figure 5.** (**a**) Part surface extracted by thresholding algorithm. (**b**) Reconstructed part surface after removal of registration landmarks. (**c**) Reconstructed surface from lowest pores in the transition zone (between sections 5 and 6) at an approximately average specimen height of 10.7 mm. (**d**) Part surface after application of deformation adjustment function extracted by thresholding algorithm.

#### 3.2.3. Estimation of the Surface Deformation History

The distribution of the pores in the transition zones between sections of standard VED followed by sections of increased VED was the basis for the estimation of the former surface deformation history. Such pores in the transition zones are called boundary pores hereafter. Due to the increased VED utilized in sections 2, 4, and 6, predominantly keyhole pores were present. Keyhole pores are likely to form at the bottom of the melt pool and be entrapped in its lower part [37]. Inspired by the findings of Ulbricht et al. [7], it is assumed that the topography of the former surface can be reconstructed from the statistically distributed pores at the boundary of the transition zone. The first step to estimate the previous surface deformation was the extraction of the boundary pores. The transition zones from section 1 to 2 and from section 3 to 4 were not regarded due to the low information density resulting from the low number of pores in these sections. The decreased number of pores contributed to the lower increase of VED [38] utilized in these sections (+25% in section 2 and +50% in section 4). Only in the transition from section 5 to 6 was a sufficient number of pores present. A data subset from height *z*- = 1050 to 1090 vox (equal to a specimen height of 10.5 μm to 10.9 μm) that contained the lowest boundary pores was extracted from

**V**proc,bin. The 3D position of each respective pore centroid in the subset was calculated (MATLAB function "regionprops3") and stored in a 2D array. The pores located at the rim of the obtained disc-shaped point cloud were extracted (MATLAB function "boundary"). For the surface reconstruction, only the pores of the bottom part of the rim were utilized since they were located in the transition zone. These centroids were denoted as **H**pores and were located at an average centroid height of approximately *z*- = 1070 voxel. Here, the same interpolation algorithm as used for the top surface [36] was applied to reconstruct the surface shape. This shape was denoted as **H**pores,rec. Additional smoothing was added to remove local inhomogeneities. **H**pores,rec is depicted in Figure 5c. Good agreement was found between the reconstructions **H**pores,rec and **H**surf,rec. Furthermore, the standard deviation (STD) σpores of the original centroid heights in **H**pores,rec was calculated to 33 μm, which is significantly lower than the STD σsurf of **H**surf,rec (95 μm).

#### 3.2.4. Determination of a Deformation Adjustment Function

Based on **H**pores,rec, a deformation adjustment function g*x*- ,*y*- (*z*- ) was determined for the compensation of the surface deformation history. As stated above, the method assumed that all surface deformations during the manufacturing had an approximately similar shape like the surface deformation **H**surf,rec determined in Section 3.2.2. However, the comparison of σpore and σsurf implied that the average height amplitude of the deformed surfaces increased with growing *z*- . This was taken into account by the introduction of a compression factor c. The idea behind c was the adaption of the average height amplitude in dependency to *z*- . Due to the given pore distribution, only three reference surfaces were available for the calculation of c: (i) The non-deformed milled surface of the dummy base volume **H**plate at *z*- = 0 vox with σplate = 0, (ii) the surface reconstruction **H**pores,rec from the boundary pores at an average height of *z*- ≈ 1070 voxel with <sup>σ</sup>pores = 33 <sup>μ</sup>m, and (iii) the surface reconstruction **H**surf,rec with σsurf = 95 μm of the specimen top. Due to this lack of information, only a sectional linear interpolation approach was feasible for the calculation of c (see Figure 6a).

**Figure 6.** (**a**) Qualitative illustration of the linear sectional fit for the determination of the compression factor c. (**b**) Cross-sectional slice of the XCT data at a depth of 3.5 mm. The height deviations corresponding to the manufacturing layers calculated from g*x*- *,y*-(*z*- ) are depicted as blue lines.

The compression factor c is given by:

$$\mathbf{c}(z') = \begin{cases} \frac{\mathbf{m}\_1 z' + \mathbf{b}\_1}{\sigma^{\text{surf}}} : \overline{\mathbf{H}^{\text{plate}}} < z' < \overline{\mathbf{H}^{\text{Process,rec}}}\\ \frac{\mathbf{m}\_2 z' + \mathbf{b}\_2}{\sigma^{\text{surf}}} : \overline{\mathbf{H}^{\text{ores,rec}}} \le z' < \overline{\mathbf{H}^{\text{surf,rec}}} \end{cases} \tag{7}$$

m1 = 3.902 × <sup>10</sup><sup>−</sup>3, m2 = 4.479 × <sup>10</sup>−<sup>3</sup> correspond to the slope and b1 = 0, b2 <sup>=</sup> −4.33 correspond to the intercept of g*x*- *,y*-(*z*- ) in the respective interpolation section (see Figure 6a). The sections were chosen corresponding to the average height of the substrate plate **H**plate = 0, the average height of the extracted pore centroids **H**pores,rec and the average surface height **H**surf,rec. To obtain values between 0 and 1, a normalization with σsurf was performed.

The local height deviation at an arbitrary voxel position resulting from the surface deformation was calculated by the deformation adjustment function g*x*- *,y*-(*z*- ):

$$\mathbf{g}\_{\mathbf{x'},\mathbf{y'}}(z') = \Delta \mathbf{H}\_{\mathbf{x'},\mathbf{y'}}^{\text{surf},\text{rec}} \cdot \mathbf{c}(z') \tag{8}$$

$$
\Delta \mathbf{H}\_{\mathbf{x'}, \mathbf{y'}}^{\text{surf}} = \mathbf{H}\_{\mathbf{x'}, \mathbf{y'}}^{\text{surf,rec}} - \overline{\mathbf{H}^{\text{surf,rec}}} \tag{9}
$$

Here, the local height deviation at voxel position *x* and *y* is given by ΔHsurf,rec *x*-,*y*- . Exemplary values of g*x*- *,y*-(*z*- ) for chosen layer heights are depicted in Figure 6b.

#### 3.2.5. Volume Reconstruction Utilizing the Deformation Adjustment Function

Equation (8) gives an incremental floating number which corresponds to the height deviation of the considered voxel with the height *z*- . The volume reconstruction was performed by the generation of a new volume **V**final from the distorted volume **V**proc,bin. Here, for each new voxel in **V**final, the position of a corresponding voxel in **V**proc,bin was calculated and its associated binary value was assigned to the new voxel:

$$\mathbf{V}^{\text{rec}}(\mathbf{x}', \mathbf{y}', \mathbf{z}') \;= \; \mathbf{V}^{\text{proc,bin}}(\mathbf{x}', \mathbf{y}', \mathbf{z}^\*) \tag{10}$$

$$\text{with } z\* = \begin{bmatrix} z' + \mathbf{g}\_{x',y'}(z') \end{bmatrix} \tag{11}$$

z\* was rounded to avoid non-integer values. Since the specimen height was locally adjusted to the CAD height, the number of voxels containing density information was larger in **V**final than in **V**proc,bin. Therefore, single voxel values from **V**proc,bin were duplicated during the assignment to **V**final. The decision to duplicate a voxel was determined by the rounding operation of z\*. The maximum percentage of duplicated voxel at a single *x*- -*y*- position was approximated to ~3% from the maximum height difference between the real specimen and the CAD (~400 <sup>μ</sup>m). The final size of **<sup>V</sup>**final was 711 × <sup>711</sup> × 1200 voxels. For evaluation, the adjusted top surface of **V**final was extracted by the thresholding algorithm described Section 3.2.2 (Figure 5d). After the removal of the cross and the label landmark (see Section 3.2.2), the STD of the surface height of **V**final was calculated to 30 μm. This is a significant decrease compared to the surface of **V**proc (STD of 95 μm). Furthermore, a comparison of the pore distribution in the transition zone pre- and post-adjustment is depicted in Figure 7. In the hypothetical case of a specimen free of surface deformations, the pores were expected to appear at an approximately similar height *z* in the specimen under the assumption of a comparatively small statistical depth variation of keyhole pores. The former dataset is distinguished by pores being distributed heterogeneously, appearing at first especially in the right half of the specimen in Figure 7a with a transition to the left half with growing *z*- . The height difference between the first appearance of keyhole pores in the cylinder right half to a pore distribution over the entire specimen cross-section amounts to approximately 10 to 11 voxels. In the case of the adjusted dataset, this height difference is decreased to approximately 5 to 6 voxels, especially when disregarding the pores present at the specimen rim. These were presumably LoF voids resulting from the interface between bulk and contour scans [7,39–41]. Furthermore, the described transition in the former dataset from right specimen half to left specimen half is no longer present here.

(**b**)

**Figure 7.** Pore distribution between section 5 and 6 starting at a specimen height of approximately 1050 voxels (10.5 mm) increasing by *z*- = 1 voxel (10 μm) per image slice (**a**) before deformation adjustment (**V**proc,bin) and (**b**) after deformation adjustment (**V**final). While the pore appearance in (**a**) is mainly starting on the right specimen half and transitions over the course of 10 image slices to the left half, the pore appearance in (**b**) begins mainly in the center and transitions faster (approximately in 5 image slices) from singular pores to a widespread distribution over the entire cross-section. The dashed red lines indicate the approximate starting and stopping points of the pore transition and are added to increase the readability of the figure. The starting points were manually approximated based on the appearance of a sufficient number of clearly identifiable pores in the cylinder bulk. The stopping points were manually approximated as the images in which pores appeared in major parts of the bulk.

Due to the performed surface adjustment, the utilization of a simple 3D image-byimage registration algorithm was enabled.

#### *3.3. Image Registration*

The spatial image registration was performed using the MATLAB Registration Estimator Toolbox. Here, several different feature-based and intensity-based algorithms for image registration are available. For this study, a monomodal intensity-based algorithm [10] was

chosen because the datasets were acquired by different imaging techniques and therefore, had different spatial resolutions and different geometric features. The thermograms were labeled as moving images which were spatially transformed to be registered on the XCT fixed images [11]. A registration function T was generated using images of the cross landmark on the specimen top surface. The cross landmark was visible in both thermography and XCT image data (see Figure 8). In the case of the XCT data, the cross was extracted from the cross-section slice of **V**final. Regarding the thermogram data, the extraction of the cross landmark was performed from a sum of intensity image from the thermograms of the landmark manufacturing. Here, the pixel temperatures of all 2D thermograms from the manufacturing series of specimen layer were summed up and normalized afterwards. Layer 242 was chosen for the sum of intensity image since the landmark structures were the most clearly identifiable here. Both images were further processed to improve the clearness of the landmark geometry. At first, noisy background elements were removed from the image using arithmetical image multiplication and a polygonal mask. The low spatial resolution of the thermographic camera demanded the use of morphological and median filters to clarify the cross edges. Furthermore, the introduced preprocessing in Section 3.1 was applied on the thermography cross landmark image. Finally, the image was binarized using a global threshold.

Four different transformation models ("similarity", "affine", "rigid", and "translation") were available in the MATLAB toolbox for the monomodal registration to produce a registration function. These models exhibit different degrees of freedom concerning the available transformations. The highest degree of freedom is given by the similarity model that allows translation, rotation, shearing, and scaling of the moving image. The affine model does not allow shearing, while only translation and rotation are available when using the rigid model. In the case of the translation model, only image translation is applied on the moving image. Due to the performed resampling and rectification from the preprocessing of the cross landmark, the moving image already had the same image scale as the XCT image and present distortions were adjusted. Furthermore, the size of the sum of intensity image of the cross landmark in the thermogram dataset may be artificially enlarged by thermal expansion and the choice of the binarization threshold. Therefore, shearing and scaling are unnecessary degrees of freedom that might introduce registration inaccuracy. Two registration functions based on the rigid and the translation model were determined. In the following, the obtained registration functions were applied on the slices of the preprocessed thermogram datasets **A**<sup>k</sup> and the preprocessed XCT dataset **V**final [34]:

$$\mathrm{T}\left(\mathrm{A}\_{z}^{\mathrm{k},2\mathrm{D}}\right)\leftrightarrow\mathrm{V}\_{z'}^{\mathrm{final,2D}}\text{ with }z=z'\tag{12}$$

Here, Ak,2D *<sup>z</sup>* correspond to a 2D *<sup>x</sup>*-*<sup>y</sup>* slice of **<sup>A</sup>**<sup>k</sup> and <sup>V</sup>final,2D *z* to the 2D *x*- -*y* slice of **V**final. As stated in Section 1, the evaluation of the registration accuracy is often challenging. In this study, a simple method was utilized to evaluate the registration results. A full dataset of layer maps from thermography (chosen feature: melt pool area) was registered with the corresponding XCT dataset. Afterwards, the contours of the registered *x*-*y* slices were approximated by a circle fit [32]. In the case of the thermogram dataset, a binarization using a manually chosen threshold was necessary for the detection of the boundary edges. From the circle fit, the average distance ΔD between the circle centroids of the registered datasets was calculated for all slices:

$$\Delta \mathcal{D} = \frac{1}{\text{n}\_{\text{slice}}} \sum\_{i=1}^{n\_{\text{slice}}} \sqrt{\left(\mathbf{x}\_{z}^{\text{cen}} - \mathbf{x}\_{z'}^{\text{cen}}\right)^{2} + \left(y\_{z}^{\text{cen}} - y\_{z'}^{\text{cen}}\right)^{2}} \text{ with } z = z' \tag{13}$$

Here, the centroid position of the thermogram feature image is given by *x*cen *<sup>z</sup>* and *y*cen *<sup>z</sup>* , while the centroid position of the XCT image is given by *x*cen *z* and *y*cen *z*- . ΔD was an indicator for the translation error that was present after the registration. Furthermore, the MAE of average difference of the circle radius Δ*R* was calculated as a measure of the scaling error. The results are shown in Table 4.

**Table 4.** Geometric errors resulting from different transformation modes of registration in the corresponding sections. Here, ΔD corresponds to the MAE of the distance between the circle fit centroids and ΔR to the MAE of the difference between the circle fit radii. The STD of both sizes is given by σΔ<sup>D</sup> and σΔR, respectively.


#### **4. Discussion**

It is important to place this investigation in the overall context of irregularity prediction in L-PBF parts. The precise prediction of irregularities based on the obtained thermographic in situ monitoring data was the objective. The registration is a necessary step to align monitoring and reference datasets. Therefore, the achieved registration precision is a crucial information because it limits the effective volume size in which irregularities can be accurately predicted.

The preprocessing of the thermogram data included, in the case of melt pool-based features, an interpolation from a sparse point cloud of voxels to a resampled 3D volume dataset. This was performed to adjust the thermogram voxel sizes to the XCT voxel size. Thus, the datasets could be registered more precisely with a theoretical accuracy lower than the pixel resolution of the IR camera, 100 μm2. Single voxel values of the interpolated datasets should be treated with care because it is uncertain if they necessarily reflect the exact thermal history of the temporally high dynamic L-PBF process. It can be concluded

that the temporal and spatial resolution of the raw thermograms is important information that should be considered for the prediction of irregularities. Especially if the original thermogram datasets have a lower spatial information density than the registered datasets, a further resampling of the registered datasets to a larger voxel size might be necessary.

In the context of XCT data preprocessing, it was found that an adjustment of the detected surface deformation is of vital importance for the overall registration accuracy. The obtained results from the introduced adjustment method are promising since they show a clear decrease in shape deformation (compare Figures 5d and 7). Nonetheless, it is necessary to critically analyze the single XCT preprocessing steps that were performed.

The basic method of reconstructing former surface deformations from the internal void distribution in the part was strongly motivated by the findings of Ulbricht et al. [7] and their observations related to the surface deformation. Here, multiple indications of the former surface deformations were visible in the XCT data due to the implementation of artificial notches in their design. In the specimen investigated in the current study, no such notches were present since their implementation might have interfered with the presence of keyhole pores whose formation was forced by the chosen design. Therefore, the available information for surface reconstruction was limited. Only pores in one section could be used for the reconstruction of the surface deformation history. From this lack of information arose the decision to utilize a linear sectional approach for the calculation of the compression factor c. This choice might be an oversimplification in terms of describing the surface deformation history. The potential need of more complex fitting approaches such as higher order polynomials or exponential functions to describe the surface deformation history will be investigated in future research. In future experimental designs, the insertion of artificial voids as references instead of boundary pores could be used for an easier determination of the deformation history.

The chosen simple fitting approach for the compression factor c well compensated the error induced by the surface deformation (Figures 5d and 7). The results show that the specimen deformation was determined accurately by the chosen customized thresholding and surface reconstruction algorithm. Here, the choice of other registration landmarks which are not positioned on the specimen top could improve this result even further, since the step of surface reconstruction of missing areas would be omitted.

In order to describe the surface deformation history, the assumption was made that all surface deformations during manufacturing had an approximately similar shape to the deformation of the specimen top. The results indicate that this assumption is promising. The deformation reconstructed from the pore centroids at an approximate specimen height of *z*- = 1070 voxel is in good agreement with the determined top surface deformation. This is remarkable since the reconstruction is based on the positional information of the present keyhole pores.

The formation of keyhole pores is connected to unstable conditions in the melt pool keyhole [37]. As a result, keyhole pores can occur spatially irregularly during the manufacturing of a scan track (compare Figure 7). Additionally, the melt pool depth varies to a certain extent. As a result, the *z* position of pores which result from a single layer manufacturing can fluctuate. The melt pool depth was shown to depend on the laser processing parameters. Mohr et al. [25] found melt pool depths of 213 ± 19 μm for a VED of 65.5 J/mm3 and 471 ± <sup>54</sup> <sup>μ</sup>m for a VED of 152.7 J/mm3 using the same machine and material that was utilized in the present study. It can be assumed that the average melt pool depths from the VED utilized in section 6 (114.45 J/mm3) lay in between these results. However, regarding the pores that were utilized for the former surface deformation reconstruction, the positional fluctuations are limited by the manufacturing of overlying layers. Here, the keyhole of the new layer can interact with the lower pores which may lead to the escape of the entrapped gas or a recombination with new pores. Therefore, the positional fluctuation is effectively limited to the layer thickness (50 μm).

The heterogeneous spatial pore distribution and the fluctuation in the vertical pore location were identified as interfering factors for the reconstruction of the former surface deformation. Nonetheless, the surface deformation calculated by pore distribution (Figure 5c) showed similar shape tendencies as the top surface deformation (Figure 5a). From that, it can be concluded that the history of surface deformation is effectively linked to the resulting pore location. Precise knowledge of the surface deformation history is, therefore, essential for an allocation of in situ sensor data to the porosity information obtained from XCT. To the best of the authors' knowledge, these findings are new and underline the importance of shape adjustment in the registration procedure for irregularity prediction.

It needs to be remarked that the density information of the manufactured specimen is effectively locally distorted by the shape adjustment to match with the "ideal" specimen geometry given by the CAD. Therefore, the quantitative void sizes in the adjusted dataset should be analyzed with care since they might differ from the results in the raw dataset. However, a quantitative void analysis can be enabled again if the applied deformation adjustment is reverted.

In terms of the image registration, the allowed transformation options of the investigated registration models were rotation and translation. Due to the performed preprocessing of both datasets, it was decided that shearing and scaling as additional transformations were unnecessary degrees of freedom. The results (Table 4) show that the lowest errors were achieved when applying the rigid model in section 3. In the section of increased VED, lower accuracy was achieved. This was presumably caused by the lateral shrinkage present in these sections (visible in Figures 4 and 6b). The shrinkage seemed to prevent the algorithm to produce even better results. The comparison between the registration functions showed that the translation model performed better in the section of increased VED. The additionally allowed rotation of the rigid model appears to be counterproductive here and the results indicate that both XCT and thermography datasets were already aligned well from preprocessing. The lower performance from the rigid transformation might result from the shape deviations between the cross landmark images that might have induced an unnecessary rotation.

The results show that already a simple transformation function with a low number of degrees of freedom is sufficient for the registration of the preprocessed datasets. For data that are not preprocessed, it might be a reasonable choice to choose a model that contains shearing and scaling. Here, the quality of the geometric landmark is a crucial factor. Furthermore, the results show the potential of the developed registration method if no lateral shrinkage is present. An extension of the algorithm to improve the registration accuracy if lateral shrinkage is present will be the objective of future studies.

#### **5. Conclusions**

In this study, a 3D image-to-image registration was performed on datasets of thermal features extracted from in situ thermography and a corresponding XCT dataset. The registration was performed as a prerequisite for irregularity prediction. Extensive data preprocessing was conducted to obtain similar data dimensionalities to enable the utilization of the chosen, simple registration method. The preprocessing of the thermal feature dataset included the compensation of image distortion, the interpolation of missing datapoints and a resampling to the voxel scale of the XCT data. In the case of the XCT dataset, vertical shrinkage was preliminary corrected from the height information of a staircase landmark structure. Furthermore, a novel shape adjustment method was introduced to eliminate the surface deformation history that was found in the entire part. An image registration function was derived from the utilization of geometric landmarks located on the specimen top surface. The registration accuracy was assessed among the obtained geometrical errors in the registered datasets. From the results of the performed image registration, the following conclusions are drawn:

• Thermally induced warping and solidification shrinkage, especially in the form of surface deformations, are a major challenge for the image registration because it prevents the application of simple registration methods. In this study, it was demonstrated that the distribution of boundary keyhole pores within the observed specimen can

be utilized to reconstruct the surface deformation for a specific point in time within the manufacturing. Furthermore, it was shown that an adjustment function based on the approximated surface deformation history enables the adjustment of the part deformation and the application of a simple 3D image-to-image registration.


In future studies, the registered datasets will be used to generate a ML-based model for the prediction of irregularities within the produced part. Here, the obtained registration error information will be incorporated to determine the spatial resolution in which the porosity can be reasonably predicted. Apart from that, we aim to improve the algorithm to make it more robust if lateral shrinkage is present in the part. The insertion of artificial voids within the specimen is a promising option to reconstruct the surface information at different specimen heights. A further option in this regard is the in situ measurement of the part surface topography by laser profilometry that can be integrated into the process. By that, a more accurate deformation adjustment can be achieved which will further increase the registration accuracy and ultimately the irregularity prediction accuracy.

**Author Contributions:** Conceptualization, S.O., T.F. and S.J.A.; methodology, S.O., T.F., A.U., G.M. and S.J.A.; software, S.O.; investigation, S.O., G.M. and T.F.; data curation, S.O., T.F. and A.U.; writing—original draft preparation, S.O. and T.F.; writing—review and editing, S.O., T.F., A.U., G.M., G.B., C.M. and S.J.A.; visualization, S.O.; supervision, G.B., C.M. and S.J.A.; project administration, G.B., C.M. and S.J.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the BAM Focus Area Materials project ProMoAM "Process monitoring of Additive Manufacturing".

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We are thankful for the financial support and the fruitful cooperation with all partners.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **Measuring the Depth of Subsurface Defects in Additive Manufacturing Components by Laser-Generated Ultrasound**

**Zhixiang Xue 1, Wanli Xu 1, Yunchao Peng 2, Mengmeng Wang 2, Vasiliy Pelenovich 1, Bing Yang <sup>1</sup> and Jun Zhang 1,\***


**Abstract:** A new method to measure the depth of subsurface defects in additive manufacturing components is proposed based on the velocity dispersion analysis of Lamb waves by the wavelettransform of laser ultrasound. Firstly, the mode-conversion from laser-generated surface waves to Lamb waves caused by subsurface defects at different depths is studied systematically. Secondly, an additive manufactured 316L stainless steel sample with six subsurface defects has been fabricated to validate the efficiency of the proposed method. The measured result of the defect depth is very close to the real designed value, with a fitting coefficient of 0.98. The defect depth range for high accuracy measurement is suggested to be lower than 0.8 mm, which is enough to meet the inspection of layer thickness during additive manufacturing. The result indicates that the proposed method based on laser-generated ultrasound (LGU) velocity dispersion analysis is robust and reliable for defect depth measurement and meaningful to improve the processing quality and processing efficiency of additive/subtractive hybrid manufacturing.

**Keywords:** additive manufacturing; subsurface defects; laser ultrasound; stainless steel

#### **1. Introduction**

Metal additive manufacturing (AM) has disruptive applications in many industries, including the aerospace, biomedical, and automotive industries [1]. Compared with traditional manufacturing methods, this layer-by-layer manufacturing technology has many advantages in the customization of products with complex geometric structures [2]. However, mainstream AM methods have interlayer defects such as inclusions and lack-offusion buried in the subsurface of the printing layer [3]. To remove the random defects, additive/subtractive hybrid manufacturing is proposed with performing additive and subtractive manufacturing (SM) alternatively until the whole part is fabricated [4]. The online detection and location of defects are indispensable for the SM processing. The more accurate the measurement of the defects' position, the faster SM can repair the defective part. Therefore, the online monitoring method is meaningful to significantly improve processing quality and processing efficiency.

The laser-generated ultrasound (LGU) has been widely used in various manufacturing fields due to its advantages of being non-contact, broadband, and high-resolution [5]. LGU is also considered to be a potential method for the online detection of metal additive manufacturing samples [6]. Current research mainly focuses on the detection of surface and subsurface defects by LGU Rayleigh waves [7]. Zeng Y. produced three kinds of artificial defects including crack, flat bottom hole, and through hole defects and carried out an LGU inspection and finite element analysis on these three kinds of artificial defects [8]. In the defect evaluation, Wang C. used the LGU Rayleigh wave to measure the thickness of

**Citation:** Xue, Z.; Xu, W.; Peng, Y.; Wang, M.; Pelenovich, V.; Yang, B.; Zhang, J. Measuring the Depth of Subsurface Defects in Additive Manufacturing Components by Laser-Generated Ultrasound. *Metals* **2022**, *12*, 437. https://doi.org/ 10.3390/met12030437

Academic Editors: Giovanni Bruno and Christiane Maierhofer

Received: 7 February 2022 Accepted: 25 February 2022 Published: 1 March 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the subsurface defects with rectangular sides. The two ends of the defects were detected separately to quantify the width of the sub-surface groove defects [9]. Chen D. used the phase evolution of LGU Rayleigh waves to detect subsurface defects [10]. Although LGU Rayleigh wave has many advantages in detecting surface and subsurface defects, there are still few applications in measuring defect depth. In a previous finite element analysis, it had been found that ultrasonic surface waves are modulated by near-surface defects, resulting in a waveform conversion from surface waves to Lamb waves. There was a finite element simulation study of surface defects with laser phased array Rayleigh waves [11]. It used the phased array principle to enhance the diffraction wave signal of the LGU detection of cracks and defects [12]. Zhou Z. performed finite element analysis on large-scale surface gaps in LGU inspection and studied the interaction between the Rayleigh wave generated by the laser and surface cracks [13]. Therefore, if we can use appropriate signal processing methods to systematically study the Lamb conversion law, it is possible to propose a defect depth method.

The Lamb waves have velocity dispersion characteristics, which means that the propagation speed of the Lamb wave is changed with frequency, sample thickness, and elastic properties. Based on the principle of velocity dispersion, many researchers focused on the estimation of a material's properties from velocity dispersion analysis using computeraided signal processing [14]. Previous studies had shown that the attenuation, velocity, frequency, and dispersion characteristics of the Lamb wave generated by the laser are closely related to the anisotropy and viscoelastic properties of the material [15]. Fourier transform and wavelet-transform are two methods to analyze the velocity and dispersion characteristics of Lamb waves. In the application of the Fourier transform, Farouk B. studied the influence of symmetry and discontinuity on the Lamb wave modes [16,17]. This is because of the multi-modal characteristics caused by the velocity dispersion characteristics of the Lamb waves, and it can be quantitatively displayed using the Fourier transform [18]. Although Fourier transform can achieve better results, wavelet-transform has better performance in the field of time-frequency analysis [19]. Amir M. combined wavelet-transform, fast Fourier transform, and modal positioning theory with variable frequency wave speed and considered specific frequency ranges through fast Fourier transform and wavelet packet analysis [20]. In particular, the wavelet-transform enables the transient signal to identify required information and irrelevant information, even overlapping each other in frequency [21–23].

This paper presents a systematic study of the mode-conversion from the LGU surface wave to the Lamb waves caused by subsurface defects at different depths. A new method to measure the depth of subsurface defects is proposed based on the Lamb waves velocity dispersion analysis by wavelet-transform. A 316L stainless steel sample with six subsurface defects is fabricated to validate the efficiency of the proposed method.

#### **2. Experimental Setup**

The experimental setup is shown in Figure 1. A Nd: YAG pulsed laser (WEDGE 1064HB DB, Pavia, Italy) with a wavelength of 1064 nm and a pulse duration of 12 ns is used to generate ultrasonic waves (Table 1). The Laser receiver (QUARTET-1500 Bossanova, Los Angeles, CA, USA), with an operating wavelength of 532 nm and a bandwidth of 102 MHz, is applied to receive the ultrasonic waves. The stainless steel (316L) plates were fabricated by the selective laser melting method (SLM AmPro SP-500, Victoria, Australia) with 30 mm in length, 5 mm in thickness, and 30 mm in width (Figure 2). A series of notch defects with a fixed area of 3.0 mm × 0.5 mm and varying depths of 0.1, 0.2, 0.3, 0.5, 0.7, and 1 mm were fabricated as subsurface defects in the specimen (Figure 2). In this paper, the pulse laser energy density E can be calculated by E = (4 × A × e)/ πd2 , where A is the laser coefficient of the sample (here, 0.1 is adopted for A), e is the pulse laser energy with a value of 2 mJ, and d is the Spot diameter with a value of 150 μm. The calculated result of E is 11.3 mJ/cm2, which is significantly lower than the stainless-steel ablation threshold of 450 mJ/cm2 (Table 2) [24]. Therefore, the LGU is controlled by a thermoelastic

mechanism. The sample surface rapidly expands and contracts in the laser heating zone, forming internal stress and strain, which propagates in the form of the elastic wave.

**Figure 1.** LGU testing system.

**Table 1.** WEDGE 1064 HB DB parameters.


**Figure 2.** Sample schematic with six embedded notches.

**Table 2.** The stainless-steel (316L) parameters.


The schematic of the mechatronic system for generating and detecting the LGU is shown in Figure 3. The laser spots of the excitation and the reception maintains a distance of D, D = 2 mm. The scanning steps - dx, dy are set to 0.1 mm. The acquired A-scans are arranged and stored into a three-dimensional matrix. The B-scan and C-scan images are plotted by extracting a sub-matrix from the acquisition data, which is helpful to find the horizontal position of the defects. Then, the depth of the defects is measured by the proposed method, explained in the next section.

**Figure 3.** LGU system and scanning imaging strategy.

#### **3. Method**

The proposed method for defect depth measurement, based on the LGU signals, consists of three steps. Firstly, the defect depth is characterized by the phase velocity and central frequency of the Lamb waves based on the velocity dispersion principle. Secondly, time-frequency analysis of the LGU signal is used to obtain its frequency, in which the wavelet-transform is employed. Finally, the velocity of the LGU Lamb waves is calculated with the time of flight from the excitation spots to the reception spots.

#### *3.1. Velocity Dispersion of the Lamb Waves*

The quantitative relation between the defect depth and the characteristics of the Lamb wave is the key point for the depth measurement. According to the velocity dispersion characteristics of the Lamb wave, the dispersion curves describing the influence of the frequency and velocity on the defect depth could be used for measurement and calibration. The dispersion curves can be calculated by the Rayleigh-Lamb equation of the Lamb wave [25] as follows.

S mode:

A mode:

$$\frac{\tanh\_s b}{\tanh\_l b} = -\frac{4k\_0 {}^2 k\_l k\_s}{\left(k\_0 {}^2 - k\_s {}^2\right)^2} \tag{1}$$

$$\frac{\tanh\_s b}{\tanh\_l b} = -\frac{\left(k\_0^{\cdot 2} - k\_s^{\cdot 2}\right)^2}{4k\_0^{\cdot 2}k\_l k\_s} \tag{2}$$

$$k\_l^2 = \left(\frac{\omega}{c\_l}\right)^2 - k\_0^2\tag{3}$$

$$k\_s^{\,2} = \left(\frac{\omega}{c\_s}\right)^2 - k\_0^{\,2} \tag{4}$$

$$
\omega = 2\pi f \tag{5}
$$

Here,

*k*0—wave number along the horizontal direction of the sample

*b*—1/2 sample thickness

*ω*—angular frequency

*cl*—longitudinal wave velocity

*cs*—shear wave velocity

According to the above equations and the stainless-steel (316L) parameters about *cl* and *cs* (Table 2), the dispersion curves of A and S mode Lamb waves are shown in Figure 4a. The dispersion curve of the A0 mode is extracted and used for the depth measurement, as shown in Figure 4b. If the velocity and the frequency changes of the Lamb waves induced by the existing defect are measured according to the LGU experiment, the depth of the defect can be calculated by the dispersion curve of the A0 mode.

**Figure 4.** (**a**) Velocity dispersion curves (**b**) A0 mode velocity dispersion curve.

#### *3.2. Time and Frequency Measurement by Wavelet-Transform*

To get the frequency of the defect signal, a time-frequency analysis based on the wavelet-transform is used. The wavelet-transform of an A-scan signal *f*(*t*) is defined as [19]:

$$(\omega\_{\psi}\mathbf{f})(a,b) = \frac{1}{\sqrt{a}} \int\_{-\infty}^{+\infty} f(t)\overline{\psi}\left(\frac{t-b}{a}\right)dt\tag{6}$$

Here, *ψ*(*t*) designates the basic wavelet, and *ψ*(*t*) means a complex conjugate. *a* and *b* are scale and shift parameters, respectively. *ψ*(*t*) must satisfy the admissibility condition by this equation:

$$\mathcal{C}\_{\Psi} = \int\_{-\infty}^{+\infty} \frac{|\Psi(\omega)|^2}{|\omega|} d\omega < \infty \tag{7}$$

At the same time, the basic wavelet must satisfy the following two constraints.

$$\int\_{-\infty}^{+\infty} |\psi(t)| dt < \infty \tag{8}$$

$$\int\_{-\infty}^{+\infty} \psi(t)dt = 0\tag{9}$$

To obtain a continuous wavelet-transform (CWT), Morlet wavelet is used in this paper; then, the mother wavelet function *ψ*(*t*) is expanded and translated by Equations (8) and (9)

$$
\psi\_{a,b}(t) = \frac{1}{\sqrt{|a|}} \psi\left(\frac{t-b}{a}\right) \quad a, \ b \text{ } \epsilon \text{R.} a \neq 0. \tag{10}
$$

The generation of *ψ*(*t*) depends on the parameters *a* and *b*. *ψa*,*b*(*t*) is the wavelet basis function. As the core part of this method, we can perform better time-frequency analysis on the signal through wavelet-transform and extract the time-frequency pairs required by our method to obtain better depth measurement results.

#### *3.3. Velocity Calculation*

The accurate measurement of time-of-flight is the key point for velocity calculation if the propagation distance is fixed. However, the actual flight time cannot be read directly on the time axis, due to the different system delays in each LGU system. The Rayleigh wave sound velocity (*CR*) of 316L stainless steel is used to calculate the actual flight time according to:

$$T\_l = d\_0 / \mathbb{C}\_R \tag{11}$$

After reading the flight time of the A-scan signal without defects, the system delay can be calculated by subtraction:

$$T\_0 = T\_t - T \tag{12}$$

*Tt*—Ultrasonic actual flight time

*T*—Ultrasonic flight time read from A-scan

*T*0—ystem delay r

*d*0—Fixed distance between generation and receiving end

Then, the phase velocity of the Lamb wave A-scan signal with defects can be calculated:

$$C\_p = d\_0 / (T - T\_0) \tag{13}$$

#### **4. Results and Discussion**

The B-scan image of the defects by LGU inspection is shown in Figure 5a. The indications marked in the red frames are the defects of 0.1, 0.2, and 0.3 mm in depth. However, the B-scan image of LGU cannot provide accurate depth information due to the wide time-domain signal modulated by the defect and sample surface. The C-scan image of the LGU detection of the pre-made six defects is shown in Figure 5b. All defects are detected with depths of 0.1, 0.2, 0.3, 0.5, 0.7, and 1 mm. The horizontal position of the defects could be located by measuring the edge of these indications. But it's still difficult to accurately measure the depth of defects, as there is only qualitative evidence that the signal strength becomes weaker as the defect depth increases. However, the C-scan image is helpful to find and extract the defect's A-scan signal for further analysis.

**Figure 5.** (**a**) B-scan and (**b**) C-scan plots of LGU inspection of defects.

Figure 6a–f are the A-scan signals of defects with six different depths extracted from the horizontal position provided by the C-scan image in Figure 5b. The black line in the figure represents the time domain A-scan signal with amplitude and time, and the blue line represents the spectrum domain signal with frequency and voltage obtained by the fast Fourier transform (FFT). Comparison of the A-scan signals reveals that the width of the signals decreases as the defect depth increases. The embedded notch of 0.1 mm and the sample surface forms a foil-like structure and induces typical Lamb waves signals, as shown in Figure 6a. When the depth of the notch becomes larger, the LGU signals are only modulated by the sample surface and induce typical surface waves signals, as shown in Figure 6f. It means that the mode conversion happens when the defects exist and the depth changes. Comparison of the spectrum domain signals shows a frequency shift, which occurs when the defect depth changes. Double frequency peaks appear when the Lamb wave and the surface wave coexist, as shown in Figure 6d, e. Further time-frequency

analysis by means of the Wavelet-transform is introduced to distinguish the Lamb wave mode and quantify the correlated central frequency and time.

**Figure 6.** (**a**) 0.1 mm, (**b**) 0.2 mm, (**c**) 0.3 mm, (**d**) 0.5 mm, (**e**) 0.7 mm, and (**f**) 1.0 mm A-scan signal of six different depth defects and the spectrum signals obtained after Fourier transform.

Figure 7a–f are the time-frequency images of the six A-scan signals obtained by the wavelet-transformation. The yellow area represents the location of a wavelet energy concentration. It can be clearly seen from the figures that, as the depth increases, the wavelet energy packet gradually shifts from low to high frequency. This is because, when the depth is small, the Lamb wave is the main signal form. When the depth is 1 mm, the surface wave is the main signal form. However, the low-frequency wavelet energy concentration of the Lamb wave can still be seen. The time-frequency images also prove the frequency shift and mode conversion of LGU waves. The propagation time of the Lamb wave can be accurately recorded if the wave mode and frequency are fixed. Then, the velocity of the Lamb wave can be calculated using the Formulas (6)–(10).

**Figure 7.** Time—frequency images of six defects with different depths of (**a**) 0.1 mm, (**b**) 0.2 mm, (**c**) 0.3 mm, (**d**) 0.5 mm, (**e**) 0.7 mm, and (**f**) 1.0 mm obtained by the A-scan wavelet-transform.

The theoretical and experimental results of the relationship between propagation velocity and defect depth are shown in Figure 8. In order to find the best matching curve for calibration, five frequencies of the low-frequency wavelet energy packets have been extracted for measurement accuracy evaluation. In Figure 8, the trends of defect depth and sound velocity curves measured from the experimental results are close to the theoretical value. It can be seen that, as the depth of the defect increases, the sound velocity increases, and the phase velocity is very close to the Rayleigh wave velocity when the depth exceeds 1 mm. The difference between the theoretical and experimental results is the smallest when the frequency is 2.2 MHz and the fitting coefficient reaches 0.98. This is because 2.2 MHz is the center frequency of the wavelet energy packet.

**Figure 8.** Theoretical and experimental relationship between phase velocity and defect depths at different frequencies: (**a**) 2.11 MHz, (**b**) 2.22 MHz, (**c**) 2.33 MHz, (**d**) 2.44 MHz, (**e**) 2.55 MHz.

Figure 9 shows the depth measurement results of the LGU detection of AM defects mentioned above. The curve correlation coefficient between the designed and measured values is 0.983. The result indicates that it is feasible to measure defect depth based on the dispersion characteristics and wavelet-transform of LGU signals. According to the extracted frequency and sound velocity, the defect can be accurately measured in depth. However, when the defect depth is too large, the main form of the ultrasonic wave is the Rayleigh wave. The energy ratio of the Lamb wave is small, as shown in the timefrequency image (Figure 7f), resulting in an error of 20% when the depth reaches 1 mm. The recommended defect depth range for accurate measurement is suggested to be lower than 0.8 mm, which is enough to meet the inspection layers thickness of AM methods, such as the selective melting method. The accurate position provided by the proposed method in this paper would be helpful for repairing the defective part rapidly and improving the printing efficiency and printing performance of additive/subtractive manufacturing methods.

**Figure 9.** Comparison chart of the experimental and theoretical value of the effect depth.

#### **5. Conclusions**

In this paper, a mode-conversion phenomenon from LGU surface waves to Lamb waves caused by subsurface defects at different depths is observed and systematically explored using LGU testing experiments. A novel method to measure the depth of subsurface defects is proposed based on the Lamb waves velocity dispersion analysis by the wavelet-transform. The conclusions are as follows:


In further work, we will consider adding material samples or exciting single-frequency Rayleigh waves for more accurate measuring of the depth of subsurface defects.

**Author Contributions:** Conceptualization, Z.X.; methodology, W.X.; software, J.Z. and W.X.; validation, Z.X.; formal analysis, Z.X.; investigation, Z.X.; resources, J.Z. and Y.P. and M.W. and B.Y.; data curation, Z.X.; writing—original draft preparation, Z.X.; writing—review and editing, J.Z. and V.P. and B.Y.; visualization, Z.X.; supervision, J.Z. and W.X. and V.P.; project administration, Z.X.; funding acquisition, J.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Key R&D Program of China (Grant No. 2018YFB1106100) and the Fast Support Project for Installation and Development (Grant No. 80904010502).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data Sharing is not applicable for this article.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Review* **Diffraction-Based Residual Stress Characterization in Laser Additive Manufacturing of Metals**

**Jakob Schröder 1,\*, Alexander Evans 1, Tatiana Mishurova 1, Alexander Ulbricht 1, Maximilian Sprengel 1, Itziar Serrano-Munoz 1, Tobias Fritsch 1, Arne Kromm 1, Thomas Kannengießer 1,2 and Giovanni Bruno 1,3,\***


**Abstract:** Laser-based additive manufacturing methods allow the production of complex metal structures within a single manufacturing step. However, the localized heat input and the layer-wise manufacturing manner give rise to large thermal gradients. Therefore, large internal stress (IS) during the process (and consequently residual stress (RS) at the end of production) is generated within the parts. This IS or RS can either lead to distortion or cracking during fabrication or inservice part failure, respectively. With this in view, the knowledge on the magnitude and spatial distribution of RS is important to develop strategies for its mitigation. Specifically, diffractionbased methods allow the spatial resolved determination of RS in a non-destructive fashion. In this review, common diffraction-based methods to determine RS in laser-based additive manufactured parts are presented. In fact, the unique microstructures and textures associated to laser-based additive manufacturing processes pose metrological challenges. Based on the literature review, it is recommended to (a) use mechanically relaxed samples measured in several orientations as appropriate strain-free lattice spacing, instead of powder, (b) consider that an appropriate graininteraction model to calculate diffraction-elastic constants is both material- and texture-dependent and may differ from the conventionally manufactured variant. Further metrological challenges are critically reviewed and future demands in this research field are discussed.

**Keywords:** laser-based additive manufacturing; residual stress analysis; X-ray and neutron diffraction; diffraction-elastic constants; strain-free lattice spacing

#### **1. Introduction**

In recent years additive manufacturing (AM) has evolved from a technology for rapid prototyping to a mature production process used in several industries from aerospace to medical applications [1]. In essence, an energy source incrementally manufactures a part in a layer-by-layer process from a wire or powder feedstock [2]. AM processes allow the fabrication of complex structures, which cannot be produced via conventional manufacturing methods [3,4]. This freedom of design enables improvements in component performance and weight reduction of parts [4,5]. In addition, the rapid solidification rates and tailored heat treatment schedules can improve certain material properties, leading to further performance and efficiency gains [6–9]. However, process-related internal stress (IS) may lead to the formation of cracks or delamination [10–13]. IS may severely reduce the applicability of the process to manufacture materials more prone to this type of inprocess damage. Moreover, very often IS locks large residual stress (RS) in the parts after production [14].

**Citation:** Schröder, J.; Evans, A.; Mishurova, T.; Ulbricht, A.; Sprengel, M.; Serrano-Munoz, I.; Fritsch, T.; Kromm, A.; Kannengießer, T.; Bruno, G. Diffraction-Based Residual Stress Characterization in Laser Additive Manufacturing of Metals. *Metals* **2021**, *11*, 1830. https://doi.org/10.3390/ met11111830

Academic Editor: Matteo Benedetti

Received: 25 October 2021 Accepted: 9 November 2021 Published: 13 November 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Therefore, certain materials, which are less susceptible to IS and to related defect formation, are generally preferred to date for the production with laser-based AM methods. These include engineering materials such as stainless steels, titanium-, aluminum-, and nickel-based alloys. In fact, alloys such as 316L, Ti6Al4V, AlSi10Mg, as well as Inconel 625 and 718 are widely used in laser-based AM. It is extremely difficult to monitor IS during production, especially in such complex AM-based processes. Therefore, extensive research has been dedicated to the topics of RS (i.e., the final footprint of IS). The RS determination and mitigation for those alloys are the subjects of this review.

The subjects have a further relevance: In recent years efforts have also been made to extend the laser-based AM production to materials more prone to IS and RS related defects, such as Nickel alloys Inconel 939 [15,16], Inconel 738 [17–20], or martensitic steels [21–23]. In these cases, the control and knowledge of the RS state gains an even greater importance. In fact, investigations have shown that even optimized process parameters (e.g., hatch spacing, laser power, scan speed or scan strategy) can result in high RS magnitudes [24,25]. In general, a careful selection of the process parameters allows the reduction of the RS level and thus increases the overall mechanical performance [26].

Several destructive and non-destructive techniques are available to determine the RS within a material. Due to their non-destructive nature diffraction methods are, naturally, the most widespread for the characterization of RS. The complete stress state within the bulk (by means of neutrons), the subsurface (by means of synchrotron X-rays) and surface (using Lab X-ray) can be characterized.

To allow the precise determination of RS using diffraction-based methods, knowledge about the microstructure, the texture and the processing conditions is required. First, a strain-free lattice spacing (*dhkl* <sup>0</sup> ) must be found as a reference to permit the calculation of the strain [27]. The situation is akin to weldments, in which a chemical gradient appears across the weld line, provoking a variation of *dhkl* <sup>0</sup> [27–30]: chemical gradients due to solute-concentration variation are present in AM alloys [31]. This poses a new challenge for the determination of strain and subsequently stress. Secondly, the anisotropic nature of most single crystals requires material specific constants to enable the precise determination of RS by diffraction-based strain measurements [32–34]. The so-called diffraction-elastic constants (DECs) are not only dependent on the alloy, but also rely on the underlying microstructure and texture. In fact, the RS determination by diffraction methods is facilitated if a non-textured polycrystal with relatively small equiaxed grains is measured: in such a case the so-called quasi-isotropic approximation can be used [32,34]. In practice, this assumption is often invalid, as the microstructure can strongly deviate from equiaxed. However, the crystallographic texture and morphology strongly depend on the processing conditions. Rolled or hot-extruded materials, for example, typically exhibit a strong crystallographic texture, which may cause an anisotropic behavior [35,36]. Methods to deal with such process-related peculiar microstructures have been developed in the past for established manufacturing methods [27]. The columnar microstructures, which develop during laser-based AM, typically exhibit a strong crystallographic texture in conjunction with an inhomogeneous grain size along the build direction [37]. Therefore, well established models to determine the DECs in conventional products may fail to predict correct values for AM alloys [38–40].

While detailed reviews on the process parameter dependence and process-specific strategies of RS mitigation can be found in the literature [14,41–44], an extensive review on the methodology of diffraction-based methods with respect to laser-based AM processes is absent.

A first assessment of the critical aspects to account for in the domain of RS determination of AM was provided by Mishurova et al. [45]. Building on this, the present paper showcases an in-depth critical review of the literature in the domain of experimental characterization of RS in laser-based powder AM via non-destructive diffraction methods: An overview of practices and related challenges in diffraction-based RS determination for laser-based AM will be given. Especially, the appropriate choice of the DECs and *dhkl* <sup>0</sup> is

paramount to provide accurate absolute RS levels [33,45]. Furthermore, it is indispensable to take the principal stress directions into account, which are for AM materials not necessarily governed by the geometry but instead by the building strategy and, consequently, by the microstructure anisotropy [46]. We will show that significant method development work is still necessary to reliably determine RS by diffraction methods in AM parts.

#### **2. Laser-Based AM Processes**

The first laser-based AM process, namely selective laser sintering (SLS), was first developed in 1979, although it took until the 1990- s until metal materials were manufacturable [47]. In this process a laser compacts loose powder in a layer-by-layer process to form a green body using a binding polymer [47]. A following infiltration fills the porosity to improve the overall mechanical performance [48]. The development of laser sources allowed EOS (Electro Optical Systems GmbH, Krailing, Germany) to develop a variant of SLS, which no longer needed a binding polymer, as the peripheral region of the powder particles was meltable [47]. The resulted parts were porous but had reasonable mechanical properties [49]. Further development in laser technology finally allowed the manufacturer to fully melt the powder bed [47]. The laser powder bed fusion (LPBF) and laser metal deposition (LMD) processes were then developed. These processes will be introduced in the next paragraphs and are the focus of this review, owing to their propensity to generate high residual stresses. These also are the leading metal AM processes for both new part production and repair engineering [50,51]. Therefore, they have high technological and environmental importance.

#### *2.1. LPBF (Laser Powder Bed Fusion)*

The usage of increasingly powerful lasers has increased the ability to fully melt the metallic powder [47]. This advance has gradually enabled the production of nearly fully dense (>99.9%) parts, if the process parameters are optimized, with mechanical properties comparable to those of conventionally produced metals [52,53]. Figure 1a illustrates the LPBF process. In a chamber flooded with a protective gas (typically Argon, to prevent oxidation during production), a recoater delivers powder from a reservoir to the build platform. A laser then melts predefined areas within the powder layer. The reservoir and build platform move accordingly to the part design and the steps are repeated in a layer-wise manner until the final part is produced.

The most relevant parameters for process optimization are laser power, scanning speed, layer thickness, hatching distance and, ultimately, the scanning strategy [54,55]. To reduce the temperature gradient during manufacturing, thereby reducing RS and distortions, preheating the baseplate is a typical approach [56]. Nowadays, preheating temperatures up to 1000 ◦C are realized [57]. The so-called inter layer time, which defines the time passed between deposition of subsequent layers can help to reduce microstructural gradients due to heat accumulation in the part [58]. Not only the process parameters but also the feedstock powder significantly influence the quality of the part. Typically, spherical particles with a size between 10–60 μm are ideal in terms of processability [59]. A comprehensive review on powders for LPBF can be found elsewhere [59]. When the process parameters are carefully controlled, parts with superior properties compared to SLS and direct metal laser sintering (DMLS) are manufacturable [52]. Due to the high heat input and high cooling rates, IS play a major role in those parts, which can lead to distortions and cracking, and remain locked in the part as RS [10,60].

#### *2.2. LMD (Laser Metal Deposition)*

While in the processes of SLS, DMLS and LPBF a first applied powder layer is selectively melted for part manufacture, during LMD a powder or wire feedstock, is directly fed into the laser beam focus [61]. In a powder-based process a carrier gas drags the powder from the feeder to the nozzle into the melt pool [62]. A second gas is used to prevent oxidation, whereby different gases are available as carrier and shielding [62,63]. Depending on the application different type of nozzles are available; they can influence the efficiency of the process [64,65]. The laser beam then fully melts the feedstock material, and the part is created in an incremental manner (Figure 1b). One of the main advantages of the LMD process is that in contrast to other processes the excess material is minimized, even though material loss can still be a problem due to overspray of the nozzle [65]. In addition, the deposition rates are higher during LMD, but the overall part quality typically suffers compared to LPBF [66]. The most relevant process parameters for process optimization are powder or wire feed rate, laser power, gas flow and scanning velocity [67]. In the LMD process layer thicknesses and particle sizes are commonly larger as compared to the LPBF process.

**Figure 1.** Simplified schematic images of the different laser-based additive manufacturing processes of (**a**) laser-powder bed fusion (adapted from [68]) and (**b**) powder-based laser metal deposition with a lateral injection nozzle (adapted from [69]).

#### **3. Definition of Residual Stress**

Residual stress (RS) is stress that exist in a manufactured part without the application of external loads, moments, or thermal gradients [34]. It is very unlikely for manufactured parts to be completely free of RS [70]. Figure 2 visualizes the different types of RS as defined in literature. Depending on the length scale over which the RS self-equilibrate, they can be categorized as the following [71]:


While the failure of materials can depend on local features, and therefore on Type II and III stresses, in engineering applications usually Type I stress dominates. Indeed, a major contributor to RS in AM polycrystalline parts is Type I RS caused by localized heating, melting, and rapid solidification during the manufacturing process [60].

**Figure 2.** Schematic representation of the different types of RS within a polycrystalline material where *σ<sup>I</sup>* , *σII*, *σIII* denote the type I, II and II stresses respectively. Adapted from [72].

#### **4. Residual Stress with Respect to Laser-Based AM**

#### *4.1. Origin of Residual Stress*

Previous studies showed that RS in AM parts is primarily caused by the thermal gradients in conjunction with the solidification shrinkage that arise due to continuous re-heating, re-melting, and cooling of previously solidified layers [60,73,74]. The local and rapid heating of the upper layer by the laser beam, combined with slow heat conduction (Figure 3a), consequently leads to a steep temperature gradient within the material [60]. However, the already solidified layers restrict the expansion of the uppermost layer, thus leading to the formation of elastic compressive strains [60]. These strains eventually become plastic upon reaching the local temperature dependent yield strength [60]. Therefore, without the presence of mechanical constraints, such plastic strains (*εpl*) would lead to bending as indicated in Figure 3a [60]. During cooling, the shrinkage (*εth*) of the plastically compressed upper layers leads to an inversion of the bending [60]. The aforementioned is accompanied by the formation of tensile RS in the locally plastically deformed region, balanced by surrounding compression (Figure 3b) [60]. Finally, solidification shrinkage of the molten layer superimposes on the solid-state mechanisms, which leads to tensile RS at the upper most surface balanced by subjacent compression [60]. Extending this phenomenon over multiple layers leads to large thermal gradients particularly along the building direction. Thus, large RS may appear in the final part. The RS itself is influenced by many manufacturing parameters, e.g., the number and the thickness of the layers [60], the geometry, the scanning strategy [38,75–77], and the laser energy density [13]. Optimization of these parameters can significantly reduce RS but also needs to be balanced against the impact on defects and microstructure. The current approach is to optimize some scanning parameters and the scanning strategy, since they highly affect thermal gradients [78]. An alternative approach is the use of stress relieving heat treatments to reduce the magnitude and subsequent impact of RS [41]. These heat treatments must also be balanced against manufacturing cost considerations and both the desired microstructure and the consequent mechanical properties of the alloys.

**Figure 3.** Schematic images showing the effect of the heat input on the stress state during (**a**) heating and (**b**) cooling in LPBF manufacturing (adapted from [60]).

#### *4.2. Distribition of Residual Stress*

An exemplary RS distribution for LPBF of 316L is shown in Figure 4, acquired on 24 mm × 46 mm × 21 mm prisms at middle height [79]. Measurements conducted by X-ray diffraction reveal the presence of high magnitude tensile RS at the surfaces [79]. Bulk neutron diffraction measurements show that stresses invert to compressive RS at an approximate distance of 6 mm from the surfaces, balancing the tensile RS [79]. In fact, it is typical that tensile stresses develop at the surfaces which are balanced by compressive stresses in the bulk [12,60,74,75,79–91]. As mentioned before, the magnitude and distribution of the RS locked in the part is dependent on the manufacturing parameters. However, the general aspects remain unchanged irrespective of the alloy being produced. To characterize the complete stress distribution within a sample, different measurement methods may be required [79]. The methods and the associated challenges to determine the RS from diffraction-based methods in the domain of laser-based AM will be introduced in the following paragraphs.

**Figure 4.** Example of a stress distribution along the build direction (σN) in LPBF of 316L prisms measured by ND (bulk) and lab X-ray (surface). Reproduced from [79].

#### **5. Determination of Residual Stresses with Diffraction-Based Methods**

The determination of RS can be categorized into destructive (e.g., hole drilling, crack compliance method, hardness testing, etc.) and non-destructive methods (e.g., Bridge curvature method, diffraction, etc.) [92]. However, this paper will solely focus on the

methodology of non-destructive diffraction-based methods for RS analysis used for laserbased AM. Therefore, in the following paragraphs the most relevant diffraction techniques will be introduced. Diffraction techniques are well established non-destructive method to evaluate RS in both academia and industry. Determining elastic strains by measuring the variation of lattice spacing provides a powerful method to identify RS at the surface (X-ray diffraction, XRD), at the subsurface (synchrotron energy dispersive diffraction, ED-XRD), as well as in the bulk (synchrotron or neutron diffraction, ND) [13,74,82,83].

#### *5.1. General Aspects of Diffraction-Based Methods*

The Bragg equation [93] (Equation (1)) describes the condition for constructive interference of spherical waves emitted by an ordered arrangement of atoms (in lattice planes with distance *dhkl*), induced by an impinging planar wave of wavelength *λ* with its order of diffraction *n*. This law provides the basis for the determination of RS with diffraction-based methods, as the lattice (quantified by the interplanar distance *dhkl*) can be used as a strain gauge. Consequently, once a material is under the effect of RS the *dhkl* are altered. Since the beam size in XRD, SXRD or ND measurements is finite, the measured diffraction peak contains a superposition of type I and type II RS within the sampling volume [71]. In all diffraction measurements, the total strain of the lattice is expressed by a shift of the respective diffraction peak (Equation (1)). For the monochromatic case, with a defined wavelength *λ*, and a known strain-free lattice spacing (*dhkl* <sup>0</sup> ), a peak shift to lower scattering angles represents a tensile strain, while a shift to larger scattering angles a compressive one. Type III stresses will mostly contribute to the broadening of the peak or changes in the peak shape [32].

$$2d^{\text{lvll}}\sin\theta = n\lambda \tag{1}$$

The strain is then calculated as

$$\left\{ \varepsilon^{hkl} \right\} = \left\{ \frac{d^{hkl} - d\_0^{hkl}}{d\_0^{lkl}} \right\} \tag{2}$$

However, to link the determined lattice strains in the laboratory coordinate systems to macroscopic stresses in the sample coordinate systems a few more considerations are necessary. A short description of the fundamentals of RS determination with diffraction-based method is, therefore, presented in the following. For a more detailed description on RS analysis by diffraction-based methods, the reader is referred to the literature [32–34,71,94].

In the general case, RS is derived from lattice strains of a particular set of lattice planes. The measured values are *dϕψ hkl*, i.e., interplanar distances at different sample orientations (*ϕ*,*ψ*). For the RS determination, the strains are calculated as in Equation (2) and successively converted to **elastic** stresses via Hooke's law. This yields the general equation for RS determination in the Voigt notation (Equation (3)). Equation (3) connects the elastic lattice strain *εϕψ hkl* (in all directions (*ϕ*,*ψ*) with the components of the stress tensor in the sample coordinate system by using a transformation matrix (Figure 5). The stress (denoted by *<sup>σ</sup><sup>S</sup>*) is averaged over all crystallites contained in the gauge volume. The values <sup>1</sup> <sup>2</sup>*S*<sup>2</sup> *hkl* (Equation (4a)) and *S*<sup>1</sup> *hkl* (Equation (4b)) represent the diffraction elastic constants (DECs), which in general depend on the measurement direction in the crystal system. These constants take the elastic anisotropy of the single crystal into account and are discussed in detail later. However, for quasi-isotropic (poly)-crystals they are independent of the sample coordinate system. The DECs serve as proportionality constants, which connect the measured *dϕψ hkl* to a macroscopic RS for the different lattice planes. A further unknown parameter is *dhkl* <sup>0</sup> , which represents the reference value for the determination of the strain. Different strategies are available to determine the *dhkl* <sup>0</sup> , which will be examined later.

$$\begin{aligned} \left\{ \begin{array}{l} \left\{ \varepsilon\_{q\eta} \right\}^{\mathsf{ML}} \right\} &= \left\{ \frac{d\_{q\eta}^{\mathsf{ML}} - d\_{0}^{\mathsf{ML}}}{d\_{0} \mathfrak{s}^{\mathsf{ML}}} \right\} \\ &= \frac{1}{2} \mathcal{S}\_{2} \mathfrak{h}^{\mathsf{ML}} \left[ \sin^{2} \mathfrak{p} \left( \langle \sigma\_{11}^{\mathsf{S}} \rangle \cos^{2} \mathfrak{p} + \langle \sigma\_{22}^{\mathsf{S}} \rangle \sin^{2} \mathfrak{p} + \langle \sigma\_{12}^{\mathsf{S}} \rangle \sin 2 \mathfrak{p} - \langle \sigma\_{33}^{\mathsf{S}} \rangle \right) + \langle \sigma\_{33}^{\mathsf{S}} \rangle \right. \\ &\left. + 2 \sin 2 \mathfrak{p} (\langle \sigma\_{13}^{\mathsf{S}} \rangle \cos \mathfrak{p} + \langle \sigma\_{23}^{\mathsf{S}} \rangle \sin \mathfrak{p}) \right] + \mathcal{S}\_{1} \mathfrak{h}^{\mathsf{ML}} (\langle \sigma\_{11}^{\mathsf{S}} \rangle + \langle \sigma\_{22}^{\mathsf{S}} \rangle + \langle \sigma\_{33}^{\mathsf{S}} \rangle) \end{aligned} \tag{3}$$

$$\frac{1}{2}S\_2^{\;hkl} = \frac{1+\nu^{hkl}}{E^{hkl}}\tag{4a}$$

$$S\_1{}^{hkl} = \frac{-\nu^{hkl}}{E^{hkl}}\tag{4b}$$

Equation (3) represents the most general case, where all stress components are present. If simplifying assumptions can be made, such as the absence of shear stress components (i.e., the fact that the sample coordinate system coincides with the principal stress system), plane stress or plane strain states, or that a particular component vanishes, the equation would simplify. Some cases are developed in more detail below. The same would happen if we can apply simplifications on the DECs, as for instance assume that the material is isotropic.

**Figure 5.** Orientation of the laboratory coordinate system (L) with respect to the sample coordinate system (S), and the associated angles *ϕ* and *ψ*. *η* denotes the rotation angle around the measurement direction (adapted from [32]).

#### *5.2. X-ray Diffraction*

5.2.1. The Monochromatic Case for Surface Analysis

The use of monochromatic X-ray sources for the determination of RS is widely spread. The penetration depth is in the order of a few μm. The general equation for RS determination (Equation (3)) can thus be simplified: The stress components normal to the measurement plane 12 [*σi*3= 0 (*i* = 1, 2, 3)] can be considered zero (Equation (5)).

$$\varepsilon\_{q\Psi}^{hkl} = \frac{1}{2} S\_2 \sigma\_\varphi \sin^2 \Psi + S\_1 (\sigma\_{11} + \sigma\_{22}) \text{with } \sigma\_\theta = \sigma\_{11} \cos^2 \varphi + \sigma\_{22} \sin^2 \varphi + \sigma\_{12} \sin 2\varphi \tag{5}$$

As laboratory setups mostly use monochromatic X-rays sources, an appropriate lattice plane representing the bulk material must be chosen. A guideline for this can be found in DIN EN 15305 [95], but will be discussed more in detail in Section 6.4. The main approach used in laboratory X-ray devices is the *sin*2*ψ* method in which the lattice spacing is measured under variation of the *ψ* angle under a (usually) fixed *ϕ* angle (Figure 5). Equation (5) can be considered a linear equation of the form *<sup>ε</sup>*(*sin*<sup>2</sup> *<sup>ψ</sup>*) <sup>=</sup> *<sup>a</sup>*·*sin*2*<sup>ψ</sup>* <sup>+</sup> *<sup>b</sup>*. The straight line has a slope of *a* =<sup>1</sup> <sup>2</sup>*S*2*σϕ* and intersects the *<sup>ε</sup>*(*sin*<sup>2</sup> *<sup>ψ</sup>*) axis at *<sup>b</sup>* <sup>=</sup> *<sup>S</sup>*1(*σ*11+*σ*22). From the linear regression of the respective *ε*(*sin*<sup>2</sup> *ψ*)—distribution the RS can be determined in the direction *ϕ* (Figure 6). In an ideal case, where an elastically isotropic or non-textured material in a homogeneous stress state is sampled, the obtained *ε*(*sin*<sup>2</sup> *ψ*) is truly linear [32]. Even though these requirements are often not fulfilled, the errors are typically of small order and can thus be neglected [32]. However, for strongly textured materials (e.g., rolled, additively manufactured) the deviations can be severe. In the case of present shear stresses (e.g., *<sup>σ</sup>*<sup>13</sup> and *<sup>σ</sup>*23) an ellipsoid is observable (different *<sup>ε</sup>*(*sin*<sup>2</sup> *<sup>ψ</sup>*) for <sup>±</sup>*ψ*) rather than a linear distribution. By the subtraction of the respective −*ψ* and +*ψ* distributions a linear equation is obtained. Finally, from its slope the shear stress component in the direction *ϕ* can be determined. Although normal stress components can also be determined within the information depth of the radiation this requires the precise knowledge of *d*<sup>0</sup> *hkl*, which is not needed for the determination of shear stresses [32]. Due to the relatively low penetration of lab X-rays into metallic materials, the surface roughness of additively manufactured material impacts the determined stress values [96].

**Figure 6.** Simplified *ε*(*sin* <sup>2</sup> *ψ*) distribution assuming an elastically isotropic or non-textured material in a homogeneous compression stress state (adapted from [32]).

#### 5.2.2. The Energy Dispersive Case

In addition to the monochromatic (angular dispersive) XRD technique, it is also possible to use polychromatic radiation (white beam) for RS determination. An energy dispersive detector detects the respective energies of the diffracted X-rays at a fixed diffraction angle *θ*. In such manner the entire diffraction spectrum of the respective material can be obtained for each measurement direction (*ϕ*, *ψ*) [32]. Due to the wide energy range used, the information retrieved arises from different depths of the specimen [97]. The information depth of the respective energy can be calculated using the following equation [97]:

$$\tau\_{\eta} = \frac{\sin^2 \theta \, - \, \sin^2 \psi + \cos^2 \theta \sin^2 \psi \sin^2 \eta}{2 \, u \left( E^{\text{lvl}} \right) \sin \theta \cos \psi} \tag{6}$$

The information depth is a function of the sample rotation around the diffraction vector *η*, the diffraction angle *θ*, the tilt angle *ψ* and the energy dependent linear absorption coefficient *u*(*Ehkl*). The latter is material dependent. *τη* defines the depth below the surface from which 63% of the total diffracted intensity comes from [98].

The Energy of each respective reflection can be directly transferred to the lattice plane spacing by rewriting the Braggs law in terms of photon Energy *Ehkl* [99]:

$$d^{hkl}(\mathbf{\dot{A}}) = \frac{\mathbf{h} \cdot \mathbf{C}}{2sin\theta} \cdot \frac{1}{E^{hkl}} \approx \frac{6.199}{sin\theta} \cdot \frac{1}{E^{hkl}}\tag{7}$$

In Equation (7) *h* is the Planck constant and *c* the speed of light. The *sin*2*ψ* method is also applicable for the energy dispersive case. The *ε*(*sin*<sup>2</sup> *ψ*) distributions are simply calculated using Equation (7) together with the strain definition (see Equation (2)). The same simplifications (as for lab X-ray) apply whenever measuring in reflection mode or a biaxial stress state can elsewise be justified. In fact, the plane stress assumption might only hold for lower energy ranges with a low penetration depth. This complicates the RS analysis of higher energy reflections, as the triaxial approach could be more suitable. The acquisition of the entire diffraction spectrum allows the stress analysis for each lattice plane observed. Therefore, a depth resolved stress analysis (near surface) is possible up to the maximum information depth (according to Equation (6)). With respect to laser-based AM, authors have extracted RS depth profiles by using the combination of different reflections (under the assumption of vanishing stress component normal to the surface) [38,96]. In addition, a full pattern refinement to obtain an average *dhkl* can be conducted (e.g., Rietveld refinement) [100]. Recently, Hollmann et al. [101] proposed methods for near surface measurements of materials with cubic symmetry and nearly single crystalline texture (e.g., additively manufactured).

Due to the high energies available in synchrotron facilities even measurements in transmission are possible both in angular (monochromatic) and energy dispersive (polychromatic) modes, depending on the material measured and the sample thickness [32]. In these cases, depending on the geometry, the out-of-plane stress cannot be neglected and hence the triaxial stress analysis approach is required. However, the ability to perform triaxial RS measurements is hampered by the use of elongated lozenge-shaped sampling volume, typical in high energy diffraction measurements (because of the required small diffraction angle [32]). On the one hand, the method therefore allows a very high spatial resolution (in the order of 10–100 μm) in the two in-plane directions, but on the other hand the spatial resolution becomes poor (several millimeters) in the out-of-plane direction. Despite this limitation, energy dispersive techniques are well suited for thick wall geometries, whereby the stress state is closer to the plane strain condition and limit gradients exist though the thickness. Moreover, significant work is reported on the use of transmission set-up for the determination of DECs through in situ tensile testing. This topic is addressed in Section 6.3.3.

#### *5.3. Neutron Diffraction*

As neutrons have a high penetration depth in most materials, fully 3D stress states can be probed. The gain in generality of the approach must be paid at a price: the strong dependence of the RS analysis on the reference interplanar spacing, *d*<sup>0</sup> *hkl*. Additional complications arise when *d*<sup>0</sup> *hkl* differs over the analyzed region due to chemical gradients over the specimen. These points are discussed in detail in Section 6.1. There are two neutron diffraction methods to determine RS: the monochromatic and the time-of-flight (TOF) method. The TOF method uses a polychromatic beam and rests on the detection of many diffraction peaks. Thus, the method leverages on the fact that the velocity of the neutrons is inversely proportional to its wavelength. In the monochromatic case, the instrument operates with a fixed wavelength, and most commonly only one peak at a time can be detected. The two methods will be introduced briefly below. For a more detailed description the reader is referred to the literature [94].

#### 5.3.1. The Monochromatic Method

In scattering, a neutron may be described by its wave vector *k*, of magnitude 2π/*λ* directed along its velocity part [94]. Due to the wave nature of matter, the de Broglie wavelength of the neutron (*λ*) is directly linked to the momentum (*p*) of the respective particle [94]:

$$p = m\_{\text{n}} \\ v = \frac{hk}{2\pi} = h\mathbf{k} \tag{8}$$

This allows the calculation of an associated wavelength in dependence of the neutron velocity *v* and mass *mn* with the Planck's constant *h.* In the monochromatic case, neutrons with a given wavelength are used to study the lattice strain within the material [102]. The wavelength of the neutrons is usually selected using a single crystal monochromator from a broader neutron wavelength spectrum [102]. Typically, the wavelength is chosen so that a diffraction angle of around 2*θ*~90◦ is used. The condition 2*θ*~90◦ allows the definition of a nearly cubic sampling (gauge) volume. Thereby, probing the same region upon any sample rotation. The diffracted signal is usually then detected on a position sensitive detector or a scanning point detector [94]. An example of a typical diffraction peak obtained is shown in Figure 7, which are typically fitted using a symmetric function (e.g., Gaussian).

**Figure 7.** Neutron peak profile. Reproduced from [102] with permission from Elsevier.

The change of diffraction angle with respect to a reference value yields variations of the lattice strain and can be expressed in the angular form as [102]:

$$
\varepsilon^{hkl} = \frac{\Delta d^{hkl}}{d^{hkl}} = -\Delta \theta^{hkl} \cot \theta^{hkl} \tag{9}
$$

Similar to the angular dispersive X-ray methods (see Section 5.2.1), an appropriate lattice-plane must be chosen, which represent the bulk behavior the best. For the stress analysis the same relations remain valid. However, the isotropic form of the Hooke's law typically is applied along three orthogonal principal strain components [94] (see Equation (14)). The consequences for the related assumptions with respect to principal directions are discussed in Section 6.2.

#### 5.3.2. The Time-of-Flight Method

The neutron diffraction (ND) time-of-flight method is the equivalent to polychromatic diffraction in the X-ray case. From the neutron travel time between source and detector, the associated wavelength can be calculated (Equation (10)) [94].

$$
\lambda = \frac{ht}{m\_n L} \tag{10}
$$

As detectors are placed at 2*θ*~90◦, using Bragg's law (Equation (1)) one can directly determine *dhkl* from the wavelength at which peaks appear in the diffraction spectrum (for a known crystal structure). A typical ND diffraction spectrum is shown in Figure 8. In contrast, to steady state sources (monochromatic), the time-pulsed source instruments (timeof-flight) typically cause an asymmetry due to the moderation process: More complicated fitting functions are typically necessary [94]. Using the TOF methods an average *d* can be obtained by a full pattern refinement, but also single peak fits are performable [102].

**Figure 8.** Time-of-flight pattern. Reproduced from [102] with permission from Elsevier.

#### **6. Peculiarities of Diffraction-Based Methods in the Case of AM**

#### *6.1. Strain-Free Lattice Spacing (d*<sup>0</sup> *hkl)*

To precisely determine RS in parts using diffraction-based techniques, the knowledge of a *d*<sup>0</sup> *hkl* as a reference is essential (see Equation (2)). A comprehensive description of the methods to obtain a *d*<sup>0</sup> *hkl* value is given by Withers et al. [27]. In the case of laboratory X-ray diffraction measurements (*sin*2*ψ*), where out-of-plane stresses can be considered to equal zero (*σi*<sup>3</sup> *=* 0), a prior knowledge of *d*<sup>0</sup> *hkl* is not required, as it can even be calculated by the combination of several measurements [32]. In addition, the method is relatively insensitive to an inaccuracy in *d*<sup>0</sup> *hkl* up to 10−<sup>3</sup> nm [32].

For example, one could measure *dhkl* vs. *sin*2*ψ* for the directions (*ϕ =* 90◦, *ψ*) and (*ϕ =* 0, *ψ*) and then determine their average value:

$$\frac{d^{\rm hkl} \left(\varphi = 90^{\circ}, \,\,\psi\right) + d^{\rm hkl} \left(\varphi = 0^{\circ}, \,\,\psi\right)}{2} = (\sigma\_{11} + \sigma\_{22}) d\_{0}^{\rm hkl} \left[2S\_{1}^{\rm hkl} + \frac{1}{2} S\_{2}^{\rm hkl} \sin^{2}\psi\right] + d\_{0}^{\rm hkl} \tag{11}$$

The right term equals to *dhkl* <sup>0</sup> , when (isotropic, no steep gradient, *σ*<sup>22</sup> = *σ*11) [34]:

$$
\sin^2 \psi = \sin^2 \psi^\* = \frac{-S\_1^{hkl}}{\frac{1}{2} S\_2^{hkl}} \left( 1 + \frac{\overline{\sigma}\_{22}}{\overline{\sigma}\_{11}} \right) \tag{12}
$$

Consequently, the *d*<sup>0</sup> *hkl* can be defined as (e.g., for *σ*<sup>11</sup> = *σ*22):

$$d\_0^{\text{lkl}} = \frac{d^{\text{lkl}}(\varphi = 0^\circ, \psi\*) + d^{\text{lkl}}(\varphi = 90^\circ, \psi\*)}{2} \text{ with } \sin^2 \psi^\* = \frac{-2S\_1^{\text{lkl}}}{\frac{1}{2}S\_2^{\text{lkl}}} \tag{13}$$

Therefore, in this particular case, the bare elastic constants define the strain-free direction *ψ*∗, and the half average of *dhkl* (*ϕ =* 90◦*, ψ*) and *dhkl* (*ϕ =* 0◦*, ψ*) at the position *sin*2*ψ*<sup>∗</sup> provides the *d*<sup>0</sup> *hkl* (at the location where the *sin*2*ψ* scan was carried out). A more detailed description and examples for other stress states to derive a *d*<sup>0</sup> *hkl* are given in [34].

Although this method leads to a simplified experimental determination of *d*<sup>0</sup> *hkl* it still bears the problem of DECs values (Equation (12)). As the determination of *d*<sup>0</sup> *hkl* by this method is dependent upon knowledge of DECs (Equation (12)), the reliability of the DECs must be high to determine a correct value for *d*<sup>0</sup> *hkl*. The determination of the DECs is a separate topic and will be examined later.

While the method is sensitive to intergranular and interphase stresses [27], a relative comparison of *d*<sup>0</sup> *hkl* near the surface is often still possible. Thiede et al. [82] used this method to determine *d*<sup>0</sup> *hkl* variations across the surface of LPBF manufactured Inconel 718 prisms (assuming *σ*<sup>11</sup> = *σ*22) (Figure 9a). A small normal stress component *σ<sup>n</sup>* was observed, which was reported to correlate with the scanning strategy. The *sin*2*ψ* method has also been used by other researchers to determine *d*<sup>0</sup> *hkl* in LPBF Ti6Al4V [83,96]. As an alternative, Pant et al. [81] used the *dhkl* value measured at *ψ =* 0◦ as *d*<sup>0</sup> *hkl* for calculating RS values.

For the cases in which the out-of-plane stress cannot be considered to equal zero (*σi*<sup>3</sup> = 0) the precise knowledge of *d*<sup>0</sup> *hkl* remains indispensable. An independent determination of *d*<sup>0</sup> *hkl* can be made by means of the following strategies:

**Figure 9.** *d*<sup>0</sup> <sup>311</sup> values extracted from *d*<sup>311</sup> versus *sin*2*ψ* plots (**a**) and from raw powder (RP), filings (SP) and cuboids (L, T, N) (**b**). Data taken from [82].

#### 6.1.1. Use of Raw Powder

In the case of AM there is also the possibility to obtain *d*<sup>0</sup> *hkl* by measurements on raw powder. This is a method, which does not require a twin specimen and is non-destructive by nature. However, the thermal history of the raw powder, and consequently the local chemical composition and microstructure, may differ significantly from that of the printed part [103]. The macro- and micro-scale differences in chemistry can significantly alter the lattice parameters of the material [104–106]. As Thiede et al. [82] have concluded, a shift due to different local chemical segregation prevented the use of it as a reference (Figure 9b). Similar findings were made by Kolbus et al. [103] and more recently Serrano-Munoz et al. [107]. While there may be examples of low alloyed or commercially pure materials, where the use of the raw powder may be applicable due to the lower amount of segregation, using raw manufacturing powder as *d*<sup>0</sup> *hkl* is generally not recommended in the domain of AM [45].

#### 6.1.2. Use of Mechanical Filings

Mechanical filings from either the specimen itself or taken from a twin specimen can be used. This approach would capture the effect of the thermal cycles on the local chemical segregation and has the advantage that in a powder the macroscopic RS is fully relieved [27]. However, the filing process tends to induce plastic deformation within the powder, leading to strong diffraction peak broadening associated with microscopic stresses (Type III and possibly Type II [103]). In addition, filings certainly contain different intergranular strain than the component, so that they cannot be considered fully stress-free [27].

It was recently shown that using the *d*<sup>0</sup> *hkl* reference value of mechanical filings, a compressive stress was found for all measured points, which contradicts the stress balance condition [107]. This mismatch was attributed to the high accumulation of plastic strain in the as-filed condition, and in fact the FWHM vastly reduced upon heat treatment (indicating a significant plastic recovery). Even if some circumstances lead to the conclusion that the filings from the material are the most suitable *d*<sup>0</sup> *hkl* [82], the applicability of mechanical filings as *d*<sup>0</sup> *hkl* shall be limited to exceptional cases and rarely be considered an appropriate approach in the general case of AM.

#### 6.1.3. Use of Macroscopically Relaxed Samples (Cubes/Combs/Arrays)

In neutron diffraction, it is common to determine the *d*<sup>0</sup> *hkl* with small cubes (or combs) cut from a sister sample. These cubes are assumed to be free of macroscopic stress. Although they appropriately represent the (possible) variation of chemical composition of the specimen, other problems must be considered: The cubes could retain intergranular stresses and are vulnerable to geometrical effects if poorly positioned on the sample manipulator [27]. Thiede et al. [82] measured small 5 mm × 5 mm × 5.5 mm cubes extracted from sister samples of LPBF Inconel 718. However, they found a significant dependence of the *dhkl* value on the measurement direction (Figure 9b). This suggests that the cubes were not fully macroscopically stress free and thus could not yield a reliable *d*0 *hkl* [82]. Nevertheless, a similar *dhkl* dependence on the measurement direction was found by Ulbricht et al. [79] for LPBF manufactured stainless steel 316L, this time using 3 mm × 3 mm × 3 mm coupons.

To obtain a representative *d*<sup>0</sup> *hkl* they averaged the values over all measured directions (which correspond to the main geometrical directions). Kolbus et al. [103] attributed the different *d*<sup>0</sup> *hkl* in different directions of reassembled DMLS Inconel 718 cubes (2.5 mm × 2.5 mm × 2.5 mm and 5 mm × 5 mm × 5 mm) to anisotropic micro stress between the fcc matrix and the precipitation phases. They applied an average obtained from measurements on reference cubes extracted from different positions but did not average over different strain directions. Regardless of the direction being measured, Pant et al. [81] found that the average value of the measured *d*<sup>0</sup> *hkl* on the LPBF manufactured Inconel 718 array (cut by wire electric discharge machining) was position independent. The average value, however, showed to not provide sufficient accuracy concerning the stress balance condition in the cross sections [81]. Other approaches based on relaxing macroscopic stresses by cutting or extracting small geometries from sister samples were conducted by several researchers [31,85,91,108–112]. Although some inconsistencies in defining a representative *d*<sup>0</sup> *hkl* from measurements on macroscopically stress-free samples have been reported, approaches to determine *d*<sup>0</sup> *hkl* using coupons (or small pieces of the printed part) are widespread; to date, this approach is considered the best to produce a reliable measured *d*<sup>0</sup> *hkl*.

6.1.4. Stress and Moment Balance

Another method to determine a *d*<sup>0</sup> *hkl* is based on the continuum mechanics-based requirements that force and moment must balance across selected cross sections or over the whole specimen [27]. Therefore, by mapping the *dhkl* in the required sample region the reference *d*<sup>0</sup> *hkl* can be iteratively found by imposing stress and moment balance, even starting from a nominal value [27]. However, great care must be taken to prove the applicability of the method: the experimental data must cover the whole cross section and it must be ensured that a global *d*<sup>0</sup> *hkl* is appropriate (i.e., the method would not work if *d*0 *hkl* varies across the sample) [27]. Serrano-Munoz et al. [107] applied this method to obtain a *d*<sup>0</sup> *hkl* for different cross sections of LPBF manufactured Inconel 718 prisms. The method produced a similar *d*<sup>0</sup> *hkl*, indicating no dependance on the scanning strategy and the cross section being analyzed (i.e., there is no spatial variation of *d*<sup>0</sup> *hkl* along the length of the sample). Therefore, an average value was used for the *d*<sup>0</sup> *hkl* in the RS calculation [107], which applicability was later shown [80].

In fact, Kolbus et al. [103] proposed the method of stress balance as a possibility to check the measured *d*<sup>0</sup> *hkl*, as also indicated by Withers et al. [27]. To cross-check the values measured on mechanically relaxed samples, Pant et al. [81] used the stress balance approach and found a significant difference. Such discrepancy was attributed to microstructural variations: the average *d*<sup>0</sup> *hkl* value obtained by stress balance was used for the final RS calculations. Stress balance is often applied as an alternative approach to obtain a *d*<sup>0</sup> *hkl* without additional experimental effort [86,113]. However, in order to check the applicability of the hypotheses mentioned above, one should always compare the results (stress fields, *d*0 *hkl*) obtained by using the stress balance condition with those obtained using experimental methods [27,80,103].

Indeed, the applicability of the stress balance approach for AM materials, which possibly exhibit 2D or 3D chemical variations due to the differential cooling rates, still requires further experimentation to test the robustness of the approach. Although this method would aid to make the RS determination by diffraction fully non-destructive, great care must be taken to avoid large errors in the RS values. In fact, Wang et al. [31] showed a LMD manufactured Inconel 625 wall displayed local variations of *d*<sup>0</sup> *hkl* due to the chemical and microstructural heterogeneity of the builds (Figure 10). This fact impeded the applicability of the stress balance condition.

**Figure 10.** Reference *d*<sup>0</sup> <sup>311</sup> as a function of distance from the build-baseplate interface measured by neutron diffraction in the 40 s dwell time stress-free reference samples without heat treatment. Reproduced from [31] with permission from Elsevier.

The following table (Table 1) summarizes available methods to obtain *d*<sup>0</sup> *hkl*. It also reports the references in which each method was applied (in the case of laser-based AM parts).



#### *6.2. Principal Stress Directions*

A simplification of Equation (3) with the hypothesis of isotropic elastic constants (i.e., with the use of *E*, Young's modulus, and *ν* Poisson's ratio) would read for normal stress and strain components (*ii* = *xx*, *yy*, *zz* in cartesian coordinates) [94]:

$$\sigma\_{\rm ii} = \frac{E^{hkl}}{\left(1 + \nu^{hkl}\right)} \left[\varepsilon\_{\rm ii} + \frac{\nu^{hkl}}{\left(1 - 2\nu^{hkl}\right)} \left(\varepsilon\_{xx} + \varepsilon\_{yy} + \varepsilon\_{zz}\right)\right] \tag{14}$$

For isotropic materials, Equation (14) is valid also in presence of shear stress [114]. However, without the knowledge about the principal stress directions, such a determination would not necessarily capture the maximum stress values. A common assumption to reduce the experimental effort is, that the principal stress directions coincide with the sample geometrical axes (e.g., see [82,83,103,110,115]). If the principal stress directions are known, Equation (14) can be used to calculate the principal stress components. This would reduce the number of measurements needed down to 3, if *dhkl* <sup>0</sup> is known. In the general case, where the principal stress axes are not known particular attention (and effort) needs to be dedicated to this aspect. In AM parts, the determination of the principal stress directions goes through the knowledge of the manufacturing process and of its impact on the principal stress directions.

Although several process parameters largely influence the magnitude of the RS, such as layer thickness, scanning speed, beam power, and vector length, the major influencing parameter on the stress distribution (and principal axes) is the relative orientation of the scanning pattern to the corresponding geometry [107].

Investigations about the principial stress direction in AM-Material started on simple geometries such as prisms [108]. Six strain directions were used for the calculation of the principal stress direction, which was not found to coincide with the sample geometrical ones. In contrast, complex structures were investigated by Fritsch et al. [116] using ND. It was shown, that for LPBF manufactured IN 625 lattice structures measurements along 6 independent strain directions are not sufficient to determine the principal stress directions and magnitudes. The authors found that at least seven independent directions are required to experimentally determine the direction of principal stress and even 8 directions are needed if the correct RS magnitude needs to be determined. In that case the calculated directions become insensitive to the choice of the measurement directions. Furthermore, it was proven that the RS tensor ellipsoid axes align well with the orientation of the struts within the lattice structure. [116].

Gloaguen et al. [46] showed, for example, that when assuming the principal stresses along the geometrical specimen axes for LPBF manufactured Ti6Al4V, the RS is affected by significant errors. This can be attributed to the fact that the principal stress axes deviate from the sample axes. This observation was made even though a simple bidirectional scanning strategy along the geometry with a 90◦ interlayer rotation was applied.

In fact, Vrancken [117] found for LPBF manufactured Ti6Al4V produced by a comparable scanning strategy, that the principal stress directions coincide with the direction of the scanning tracks. In other studies researchers found the principal stress directions to align with the sample geometrical axes [76,82], if the scanning strategy is more complicated (e.g., rotation between subsequent layers etc.).

These results emphasize that an increasing part complexity requires advanced measurement techniques and strategies to reach the desired precision for a reliable assessment of RS states. Again, given the complexity of laser-based additive manufacturing processes, the general assumption that the principal stress directions are governed by the sample geometry must be used carefully [46]. Therefore, for the alignment of the specimen in the laboratory coordinate system it is recommended not to make any assumption about the principal direction of stress and measure at least eight independent directions at all locations.

#### *6.3. Diffraction-Elastic Constants (DECs)*

To obtain stress values, the DECs act as proportionality constants to link the measured microscopic (i.e., lattice) strains to macroscopic stresses (see Equation (3)). Their precise knowledge is important, because the magnitude of the resulting RS depends on the values of the DECs (see Equation (3)). RS are thus highly vulnerable to errors if reliable values of the DEC are not used.

Two methods are available to obtain the DECs: They can be calculated from the single crystal elastic constants (SCEC) using different theoretical schemes (for instance a grain interaction model for the polycrystalline aggregate). This method is to be preferred if the SCECs are reliably known (note that much work needs still to be made for AM materials). The presence of a strong crystallographic texture in conjunction with crystal anisotropy can hamper the determination of the DECs by theoretical calculations, as one must properly take the texture into account. Alternatively, one can directly determine them in an in situ deformation test during diffraction. In this case, the microscopic response is monitored during a macroscopic deformation, and the proportionality constant between applied stress and lattice strain is the plane-specific Young's modulus *Ehkl*. A guideline for this is given in DIN EN 15305 [95]. The latter method, however, is connected to a relatively high experimental effort.

6.3.1. The Anisotropy of Single Crystals

The anisotropy of the single crystal can be expressed by the differences of the different elements of the compliance tensor. For cubic materials Zener [118] proposed the following coefficient, written in the Voigt notation, to calculate the anisotropy of the single crystal:

$$A^Z = \frac{2 \cdot \mathbb{C}\_{44}}{\mathbb{C}\_{11} - \mathbb{C}\_{12}} \tag{15}$$

In this definition, full isotropy is expressed by a value of *AZ* = 1. Any deviation from *A<sup>Z</sup>* = 1 signifies a certain degree of crystal anisotropy. However, as the Zener ratio only remains valid in the cubic case, researchers were motivated to formulate a more general anisotropy index, which would be valid for an arbitrary crystal structure. Such an index (*AU*) was derived by Rangathan and Ostoja-Starzewski [119]. It is based on the fractional difference between the upper (Voigt) and lower (Reuss) bounds on the bulk (*κV*, *κR*) and shear (*μV*, *μR*) moduli. The values can be determined by the following equation (Equation (16)).

$$A^{\ U} = \frac{\kappa^{\upsilon}}{\kappa^{\overline{\kappa}}} + 5\frac{\mu^{\upsilon}}{\mu^{\overline{\kappa}}} - 6\tag{16}$$

The main advantage of this formulation is its applicability to any type of crystal symmetry. However, it remains a relative measure of anisotropy. In fact, it has not been proven, that a crystal with twice an *AU* also is twice as anisotropic. Therefore, Kube [120] provided an alternative definition, the anisotropy index *A<sup>L</sup>* (Equation (17)), whereby the value of *AL* = 0 expresses isotropy.

$$A^L(\mathbb{C}^\upsilon, \mathbb{C}^R) = \sqrt{\left[\ln\left(\frac{\mathbb{x}^\upsilon}{\mathbb{x}^R}\right)\right]^2 + 5\left[\ln\left(\frac{\mathbb{u}^\upsilon}{\mathbb{u}^R}\right)\right]^2} \tag{17}$$

There are also different approaches such as the Ledbetter and Migliori ratio [121] or the method proposed by Chung and Buessem [122]. However, we will use *AL* in the following to compare the single crystal anisotropy of the commonly materials used in laser-based AM. One last important remark must be made: the applicability of all DEC calculation schemes heavily rests on the availability of reliable SCEC. A compiled list with the single crystal elastic constants (SCEC) of important alloys for laser based additive manufacturing is given in Table 2. The significant difference in the elastic anisotropy of the different single crystals is evident. The data shown are mainly inferred from measurements on conventionally produced polycrystalline materials or represent measurements on the respective single crystals. Data directly related to additively manufactured materials are still lacking. This may have an impact on the determination of the DECs and of RS. This is because the calculation of DECs is made under the assumption, that tabulated SCECs are still suitable for additively manufactured materials. Nevertheless, some authors have already tackled the problem of the determination of SCEC from experimental data on textured polycrystalline alloys [123].

**Table 2.** Single crystal elastic constants (SCEC) of several engineering alloys in GPa, with their dimensionless calculated Zener (*Az*) and universal (*AL*) anisotropy ratios. For the calculation of *AL* the Matlab script provided by Kube [120] was used.



**Table 2.** *Cont.*

6.3.2. Grain Interaction Models for the Calculation of DECs

Several models have been developed to calculate DECs from SCEC. The first model developed by Voigt [138] (Figure 11a) assumes that adjacent grains undergo the same strain during deformation. However, this assumption violates the equilibrium of forces at the interfaces. On the other hand, Reuss [139] later proposed a model where the equilibrium of forces is fulfilled as a homogenous stress state is assumed (Figure 11b). This leads to the problem, that the different crystals undergo different strains, which would not satisfy the compatibility conditions [114]. To solve these problems Kröner developed a model based on Eshelby's theory [140], which fulfills the interface and the compatibility conditions (Figure 11c). Such scheme considers a spherical particle of arbitrary anisotropy embedded in an isotropic material. With the assumption of spherical particles and isotropic matrix, Kröner derived a closed (analytical) solution to the problem [141]. If the surrounding matrix is not texture free (e.g., as in the case of AM materials), numerical approaches must be considered [141]. In general, the Voigt model is the least applicable, as it results in elastic properties, such as *Ehkl*, that are independent on the plane {hkl}. This does not apply for most crystals. In contrast, the Kröner model has been shown to well match to experimentally determined values in an excellent manner for non-textured microstructures [142–144]. Interestingly, if a strong texture is present, as it has been observed in certain cases (including AM materials), the Reuss model displays better agreement with experimental data [32]. In fact, for columnar structures (the case of AM microstructures) the assumption that each crystal undergoes the same stress could be a good approximation.

From the discussion above, it is clear that for the application of each model, the microstructure and texture present in the material must be considered to determine appropriate values for the DECs. Indeed, many modifications and developments of the three schemes mentioned above have been made over the past years, to encompass the microstructure in the calculation of DECs. Initially, Dölle and Hauk [145] introduced the so-called stress factors to account for the texture using the crystallographic orientation distribution function (ODF). Several authors (e.g., Slim et al. [146], Brakman et al. [147], Welzel et al. [148–150], Gnäupel-Herold et al. [151]) proposed alternative approaches to embed the ODF in the determination of the DECS. More recently Mishurova et al. [40] have shown, that the use of Wu's tensor [152] is equivalent to using Kröner´s approach. In addition, they showcased the applicability of the procedure to LPBF Ti6Al4V. They concluded that, since hexagonal polycrystals possess transverse isotropy and LPBF Ti6Al4V had a fiber texture, the calculated DECs (using the best-fit isotropy assumption) reasonably agreed with experimentally determined values.

6.3.3. Experimental Determination of Diffraction Elastic Constants

The main method for the experimental determination of DECs are in situ mechanical tests, i.e., during high-energy X-ray or neutron diffraction experiments. The response of each lattice plane is monitored as a function of applied stress. It is important to mention that this approach rests on the hypothesis that a statistically significant ensemble of grains with the normal to the planes {*hkl*} is oriented along the load axis. From these datasets, the DECs for each monitored plane then can be derived (see Table 3). For LPBF Ti6Al4V and IN718 a comparison of the model prediction with experimentally obtained values is given in Figure 12.

**Figure 11.** Overview of different model approaches for the calculation of the diffraction elastic constants. (**a**) Voigt model [138] (**b**) Reuss model [139] (**c**) Eshelby–Kröner model [141].

**Table 3.** Experimentally determined diffraction elastic constants by the means of diffraction methods. The plane-specific elastic moduli (*Ehkl* ) are given in GPa.


\* FHT (◦C/h/MPa): 1066/1.5 + 1150/3/105 + 982/1 + 720/8 + 620/10, \*\* DA (◦C/h): 1066/1.5 + 720/8.

**Figure 12.** Comparison of the model predictions of Reuss, Voigt and Kröner for Ni-based alloys Inconel 718 (**a**), Inconel 625 (**b**) [39] and Ti6Al4V [155,156] (**c**).

For the alloys 316L and AlSi10Mg such a comparative figure is not necessary, since the model prediction of Kröner nearly perfectly matches the experimental values of the elastic moduli [153,154]. This is different for additively manufactured Ti6Al4V, Inconel 718 and Inconel 625. For a recrystallized and, thus, untextured microstructure (FHT) the Kröner model best matches the experimental values (Figure 12a) [39]. When, on the contrary, the columnar as-built microstructure (exhibiting relatively strong crystallographic texture) was retained, the model prediction of Reuss best fit the experimental data for Inconel 718 and 625 (Figure 12a,b) [39,131]. The AM Ti6Al4V alloy seems to deviate from this behavior: Mishurova et al. [156] showed, that for low *H*<sup>2</sup> (prismatic planes) the model predictions by Kröner agreed better with experimental data than other schemes (Figure 12c). In contrast, for higher *H*<sup>2</sup> (basal planes) the model prediction of Reuss better matched with the data [156]. This can be explained by the transverse isotropy of the single crystal elastic tensor, exhibiting an isotropic behavior in the basal directions but a strong anisotropy along its c-axis. It has been shown that when considering the transversal isotropy in the material model a reasonable agreement between model and experimental data can be obtained [40]. In presence of crystallographic texture, materials with a higher anisotropy factor (Table 2) tend to be better described by the predictions of the Reuss model than by those of Kröner's scheme. The exception to this trend is given by the alloy 316, for which the model approach of Kröner yields a good prediction of the polycrystal behavior, although the single crystal itself is highly anisotropic [154]. Such an agreement can be explained by the rather weak crystallographic texture along the loading direction in conjunction with the relatively small grain size [154].

As Mishurova et al. [45,156] argue, it is mandatory to report the DECs used to obtain stress values if one wants to compare own data with literature. Severe differences in the RS magnitude are the consequence if different model predictions considered for the determination of DEC. This was shown by Serrano-Munoz et al. [38] for LPBF manufactured Inconel 718: Applying the Kröner model led to a spiky stress depth profile. Stress values of 1200 MPa were reached, which far exceed the yield strength of the non-heat-treated material (630–800 MPa). Much more realistic stress values (up to 870 MPa) were obtained by applying the Reuss model to the experimental data. Also, the spikes of the stress depth profile were smoothed. This indicates the ability of the Reuss model to reasonably describe the intergranular behavior of LPBF Inconel 718 [157]. This was also supported by the findings of Pant et al. [81], who found stresses up to 1000 MPa in their study of as built LPBF manufactured Inconel 718. They used DECs measured for conventionally manufactured Inconel 718 and nearly equal to the Kröner model calculations [158].

Currently, a lack of consistency is observable in the open literature, as summarized in Table 4. It is to remark that, so far, DECs of additively manufactured microstructures have been mainly determined for loading along the building direction. The micromechanical behavior of the microstructure perpendicular to the build direction is, to the best of the authors' knowledge, not yet reported.

**Table 4.** Origins of applied diffraction elastic constants used for stress calculation in additively manufactured specimens.


To summarize, in order to reliably calculate the DECs the proper SCECs of the material and both the microstructure and texture of the specimen should be considered. The crystal and macroscopic anisotropy provide guidance for the choice of the model to consider.

One last remark must be made: To obtain the plane specific Poisson ratio (*νhkl*) one would have to track the same set of grains during the deformation in both, the transverse and axial direction (i.e., along the tensile axis) [156]. However, this is practically impossible. In the case of nearly texture-free conventionally manufactured materials with small grain size the calculation of the *νhkl* using measurements in two perpendicular sample direction is a good approximation, as the gauge volume contains a sufficient amount of randomly oriented crystals. This approximation, in contrast, cannot be made for strongly textured AM materials. In this case, the use of suitable model schemes is recommended.

#### *6.4. Choice of the Appropriate Lattice Planes*

In the angular dispersive (monochromatic) case, one uses specific grains with specific lattice orientations as strain monitors [172]. It is assumed that the statistical ensemble is representative of the material. However, because of their particular elastic and plastic response, these grains are not necessarily representative of the overall stress state [172]. Consequently, the choice of a suitable reflection, whose grains represent the macroscopic RS in a body, is of utter importance [172,173]. Thereby, three main aspects need to be addressed:


Whenever a sample is under stresses, a superposition of macroscopic (Type I) and intergranular stress (Type II) occurs [172]. If our goal is to determine the macroscopic stress state, a lattice plane, which exhibits a low tendency to accumulate intergranular stresses during deformation should be chosen. This tendency can be tested during in-situ loading experiments. Increasing non-linearity of the lattice plane response to a macroscopic load is an indication for the intergranular strain accumulation [174,175]. In fact, if the lattice strain vs. applied stress curve is non-linear residual strain is retained upon unloading. Such residual strain increases with increasing macroscopic plastic deformation.

The accumulation of intergranular stresses is critically dependent on the elastic and plastic anisotropy of the material [175]. In general, it is advisable to choose the lattice planes with the lowest Miller indices possible, as a high multiplicity of the lattice plane helps to reduce the required measurement time.

Besides these general considerations, one should take the underlying texture into account [176]. For example, for a (cubic) material with a strong cube texture, one should use the 200 reflection in spite of its typically high sensitivity to intergranular strains [172]. In fact, the 200 reflection represents most of the grains in such particular case [172]. For conventionally manufactured materials a general guideline on the selection of an appropriate lattice plane is given in ISO-21432 [177]. However, for AM the situation might be different, as strong textures typically prevail.

Very little studies on the topic of the accumulation of intergranular strains in laserbased AM materials are available in the open literature. Table 5 shows the lattice planes typically considered for RS analysis of different laser-based AM materials and outlines their suitability compared to their conventionally manufactured counterparts. In the case of fcc materials the 311 reflection is almost exclusively used [26,74,82,83,103,108]. However, it has been shown by Choo et al. [178] for LPBF 316L that the {311} oriented grains accumulate more intergranular strain than the {111} and {220} grains, which is in contrast to conventional rolled 316L [179]. In fact, considering the <220> texture along the building direction [178], the 220 reflection is more easily detected than others, and yields less data scatter. Likewise, Wang et al. [180] observed a strong nonlinear micromechanical response during initial loading of LPBF manufactured 316L, which has been attributed to anisotropic residual strains within the as-built samples. Consequently, the hierarchical heterogenous microstructures of AM 316L may give rise to significant differences in the buildup of intergranular stresses and should be accounted for.

For hexagonally closed packaged (hcp) materials the pyramidal planes {102} and {103} are considered to exhibit low intergranular stress (for conventionally processed materials) [181,182]. However, Cho et al. [183] showed for conventionally manufactured α-Ti-834 that the first eight diffraction peaks (i.e., those with the lowest Miller indices) accumulate significant intergranular strains. In fact, studies on the topic of intergranular strain accumulation are absent for additively manufactured hcp materials. Although Zhang et al. [155] showed that a high dislocation density is present within the α' Phase of as-built LPBF Ti6Al4V, the micromechanical response show anomalies to conventional Ti6Al4V: sometimes it remains linear well beyond the early stages of loading, sometimes it shows footprints of twinning [184,185]. Thus, the question of the accumulation of intergranular strains is yet far from fully elucidated in AM hcp materials.

In general, more research needs to be dedicated to the topic of intergranular stresses within the domain of laser-based AM materials. One must carefully evaluate whether the requirements are fulfilled for a certain lattice plane to represent the bulk behavior. The approach of using the full pattern refinement of the lattice parameter minimizes (actually, averages) the possible contributions of high intergranular stress to the determined macroscopic type I RS.




*Metals* **2021**, *11*, 1830

#### **7. Summary & Outlook**

Additive manufacturing (AM) methods allow the fabrication of complex structures within a single manufacturing step. Still the heterogeneity of the process often leads to mechanically anisotropic, columnar, and textured microstructures. While one of the biggest challenges in AM is to develop mitigation strategies for the large residual stress that inevitably appears after production, the precise determination of such residual stress remains challenging. Diffraction-based methods provide a powerful tool to non-destructively determine the residual stress. However, the peculiar microstructures of AM materials pose challenges for the characterization of residual stress. Therefore, assumptions and measurement conditions must be chosen with great care:


The amount of research dedicated to the methodology of diffraction-based methods in the domain of AM is increasing but still limited. In particular, the understanding of the influence of the microstructure and texture on the DECs should be addressed for all metal AM processes. This would aid to provide a general strategy to determine the DECs for an additively manufactured material. Further research is needed to develop a uniform strategy to determine an appropriate *d*<sup>0</sup> *hkl*; this would increase the comparability of results. It is also worthwhile to dedicate research to gain a better understanding of intergranular stress accumulation for the hierarchical structures occurring in laser-based AM.

**Author Contributions:** Conceptualization, J.S., A.E. and M.S.; methodology, J.S. and A.K.; validation, J.S., T.M. and I.S.-M.; formal analysis, T.M.; investigation, J.S. and A.U.; resources, G.B.; writing original draft preparation, J.S., A.E. and A.U.; writing—review and editing, J.S., A.E., T.M., A.U., M.S., I.S.-M., T.F., A.K., T.K. and G.B.; visualization, J.S., A.K. and T.F.; supervision, A.E., G.B. and T.K.; project administration, G.B. and T.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors kindly acknowledge the fruitful scientific discussions on the topic with Michael Hofmann (TU Munich), Winfried Petry (TU Munich), Christoph Genzel (HZB, Berlin), and Manuela Klaus (HZB, Berlin). This work was supported by the internal BAM focus area materials project AGIL "Microstructure development in additively manufactured metallic components: from powder to mechanical failure" and the internally funded project MIT1-2019-45.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **Relative Density Measurement of PBF-Manufactured 316L and AlSi10Mg Samples via Eddy Current Testing**

**Marvin Aaron Spurek 1,2,\*, Viet Hiep Luong 2, Adriaan Bernardus Spierings 1, Marc Lany 3, Gilles Santi 3, Bernard Revaz <sup>3</sup> and Konrad Wegener <sup>2</sup>**


**Abstract:** Powder bed fusion (PBF) is the most commonly used additive manufacturing process for fabricating complex metal parts via the layer-wise melting of powder. Despite the tremendous recent technological development of PBF, manufactured parts still lack consistent quality in terms of part properties such as dimensional accuracy, surface roughness, or relative density. In addition to process-inherent variability, this is mainly owing to a knowledge gap in the understanding of process influences and the inability to adequately control them during part production. Eddy current testing (ECT) is a well-established nondestructive testing technique primarily used to detect near-surface defects and measure material properties such as electrical conductivity in metal parts. Hence, it is an appropriate technology for the layer-wise measuring of the material properties of the fused material in PBF. This study evaluates ECT's potential as a novel in situ monitoring technology for relative part density in PBF. Parts made from SS316L and AlSi10Mg with different densities are manufactured on a PBF machine. These parts are subsequently measured using ECT, as well as the resulting signals correlated with the relative part density. The results indicate a statistically significant and strong correlation (316L: *r*(8) = 0.998, *p* < 0.001, AlSi10Mg: *r*(8) = 0.992, *p* < 0.001) between relative part density and the ECT signal component, which is mainly affected by the electrical conductivity of the part. The results indicate that ECT has the potential to evolve into an effective technology for the layer-wise measuring of relative part density during the PBF process.

**Keywords:** powder bed fusion (PBF); eddy current testing (ECT); part quality; in situ relative part density measurement; quality management

#### **1. Introduction**

In the last decade, additive manufacturing technologies have evolved from rapid prototyping to established manufacturing technologies that are increasingly used in industrial production. Powder bed fusion (PBF) is the most commonly used additive manufacturing process for fabricating metal parts, and has evolved to a state-of-the-art technology adopted in various industrial fields such as aerospace, medical, defence, as well as tool, and mould making [1,2]. The PBF process is characterized by the layer-wise melting of a powder bed using a laser beam; hence it enables the direct manufacturing of complex-shaped parts. Despite the tremendous recent technological development of PBF, Debroy et al. [3] identified the lack of consistent part quality as a major challenge impeding the wider commercial adoption of PBF. Part quality is mainly characterized by mechanical properties such as Young's modulus, and part properties such as dimensional accuracy, surface roughness,

**Citation:** Spurek, M.A.; Luong, V.H.; Spierings, A.B.; Lany, M.; Santi, G.; Revaz, B.; Wegener, K. Relative Density Measurement of PBF-Manufactured 316L and AlSi10Mg Samples via Eddy Current Testing. *Metals* **2021**, *11*, 1376. https://doi.org/10.3390/met11091376

Academic Editor: Giovanni Bruno

Received: 2 August 2021 Accepted: 26 August 2021 Published: 31 August 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

and relative density [4]. Process-inherent variability, a remaining knowledge gap in understanding the influences on part quality, and the inability to adequately control these influences during part production are the main reasons for inconsistent part quality [3]. In situ process monitoring technologies are expected to play a major role in obtaining consistent part quality in the future by improving the repeatability of the process as stated by Debroy et al. [3]. The majority of in situ monitoring technologies available today focus on monitoring the melt pool shape, size, or temperature [4–11]. Melt pool monitoring could be a reasonable choice for real-time controlling process parameters, such as laser power, which can help to avoid pore formation owing to local overheating of the melt pool [12]. However, owing to the nature of the PBF process, each solidified layer is remolten at least once. Hence, initially present defects can be healed, as determined by Ulbricht et al. [13], and new ones introduced during the layer remelting. Therefore, only the material integrity of the layer after remelting is relevant for the quality of the part. Although, there have been attempts to spatially map defects via melt pool monitoring [6,14], the detection of defects, which were not artificially introduced, lacks reliability. Owing to the inability to reliably monitor the part quality during production, the part certification for industrial use still requires a brute force approach, which involves time-consuming and expensive material tests such as CT scanning [3].

Eddy current testing (ECT) is a standardized nondestructive testing technique [15] that is adopted in various industries to control and certify the quality of electrically conductive parts. ECT can detect surface and near-surface defects such as cracks [16], as well as measure material properties such as electrical conductivity [17]. The industrial application of ECT to PBF remains limited to the quality control of parts during post-processing [18]. This limits the testable area of the part to the region near the surface. In contrast, integrating ECT into the PBF process cycle enables the layer-wise measurement of previously fused layers that provides quality information on the entire part volume after finishing the build cycle. Therefore, the ability of ECT to measure surface and near-surface defects fits well into the layer-wise build process in PBF. Available studies on ECT as a monitoring technology for PBF are summarized as follows: Todorov et al. [19] developed and patented a sensor array and method [20] and integrated it into a laboratory PBF machine. The system was tested in situ on parts with artificially introduced defects such as notches and regions of unfused material, being able to detect these defects. The authors claim that the regions of unfused material with sizes of 10 × <sup>3</sup> × 0.12 mm3 and 10 × <sup>3</sup> × 0.044 mm3 are good representations of lack of fusion in PBF. However, research on defect formation in PBF suggests that lack of fusion pores are often smaller than 100 μm in diameter [3]. Ehlers et al. [21] developed a sensor array using giant magnetoresistance (GMR) sensors and studied the capability of the system to detect artificially introduced surface defects in a wrought sample and in a PBF-manufactured sample both made from 316L stainless steel. However, the majority of defects in PBF-manufactued parts are located below the surface [22]. Both of the study presented by Todorov et al. [19] and Ehlers et al. [21] used parts with artificially introduced defects to demonstrate the capability of their ECT systems falling short of providing evidence that real defects caused during the PBF process can be detected reliably. In contrast to detecting individual defects, measuring the porosity of a certain part volume, including regions beyond the remelting zone, is an alternative approach to monitoring the process and part quality. Eisenbarth et al. [23] adopted ECT to identify unique keys designed by introducing porosity in 316L samples by adjusting the process parameters on an industrial PBF machine. However, the authors did not achieve the required sensitivity to distinguish between all different PBF samples sufficiently well and did not compare the ECT results to the relative sample density. Obatron et al. [24] studied ECT's ability to distinguish between PBF-manufactured lattice structures with different overall densities by measuring the electrical conductivity of the lattice. Hippert [25] used a similar approach correlating the electrical conductivity of the sample with its relative density. However, Hippert used samples with large artificially introduced holes and could only distinguish between samples with a density difference of 4% relative density.

72

Nevertheless, the approach of Hippert and Obaton et al. is promising if sufficiently small relative part density differences in PBF-manufactured parts can be measured.

In this study, the feasibility of ECT to measure relative part density variations owing to defects caused by the PBF process is evaluated. The prerequisite is that the electrical conductivity which can be measured by ECT is sufficiently correlated with the relative part density. To investigate this, parts made from AlSi10Mg and 316L stainless steel are manufactured on a PBF machine with varied process parameters to create different densities caused by lack of fusion and keyhole. The parts are subsequently measured using ECT and the results correlated with the relative part density.

#### **2. Materials and Methods**

#### *2.1. Part Production*

One cuboid part per scan speed with a size of 25 × <sup>30</sup> × 10 mm<sup>3</sup> was manufactured using a Concept Laser M2 PBF machine (Concept Laser GmbH, Lichtenfels, Germany) with the process parameters presented in Table 1. An additional cube per scan speed with a size of 10 × <sup>10</sup> × 10 mm3 was fabricated in close proximity to the cuboid parts to study the pore distribution and the melt pool shape. Gas atomized PBF powders by the Carpenter Technology Corporation were used with particle size distributions of 15–45 μm (316L) and 10–60 μm (AlSi10Mg). All parts were fabricated on a 1-mm thick support structure onto <sup>245</sup> × 245-mm2 build plates and afterwards removed by wire cutting.

**Table 1.** Powder bed fusion (PBF) process parameters.


#### *2.2. Part Characterization*

The relative part density of the cuboid parts was measured via the Archimedes method, utilizing an AE200 balance with the measuring unit AB33360 (Mettler Toledo Inc., Columbus, OH, USA). The cubes were cut perpendicular to the scan direction of the top layer, embedded in epoxy resin, ground using SiC grinding paper (320, 600 and 1200 grit sizes), and polished up to 0.5 μm using SiO2 suspension. Images showing the porosity in the cross sections were taken at 50× magnification using a DM6 optical microscope (Leica Microsystems GmbH, Wetzlar, Germany). To reveal the melt pool boundaries, the 316L parts were etched in V2A etchant at 60 ◦C for 60 s, and the AlSi10Mg parts were etched in NaOH at room temperature for 12 s. The melt pools were subsequently characterized using the aforementioned optical microscope.

#### *2.3. Eddy Current Testing*

#### 2.3.1. Measurement Principle

The physical theory of ECT is explained by Maxwell's equations [26], which are not comprehensively discussed here. The simplified principle is explained using Figure 1a as follows.

**Figure 1.** (**a**) Eddy current testing (ECT) measurement principle. (**b**) Impedance plane representation. Adapted from Hippert [25].

A coil is excited with an alternating current with predefined amplitude and frequency *f* , which generates a time-varying primary magnetic field around it. In proximity to conductive material, the primary magnetic field induces eddy currents in the material. The eddy currents create a secondary magnetic field, which opposes the primary magnetic field that alters the impedance of the coil. Discontinuities of the electrical conductivity *σ* and magnetic permeability *μ* in the material triggered by defects such as cracks affect the eddy currents and the secondary field. The impedance change of the coil owing to the secondary magnetic field is measured and evaluated to characterize the material discontinuity. The impedance *Z* of the coil is calculated as:

$$Z = \frac{V}{I} = R + iX = R + i\omega L \tag{1}$$

where *V*, *I*, *R*, *X*, *ω*, and *L* represent the voltage across the coil, current in the coil, coil resistance, reactance, angular frequency and coil inductance, respectively [25]. The impedance is typically visualized in a normalized form relative to the impedance in air, as presented in Figure 1b. Reducing the distance between the coil and the conductive material leads to a signal transition from the air point to the material point along the lift-off direction. The location of the material point in the impedance plane changes as a function of √*aωσμ*, where *a*, *ω*, *σ*, and *μ* denote the coil radius, angular frequency, electrical conductivity, and magnetic permeability of the material, respectively. The red dots moving from the air point along the blue curve presented in Figure 1b represent material points of different alloys. Signal responses to defects such as cracks or changes in electrical conductivity are identified by characteristic phase angles in the impedance plane, which differ from the phase angle of a lift-off variation, as presented in Figure 1b. By rotating the signals, i.e., adjusting the phase angle in the impedance plane for a given material, undesired alterations in lift-off during ECT can be shifted to the x-component of the signal in the impedance plane. Therefore, the y-component of the signal in the impedance plane represents the lift-off independent signal response owing to the property of interest. The principle is explained comprehensively in the book of Udpa et al. [27].

#### 2.3.2. Measurement Equipment and Experimental Setup

A standard UPEC tester made by the Sensima Inspection SARL was adopted for the ECT, as presented in Figure 2a. The selected sensor was a ferrite rod coil sensor with a 3-mm diameter (*L* = 47 μH) operated in absolute mode. Absolute mode means that the measured signal is simply the value of the coil impedance itself [26]. The sensor was connected to the UPEC tester in a bridge configuration with an identical coil for balancing, including two 50-Ω resistors. The standard penetration depth *δ* is defined as the depth at

which the eddy current density decreases to approximately 37% of its surface value [16]. It is calculated as:

$$\delta = \frac{1}{\sqrt{\pi f \sigma \mu}}\tag{2}$$

where *f* is the frequency of the excitation current, *σ* the electrical conductivity and *μ* = *μ*0*μ<sup>r</sup>* the magnetic permeability of the material, with *μ<sup>r</sup>* being the relative magnetic permeability and *<sup>μ</sup>*<sup>0</sup> = 1.256 × <sup>10</sup><sup>6</sup> H/m being the magnetic permeability in vacuum [26]. An excitation frequency of *f* = 201.6 kHz was set to ensure a sufficiently high penetration depth for both materials used. The penetration depths for 316L and AlSi10Mg, which were calculated according to Equation (2) are presented in Table 2.

**Table 2.** Calculated standard penetration depths for 316L and AlSi10Mg. \* assumed because Aluminum alloys are paramagnetic [26].


The system was mounted onto a X-Y table laboratory test bench illustrated in Figure 2b. Linear encoders with a resolution of 0.1 mm were mounted on the axes and connected to the UPEC tester to map measured data to the sensor position during an acquisition. The cuboid parts were clamped onto the test bench as presented in Figure 2b to ensure a constant lift-off of 0.5 mm, which is the distance between the sensor and part surface. The as-built parts were orientated with the final layer created in the PBF process facing the sensor. Two-dimensional images were obtained by performing a raster scan with a pitch in the y-direction of 0.5 mm on the test bench guiding the sensor over the parts. Prior to the experiments, the lift-off phase angle in the impedance plane was determined for both materials by measuring one of the respective parts with different lift-offs. Accordingly, counter clockwise phase rotation angles of 69◦ and 79◦ for 316L and AlSi10Mg were obtained, respectively. The respective phase rotation filter was applied to the ECT data, and the absolute value of the lift-off independent signal component was analyzed, which is named rotated signal in the following chapters.

**Figure 2.** Measurement setup used for ECT. (**a**) Standard UPEC tester of Sensima Inspection SARL. (**b**) X-Y table laboratory test bench.

#### **3. Results**

#### *3.1. Relative Part Density*

To assess the feasibility of ECT in measuring the relative density of PBF-manufactued parts, process parameters (Table 1) were chosen to cover a wide range of part densities and to include the primary causes of porosity in the PBF process. Figure 3 presents the relative

density of the cuboid parts manufactured from AlSi10Mg and 316L, as a function of the scan speed.

**Figure 3.** Relative part density of parts manufactured from AlSi10Mg and 316L powder using varied scan speeds. The error bars depict the standard deviations of three density measurements per part. The micrograph and melt pool images were taken from x-z cross sections of cubes (10 <sup>×</sup> <sup>10</sup> <sup>×</sup> 10 mm3) manufactured in close proximity to the parts on the build plate, using the same process parameters.

The variation of the scan speed yields relative part densities covering a range of 89–99.5%. According to the widely used definition of the volumetric energy density by Stoffregen et al. [28], the energy input into the melt pool is inversely related to the scan speed. By adjusting the scan speed, the resulting relative density of the part can be controlled. In the process region, where insufficient energy input triggers lack of fusion, increasing the scan speed decreases the relative part density, which is consistent with the data presented in Figure 3. The micrograph images presented at the highest scan speeds in Figure 3 exhibit several irregularly shaped pores. These pores are characteristic for lack of fusion as studied extensively in the literature [22,29–32]. The lack of fusion is primarily triggered by the insufficient penetration of the melt pool into the previous layer as determined in different studies [33–35]. At the other end of the process window, low scan speeds yield an increased energy input into the melt pool. Consequently, the temperature of the melt pool at the center of the laser beam can reach the boiling temperature of the material, which substantially increases the amount of material evaporation and triggers the formation of a keyhole-shaped melt pool, as demonstrated by King et al. [36]. In the keyhole region of the process window, the collapse of the keyhole can lead to the formation of entrapped vapor, which causes keyhole porosity in the solidified material [36]. The micrograph images presented at the lowest scan speed in Figure 3 exhibit an increased amount of keyhole porosity, which was confirmed by melt pool shape analysis. Exemplaric images of the melt pool shapes in the different regions of the process window are presented in Figure 3. For most industrial use cases, PBF process windows are experimentally obtained to ensure dense parts; hence, the keyhole formation and lack of fusion are

circumvented via the appropriate process parameter selection. Nevertheless, geometrical features of the parts, such as overhang areas, can lead to keyhole porosity owing to the local overheating of the material [37] while process influences, such as smoke obscuring the laser beam, can cause lack of fusion porosity [38]. Hence, relative part density monitoring systems for PBF must at minimum be able to detect porosity coming from these causes.

#### *3.2. Eddy Current Testing*

The 2D image obtained from measuring the 10 cuboid parts made from 316L using ECT is illustrated in Figure 4. The positions represented on the x- and y-axes reflect the position of the sensor during the raster scan. The signal weakening that is visible at the edge of the parts is owing to the edge effect, which has been extensively studied in the literature on ECT [39–41]. The size of the edge effect can be reduced, e.g., by adjusting the sensor design [41]; however, this is not the focus of this work.

**Figure 4.** Image obtained from the 2D scan of the 316L parts. The data contain the rotated signal mapped to the X and Y positions of the sensor during the raster scan, as described in Section 2.3. Below each part, the part description and relative density are presented. Non-significant differences between mean rotated signals of samples are indicated by grouping the respective parts. One sample used for the statistical analysis obtained from the central region of the part 2 <sup>×</sup> 5 mm<sup>2</sup> (X <sup>×</sup> Y) is highlighted with a red rectangle on part S10.

Therefore, the following analyses are focused on the values of the rotated signal in the central region of the parts, where there is no influence exerted by the edges. This was ensured by measuring the size of the edge effect for the specific materials and making the parts sufficiently large. Samples of *n* = 209 individual measurements per part were selected from an area of 2 × 5 mm<sup>2</sup> (X × Y) at the center of each part. The corresponding area is highlighted with a red rectangle on part S10 in Figure 4. To determine statistically significant differences between sample means, Welch's analysis of variance and the Games– Howell post hoc test were applied.

The results of the statistical analysis are summarized in Table 3, which presents the p-values of the pairwise multiple comparisons between samples S1–S10 using the Games– Howell post hoc test. *p* < 0.05 is considered statistically significant. Most of the pairwise comparisons are statistically significant, which means that the respective parts can be statistically significantly distinguished from each other by the rotated signal. The relative density *ρ<sup>r</sup>* of the samples is reported alongside the sample description in Table 3. Even parts with small differences in relative density, such as S2 and S3, with a difference in relative density of 0.05%, can be statistically significantly distinguished by the rotated signal (*p* < 0.01). Non-significant sample differences, i.e., pairwise comparisons of samples with *p* ≥ 0.05, are indicated by grouping the respective parts in Figure 4. The parts of each group have differences in relative density smaller than 0.2%. Although S3 has a similar relative density as the parts in Group 1, the rotated signal is significantly smaller

in the central region. This is probably attributed to the limitations of the Archimedes density measurement, which only provides the relative density of the entire part, but not of the near-surface volume fraction in the center of the part, which is measured by ECT. The relative density of the entire part is not necessarily equal to the relative density in the near-surface region owing to a potential inhomogeneous pore distribution within PBF-manufactured parts, as determined by Carlton et al. [22].

**Table 3.** Results of the pairwise multiple comparisons using the Games–Howell post hoc test based on Welch's analysis of variance (*F*(9, 844) = 59847, *<sup>p</sup>* <sup>&</sup>lt; 0.01). The samples with sample size *<sup>n</sup>* <sup>=</sup> 209 were obtained from a 2 <sup>×</sup> 5-mm2 (X <sup>×</sup> Y) region in the center of each of the 10 parts (316L). \*\* *p* < 0.01, \* *p* < 0.05, *ns* not significant.


The 2D image obtained from measuring the 10 cuboid AlSi10Mg parts using ECT is presented in Figure 5. The same statistical analysis used for the 316L parts was conducted on the AlSi10Mg parts, and the results are summarized in Table 4. Similar to the 316L parts, most of the AlSi10Mg parts can be statistically significantly distinguished from each other by the rotated signal. The parts in each group have relative density variations smaller than 0.1%. However, the differences in relative density between part A3, A4, and A5 are also smaller than 0.1%, and these parts can be statistically significantly distinguished from each other by the rotated signal. As previously discussed, this is probably attributed to the different fractions of the part volume measured by the Archimedes density measurement and ECT. Hence, it is inferred that parts with small differences in relative density within the near-surface region can be statistically significantly distinguished by the rotated signal obtained from ECT.

The samples containing *n* = 209 individual measurements from the aforementioned area of 2 × 5 mm2 (X × Y) at the center of each part were used to analyze the correlation between the rotated signal and the relative density of the 316L and AlSi10Mg parts. In Figure 6, the correlation plots for 316L (a) and AlSi10Mg (b) are presented. The correlation is strong and significant for both materials with Pearson correlation coefficients of *r*(8) = 0.998, *p* < 0.001 (316L) and *r*(8) = 0.992, *p* < 0.001 (AlSi10Mg), respectively. Based on the theory of Dodd et al. [42], the impedance of the coil solely depends on the lift-off and electrical conductivity of the material for a fixed magnetic permeability, coil size, and excitation frequency, as given in the experiments. The influence of lift-off was eliminated from the data by phase rotation, such that the presented rotated signal primarily depends on the electrical conductivity of the material. Therefore, by measuring the electrical conductivity of a part using ECT, its relative density can be determined using alloy-specific correlation curves, equal to those presented in Figure 6. These correlation curves serve the calibration, i.e., converting the respective rotated signal to relative density. The correlation between the electrical conductivity and relative part density has already be demonstrated in the literature for metal foams [43,44], as well as the PBF-manufactured parts with internal cavities [25,45]. However, the correlations presented in this work are based on PBF-manufactured parts with relative density variations caused by introducing porosity owing to the two primary causes in PBF, which are lack of fusion and keyhole [3]. Hence, the data represent more realistic conditions for the PBF process.

**Figure 5.** Image obtained from the 2D scan of the AlSi10Mg parts. The data contain the rotated signal mapped to the X and Y position of the sensor during the raster scan as described in Section 2.3. Below each part, the part description and relative density are presented. Non-significant differences between mean rotated signals of samples are indicated by grouping the respective parts.

**Table 4.** Results of the pairwise multiple comparisons via the Games–Howell post hoc test based on Welch's analysis of variance (*F*(9, 845) = 18760, *<sup>p</sup>* <sup>&</sup>lt; 0.01). The samples with sample size *<sup>n</sup>* <sup>=</sup> 209 were obtained from a 2 <sup>×</sup> 5-mm<sup>2</sup> (X <sup>×</sup> Y) region in the center of each of the 10 parts (AlSi10Mg). \*\* *p* < 0.01, \* *p* < 0.05, *ns* not significant.


**Figure 6.** (**a**) Correlation of the rotated signal and the relative part density of 316L parts. (**b**) Correlation of the rotated signal and the relative part density of AlSi10Mg parts. The ECT data presented is extracted from a 2 <sup>×</sup> 5-mm2 (X <sup>×</sup> Y) region in the center of each part to exclude the edge effect. The error bars depict the standard deviation of the rotated signal across the extracted area (horizontal) and the standard deviation of three density measurements per part (vertical). The curve was fitted to the given data via the least squares method.

#### **4. Discussion**

In this study, part densities were measured using the Archimedes principle, which provides the relative part density averaged across the entire volume of the part. ECT measurements were performed on the last layers of the parts, and only the central region was considered for the correlation analysis to eliminate the influence of the edge effect. The pore distribution within PBF-manufactured parts is not homogeneous [22]. Therefore, the relative density of the entire part measured by the Archimedes principle does not necessarily accurately represent the actual relative density in the near-surface volume fraction measured by ECT. Hence, it can be assumed that a large fraction of the signal variance indicated by the standard deviations of the rotated signal presented in Figure 6 is owing to actual small relative density differences in the parts. Accordingly, only a small fraction of this signal variance is caused by limitations of the ECT system itself, which could solely be verified by comparing relative density and ECT data obtained from the same fraction of the part volume.

To assess the limitations of the ECT system, the uncertainty of the determined relative density via ECT due to the instrument noise *UI* is calculated based on the principle of the expanded uncertainty explained in the Guide to the Expression of Uncertainty in Measurement (GUM) [46] as:

$$
\Omega I\_I = k u\_I \tag{3}
$$

where *k* is the coverage factor and *uI* is the standard uncertainty. A coverage factor *k* = 3 is selected, which corresponds to a confidence level of 99.7% given the sampling distribution of the sample mean is normal. The sampling distribution of the mean is the distribution of the mean as a random variable derived from random samples with the size n. According to the central limit theorem [47], normality of the sampling distribution of the mean can be assumed, because of the sufficiently large sample size *n* = 209 per part measured. The standard uncertainty *uI* owing to the instrument noise is calculated as:

$$
\mu\_I = \frac{\sigma \eta}{\sqrt{n}} \tag{4}
$$

where *σ<sup>I</sup>* is the standard deviation of the instrument noise and n is the sample size, which is *n* = 209 in this study. Equations (3) and (4) are combined, and the unit of *UI* is converted to % relative density by multiplying it with sensitivity b, which is the slope of the respective least-square fitted curve presented in Figure 6, as:

$$
\hbar L\_I = k b \frac{\sigma\_I}{\sqrt{n}} \tag{5}
$$

The results of the uncertainty calculation are presented in Table 5. The uncertainty in the determined relative density via ECT due to the instrument noise *UI* is 0.02% (316L) and 0.06% (AlSi10Mg), which indicates that small differences in average relative part density can be measured at high confidence levels.

**Table 5.** Estimation of the uncertainty of the determined relative density due to the instrument noise *UI*.


Note that the error bars in Figure 6 are significantly larger than these estimated uncertainties as they represent the standard deviations of the observed signals, which include fluctuations due to inhomogeneities, e.g., local density differences, in the material itself. Furthermore, the aforementioned standard deviations simply describe the data variability within the actual sample, whereas the calculated uncertainty *UI* refers to the accuracy with which the mean value of each sample can be determined. The following remarks have to be considered while interpreting the results of this study. Standard instrument settings were adopted, that means that by optimizing parameters, such as gains, the sensitivity can be further increased. Moreover, the sensitivity can be improved by reducing the lift-off and applying more sophisticated signal processing methods, as well as an improved sensor design. Hence, this study demonstrates that such an ECT system mounted onto the recoater of a PBF-machine has the potential to evolve into a effective technology for layer-wise measuring the relative density of PBF-manufactured parts.

#### **5. Conclusions**

This study investigates the feasibility of measuring the relative part density of PBFmanufactured parts by ECT. Parts made from AlSi10Mg and 316L were manufactured with different process parameters yielding different densities. The relative part density differences were triggered by the two primary reasons for porosity in PBF, which are lack of fusion and keyhole. The parts were measured by ECT, and the results were correlated with the relative part density.

The ECT signal component, which mainly contains the electrical conductivity of the parts is strongly and significantly correlated with the relative part density for both 316L (*r*(8) = 0.998, *p* < 0.001) and AlSi10Mg (*r*(8) = 0.992, *p* < 0.001). Considering that the measured relative density is an averaged relative density across the entire part volume, and that the ECT data were obtained on the final layers, the correlation between the relative part density and the ECT signal is excellent. The sensitivity of the system can be further increased by reducing the lift-off, applying advanced signal processing methods, and adopting an improved sensor design.

This study presents a pathway for directly layer-wise measuring relative part density during the PBF process using an ECT system mounted on the recoater of a PBF-machine. Because the adopted ECT system is a compliant nondestructive testing instrument, it can furthermore serve the direct qualification and certification of PBF-manufactured parts. By measuring some additionally introduced test geometries to a build job, the system can also be used to assess the process window stability or to monitor the machine condition. Compared to monitoring techniques such as melt pool monitoring, where it is challenging to translate the large amount of generated data to relevant part properties, ECT can provide relevant and compliant part and process information obtained from direct measurements during the PBF process.

**Author Contributions:** Conceptualization, M.A.S. and A.B.S.; methodology, M.A.S., A.B.S., M.L., G.S., B.R.; formal analysis, M.A.S.; investigation, M.A.S., V.H.L.; resources, K.W.; data curation, M.A.S.; writing—original draft preparation, M.A.S.; writing—review and editing, M.A.S., A.B.S., G.S., K.W.; visualization, M.A.S.; supervision, K.W.; project administration, M.A.S.; funding acquisition, A.B.S., B.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** Open Access funding provided by ETH Zurich. The authors like to thank Innosuisse—Swiss Innovation Agency for co-financing the investigations within the frame of innovation project 33657.1.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available from the corresponding author on reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **Process Induced Preheating in Laser Powder Bed Fusion Monitored by Thermography and Its Influence on the Microstructure of 316L Stainless Steel Parts**

**Gunther Mohr 1,2,\*, Konstantin Sommer 1,3, Tim Knobloch 1,2, Simon J. Altenburg 1, Sebastian Recknagel 1, Dirk Bettge <sup>1</sup> and Kai Hilgenberg <sup>1</sup>**


**Abstract:** Undetected and undesired microstructural variations in components produced by laser powder bed fusion are a major challenge, especially for safety-critical components. In this study, an in-depth analysis of the microstructural features of 316L specimens produced by laser powder bed fusion at different levels of volumetric energy density and different levels of inter layer time is reported. The study has been conducted on specimens with an application relevant build height (>100 mm). Furthermore, the evolution of the intrinsic preheating temperature during the build-up of specimens was monitored using a thermographic in-situ monitoring set-up. By applying recently determined emissivity values of 316L powder layers, real temperatures could be quantified. Heat accumulation led to preheating temperatures of up to about 600 ◦C. Significant differences in the preheating temperatures were discussed with respect to the individual process parameter combinations, including the build height. A strong effect of the inter layer time on the heat accumulation was observed. A shorter inter layer time resulted in an increase of the preheating temperature by more than a factor of 2 in the upper part of the specimens compared to longer inter layer times. This, in turn, resulted in heterogeneity of the microstructure and differences in material properties within individual specimens. The resulting differences in the microstructure were analyzed using electron back scatter diffraction and scanning electron microscopy. Results from chemical analysis as well as electron back scatter diffraction measurements indicated stable conditions in terms of chemical alloy composition and austenite phase content for the used set of parameter combinations. However, an increase of the average grain size by more than a factor of 2.5 could be revealed within individual specimens. Additionally, differences in feature size of the solidification cellular substructure were examined and a trend of increasing cell sizes was observed. This trend was attributed to differences in solidification rate and thermal gradients induced by differences in scanning velocity and preheating temperature. A change of the thermal history due to intrinsic preheating could be identified as the main cause of this heterogeneity. It was induced by critical combinations of the energy input and differences in heat transfer conditions by variations of the inter layer time. The microstructural variations were directly correlated to differences in hardness.

**Keywords:** additive manufacturing; laser powder bed fusion; selective laser melting; laser beam melting; in-situ process monitoring; thermography; heat accumulation; inter layer time; cellular substructure

#### **1. Introduction**

Additive manufacturing (AM) technologies provide promising advantages for the production of highly individual and complex structures, mass customization, the integra-

**Citation:** Mohr, G.; Sommer, K.; Knobloch, T.; Altenburg, S.J.; Recknagel, S.; Bettge, D.; Hilgenberg, K. Process Induced Preheating in Laser Powder Bed Fusion Monitored by Thermography and Its Influence on the Microstructure of 316L Stainless Steel Parts. *Metals* **2021**, *11*, 1063. https://doi.org/10.3390/met 11071063

Academic Editor: Sergey N. Grigoriev

Received: 7 June 2021 Accepted: 29 June 2021 Published: 1 July 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

tion of functional designs, and the reduction of lead times [1,2]. The working principles of various metallic AM processes are described, e.g., by DebRoy et al. [3]. Although laser powder bed fusion (L-PBF) is the most prevalent AM technology for metal part production [4], the homogeneity of the material produced is still problematic. Inhomogeneity of the microstructure, defect density, and resulting mechanical properties within parts or in comparison of different parts have been alluded by several authors [3,5–7]. Microstructural variations in AM components are a major challenge, especially for safety-critical components [6,8,9].

A high degree of freedom in design in L-PBF offers the chance to produce complex shaped geometries. However, the geometry itself can influence the thermal history of a part during manufacturing as it might change the conditions of heat dissipation [10–12]. A detrimental change of the heat conduction through the part towards the base plate, as well as a significant change of the inter layer time (ILT), can lead to severe heat accumulation of the part or areas of local overheating. This, in turn, results in deviations of the thermal history and eventually affects part quality [5,10,13]. In addition to the geometry, there are many other influencing factors on the thermal history of a L-PBF component. These comprise, for instance, processing parameters, scanning strategies, support design, or ratio of area exploitation [3,5,11,12]. The thermal history of an L-PBF process is an important factor for the development of the microstructure, as it is influenced by the transient temperature fields during manufacturing. It is well known that variations of temperature gradients can significantly affect the microstructural development. Lower cooling rates are generally expected to develop a coarser microstructure than higher cooling rates [1,14].

The microstructure of 316L processed by L-PBF typical shows features that can be observed over a broad range of length scales. The features include melt pool boundaries, grains and sub-grains, cellular substructures of grains, segregations, dislocation networks at the boundaries of cell structures, and nanoscale precipitations [15–18]. The shape of melt pool boundaries is influenced by the scanning strategy and process parameters. Their shape and penetration depth strongly depend on the melting mode [19]. Patel und Vlasea [20] reported on the occurrence of deep penetration mode welding (keyhole mode welding) and transition mode welding over a broad range of process parameters in L-PBF processing of 316L. According to Krakhmalev et al. [16], the grains consist of cellular substructures due to high cooling rates, whereby the cells grow epitaxially, starting at melt pool boundaries. The cellular substructures grow competitively based on their crystallographic orientation and the local thermal gradients inside the melt pool [16]. The growth of cellular substructures in 316L processed by L-PBF typically leads to segregation of Mn, Mo, and Cr and dislocation networks at cell boundaries [15,16]. The features of these cellular substructures, namely, the cell size and the occurrence of micro-segregations, strongly depend on the local directional solidification conditions [9]. Pinomaa et al. [9] recently quantified the influence of the local thermal gradient and local melt pool solidification rate on these features as well as on the mode of growth by conducting phase field simulations.

David et al. [21] investigated the effect of rapid solidification on the weld metal microstructures in different stainless steel compositions in the late 1980s. They integrated the influence of the cooling rate into the Schaeffler diagram [21]. It can be derived from their work that 316 stainless steel solidifies as fully austenitic at cooling rates above 0.28 × <sup>10</sup><sup>6</sup> <sup>K</sup>·s<sup>−</sup>1. Due to the lower austenite stabilizing carbon content in 316L stainless steel, these cooling rates might shift to slightly higher values for 316L. Bajaj et al. [22] conducted an intense review on steels in L-PBF and direct energy deposition. They reported fully austenitic phase for 316L when processed by L-PBF. Krakhmalev et al. [16] also mentioned a fully austenitic phase with some very exceptional cases of the occurrence of a ferritic phase.

Additionally, the occurrence of spherical nano-sized oxide inclusions has been reported for 316L produced by L-PBF [16]. Lou et al. [23] investigated the influence of these Si- and Mn-rich oxide inclusions. They concluded that these oxide inclusions can be responsible for the initiation of micro-voids with detrimental effects on impact toughness. They compared the measured impact toughness with values from literature for specimens produced by powder metallurgy route and wrought material, revealing distinct beneficial effects when the oxygen content was below 0.02%.

In addition to these crystallographic features of the microstructure, internal defects such as delamination, cracks, and pores can occur [24]. Pores can be categorized into so-called lack-of-fusion defects and gas porosity [25]. Lack of fusion defects are irregularlyshaped pseudo pores, which essentially are cavities resulting from insufficient melting and insufficient material cohesion due to deficient melt pool dimensions or inadequate choice of processing parameters such as the hatch distance between single melt tracks [25,26]. A main source of spherical gas porosity can be found in detached and entrapped vapor bubbles of the vapor capillary in an instable keyhole welding mode [25,27].

The possibility to influence the temperature gradients occurring in the process has been shown in different studies. On the one hand, there are approaches to tailor a microstructure during the L-PBF process by adjusted sets of processing parameters [28,29] or modifications of the laser beam shape and intensity profile [30,31]. On the other hand, there are approaches to decrease residual stresses or crack susceptibility by, e.g., remelting or platform preheating adjustments [32,33]. These approaches have in common the aim to purposely influence the initial resulting microstructure of an L-PBF specimen or component either throughout the entire geometry or within particular regions. However, there are further situations where variations of microstructures in L-PBF processes should be considered. This includes unplanned microstructural variations that are induced due to heat accumulation during the process.

The accumulation of heat during the build-up of an L-PBF part essentially alters the preheating condition at the surface to be coated by the new powder layer which is subsequently exposed by laser radiation. Therefore, the initial thermal conditions prior to the exposure by laser radiation are altered. As a result, the thermal gradients during melting and solidification might change with varying initial preheating temperature. A significant change of the preheating temperature of the part can alter the melt pool dimensions and their solidification conditions [5,34]. As pointed out by Krakhmalev et al. [16], the cellular mode of solidification in 316L processed by L-PBF occurs at high solidification rates and steep thermal gradients. The resulting microstructural feature sizes such as cell spacing depend on these conditions [16]. They might change when the preheating temperature increases due to heat accumulation. Depending on the magnitude of the variation in preheating condition, the induced variations on the microstructure can be strong enough to affect the mechanical properties of a component [5]. In addition to potential changes of the melt pool shape and the melt pool dimensions, as well as potential changes of crystallographic features, an increase of the preheating temperature may also be able to shift the melting mode to an unstable region with propensity to develop detrimental keyhole porosity [5].

The authors [5] investigated process conditions where heat accumulation was provoked to occur during the L-PBF fabrication of simple cuboid specimens of 316L stainless steel at application relevant build heights, i.e., the specimens height was bigger than 100 mm. Using a mid-wavelength infrared thermography camera as an in-situ thermal monitoring device, significant differences in cooling behavior were revealed. Specimens were produced applying three distinct ILT and three distinct volumetric energy densities (VED). The build height was also identified as an affecting factor. The authors correlated the differences in cooling conditions with differences in apparent sub-grain sizes measured by light microscopy, melt pool depths, and hardness values. To refine the knowledge of process-property-relationship and to prove the relationships measured by light microscopy, a more detailed analysis of the influence of in-situ heat accumulation on the microstructure of 316L components is required. Therefore, this study pursues the examinations of the same specimens used in [5] and investigates the microstructure by means of electron back scattered diffraction (EBSD) in greater detail. In addition, scanning electron microscopy (SEM) is used to compare the feature size of the cellular substructure. The alloy composition

of the produced specimens as well as a potential oxygen intake is measured by different methods of chemical analysis. By applying recently conducted temperature adjustments of the infrared (IR) monitoring set-up [35], real temperatures of the powder surfaces could be quantified. The layer-wise increase of the preheating temperatures of the specimens was measured in-situ over the entire build process of the specimens. The results are discussed with respect to recent publications. Results of hardness measurements were taken from [5].

Although there have been extensive investigations on L-PBF of 316L, a quantification of process-induced preheating of the specimens during manufacturing and its correlation to changes in crystallographic features is currently missing. Information about the magnitude of microstructural changes induced by critical but still realistic process conditions is important. It will help to improve the evaluation of a real part of the production and the comparability of test coupons that are manufactured under certain processing conditions. Effects of processing parameters such as scanning velocity or laser power have been studied extensively. However, the build height and the ILT are often not considered. Their influence may not be considered significant in the case of typical 10 mm cubic specimens or in the case of high ratios of area exploitation within the powder bed. They may become an affecting factor in the case of complex real part geometries with varying area exploitations over the build height. Additionally, the current trends in the development of new L-PBF machines (e.g., multi laser machines) are expected to decrease the ILT, which increases the need for reliable data about potential microstructural heterogeneity.

#### **2. Materials and Methods**

#### *2.1. Material and Specimen Manufacturing by L-PBF*

In this section, the key facts about the L-PBF processing conditions and specimens are mentioned. Details were published in [5] where the same set of specimens was examined. Upstanding cuboid-shaped specimens of the dimensions (13 × <sup>20</sup> × 114.5) mm3 were manufactured on a commercial L-PBF single laser system of type SLM280HL (SLM Solutions Group AG, Lübeck, Germany) using a commercial 316L stainless steel powder. Table 1 shows the chemical composition of the powder material according to supplier's information. Figure 1 depicts the geometry of the specimens and contains a schematic of the applied bidirectional scanning strategy with 90◦ rotation between layers. It also highlights the parts of the specimen that were taken for the deeper analysis in this study in grey color. These were basically the volumes of the lower 12.5 mm (including excess material for part removal) and of the upper 10 mm of each specimen.


**Table 1.** Chemical composition of the 316L raw powder material according to supplier's information and the respective min. and max. values as per the material specification by DIN EN 10088-3 [36]. The figures express mass fractions in %.

The specimens were manufactured at three distinct ILT and at each ILT at three distinct levels of VED by varying the scanning velocity *v*s, i.e., nine different types of specimens were built. Each specimen type was built up twice, as stated in [5]. The other manufacturing parameters were kept constant. All process parameters are summarized in Table 2.

**Figure 1.** Specimens' geometry. Grey volumes were designated for microstructure analysis and were cut according to the preparation planes in the schematic. Adapted from ref. [5].



The ILT of layer number *n* was defined in [5] and is explained by Equation (1).

ILTlayer *<sup>n</sup>* = time for powder recoating + time for laser exposing in layer *n* (1)

The ILT values for specimen production were chosen according to calculated values from a real part production as compared in [5]. The basis VED parameters represent parameters for the machine and material recommend by the machine's manufacturer but with a simplified scanning strategy. Low VED and high VED parameters were chosen to broaden the energy input, adjusting the VED by plus 25% and minus 25%.

Table 3 gives an overview of the combinations of variable parameters used for specimen production. It also contains the applied methods of analysis, which are described in the following subsections.


**Table 3.** Matrix of parameter combinations and methods of analysis.

The specimens were heat-treated under argon gas atmosphere before removal from the base plate. The heat treatment was conducted at 450 ◦C for 4 h after the process to relieve residual stresses without changing the as-built microstructure.

#### *2.2. In-Situ Thermographic Monitoring and Temperature Analysis*

The production of the specimens was in-situ monitored using an off-axis infrared camera of type ImageIR8300 (InfraTech GmbH, Dresden, Germany), which was installed on top of the L-PBF system as schematically shown in Figure 2. The camera was calibrated by its vendor for black body radiation. A temperature adjustment was conducted by a determination of emissivity values of 316L powder layers and 316L L-PBF surfaces for the same set-up in previous work [35]. The camera was sensitive in the spectral range from 2 μm to 5.7 μm. The cooled InSb-focal-plane-array of the camera was of size 640 pixel × 512 pixel. The frame rate of the camera was 300 Hz for full frame. The measurements were conducted using a subframe image of 160 pixel × 200 pixel. The resulting spatial resolution in the field of view corresponded to approximately 420 μm/pixel. The subframe measurements were conducted at a frame rate of 600 Hz, and a bit resolution of 14 bits was used. The layer-wise recording was triggered by the first overall infrared signal rise above a predefined threshold value. Then, a predefined number of 40 bygone time steps were taken as start of the recording by using a circular buffer. The duration of the recording was set by the definition of a certain number of frames to acquire. Further details on the thermographic set-up can be found in [5,10], which show qualitative comparisons of the same thermographically gained process information using this set-up.

During the IR measurements of the processes, various internal black body calibration ranges of the camera were used to capture the IR data, since the relevant apparent temperature range succeeded the dynamic temperature range of a single calibration range. The change of the calibration ranges had to be done manually using the camera control software. The following black body calibration ranges were used at a converter resolution of 14 bit: 60 ◦C–200 ◦C at an integration time of 89 μs, 125 ◦C–300 ◦C at an integration time of 27 μs, 200 ◦C–400 ◦C at an integration time of 193 μs, and 300 ◦C–600 ◦C at an integration time of 45 μs. They are referred to the following abbreviation scheme: IR-CB 60–200 for the calibration range of 60 ◦C–200 ◦C. The conversion of the received IR signal values (apparent temperatures) into temperatures was conducted using a MATLAB (The Mathworks Inc., Natick, MA, USA) routine considering the experimentally determined apparent emissivity values of 316L powder from previous work [35]. For simplification, a constant apparent emissivity value was used over each respective calibration range, i.e., *ε* = 0.33 for IR-CB 60–200 and for IR-CB 125–300, *ε* = 0.43 for IR-CB 200–400 and for IR-CB 300–600. Additional information about the temperature adjustment and emissivity

determination using this set-up as well as some theoretical background on that matter can be found in [35].

**Figure 2.** Schematic of the off-axis thermographic monitoring. Reprinted from ref. [10].

In this study, the surface temperatures of the specimens before laser exposure were investigated using the IR camera. Therefore, uncorrected IR signals of an area of 11 pixels × 11 pixels in the manually selected center of each specimen were averaged and processed using a GNU Octave (open source software) routine. A peak detection was implemented to get comparable sampling times and related values of the preheating IR signals of each specimen for each layer. To this end, the slope of the averaged IR signals was derived and smoothed by using a moving average method. If the slope of the smoothed IR signal is rising above a predefined threshold, it describes the start of the scan process in that area and thereby the interval of interest. The affiliated IR signal value and the timestamp are extracted from the minimum of this interval. These values describe comparable states of each specimen's surface coated with a new powder layer right before the start of the laser exposure of the respective area. Additionally, if there is a temporary drop in the IR signal values the peak detection can be heavily disturbed. This applies, for instance, when the recoater is moving through the field of view during the IR signal recording. The recoating process is accidentally recorded in some cases when, e.g., the layer-wise recording time is too long after the IR camera has been triggered. In this case, the averaged IR signals are filtered beforehand by an optional recoating filter with manually predefined parameter settings. As a last step, the extracted IR value of the comparable state of the specimen is converted to a temperature, using the emissivity values mentioned above. This value is then defined as current preheating temperature of the respective specimen. The measurement uncertainty of the emissivity determination has to be considered [35].

#### *2.3. Analysis of Microstructure Using Electron Back Scatter Diffraction (EBSD)*

Electron back scatter diffraction (EBSD) measurements were performed, to investigate the grain structure and phases of the produced specimens. For the measurements, the part II cross sections (see separation plane 1 in Figure 1) were ground with 180, 320, 600, and 1200 grits emery papers and polished using clothes with 3 μm and 1 μm particle suspensions, followed by MasterMet-2 (Buehler, ITW Test & Measurement GmbH, Esslingen am Neckar, Germany) amorphous 0.02 μm colloidal silica suspension. The microscopic measurements were executed on a scanning electron microscope (SEM) Tescan VEGA 3 (TESCAN ORSAY HOLDING a.s., Brno-Kohoutovice, Czech Republic) equipped with an EBSD detector Nordlys (Oxford Instruments plc, Abingdon, England). For acquisition, indexing, and post-processing, the software Aztec 4.1 (Oxford instruments plc, Abingdon, England) was used. An area of 2.25 mm × 3 mm was measured for every cross section, using an acceleration voltage of 20 keV, a beam current of approximately 10 nA, a step size of 5 μm, and a pattern size of 168 × 128 pixels. The low-angle grain boundary (LAGB) criterion was set to 5◦ to discriminate distinct sub-grains. In addition, for grain discrimination, the high-angle grain boundary (HAGB) criterion was set to 15◦.

#### *2.4. Analysis of Cellular Substructures by Scanning Electron Microscopy (SEM)*

The investigation of cellular substructures within the grains was performed on the same cross sections after the EBSD measurements. The polished surfaces were etched with Bloech and Wedl II agent (50 mL H2O, 50 mL HCl, and 0.6 g K2S2O5) [37] to contrast the cellular substructure. The measurements were performed on a scanning electron microscope (SEM) Leo Gemini 1530VP (Leo Electron Microscopy Inc., New York, NY, USA) detecting back scattered electrons. Electrons of 20 keV energy were used.

SEM captures of these substructures were made at different locations of the crosssections, to qualitatively estimate the size distribution of the cells. Cells that grew parallel or close to parallel to the preparation plane were used for the measurement. The cell walls can be imaged due to the topographic effect (bright lines in Figure 3) after etching. The measurement was focused on the number of cell walls within a defined distance in the style of the well-known metallographic grain size measurements by a line intercept method as described in, e.g., DIN EN ISO 643 [38]. To this end, five lines per SEM image with 10 μm length were placed perpendicular to the cell walls which were cut parallel or close to parallel to the preparation plane. Then, the number of intersections with the cellular walls were counted. The number of intersections can be used for relative comparison of the cell size. The lower the number of intersections, the wider are the cells. Three different regions were investigated for each section. In addition, a quantitative estimation can also be derived by dividing the length of the lines by the counted number. Figure 3 depicts an example of the measuring procedure, also presenting the number of intersections with each individual line.

**Figure 3.** Example of SEM captures of cellular substructures used for estimation of their size distribution by a line intercept method. The numbers in the circles depict the number of intersections of the respective line.

Deng et al. [39] also used such a line intercept method to determine cell sizes of 316L. In contrast to the approach of this study, they applied the line intercept method to cells cut perpendicular to their growth direction. These cells, therefore, appeared in a honeycomb like structure, as visible in the left lower region of the SEM image in Figure 3.

However, the sensitivity to measurement errors seems to be higher in this case as compared to a line intercept measurement through the parallel cell walls. This is due to a minor effect of a potential tilt angle of the cross section induced by the mechanical preparation would have in the latter case. Pinomaa et al. [9] also measured cell sizes derived from simulations by line interception through parallel cell wall regions, as this was conducted in the present study.

#### *2.5. Analysis of Chemical Composition*

The mass fractions of the elements given in Table 1 and of oxygen were determined for selected specimens (see Table 3) using the measurement techniques listed in Table 4. The alloying elements Cr, Ni, Mn, and Mo were determined using X-ray fluorescence spectrometry. Two certified reference materials were used for calibration (ECRM 284-2 and ECRM 284-3, BAM, Berlin, Germany). Since this method is not sufficiently sensitive for each alloying element, traces of Si and P were determined using inductively coupled plasma optical emission spectrometry after decomposition of the material using microwave digestion. For the determination of the non-metals C, S, O, and N, element-analyzers were used, calibrated with different certified reference materials. The analysis was conducted using material of section III in the lower part and upper part of the specimen (see Figure 1). Oxygen measurements were conducted at two separate specimens manufactured under the same processing conditions also using material of section III of the respective parts.

**Table 4.** Measurement techniques used for precise determination of chemical composition for selected specimens.


#### **3. Results**

#### *3.1. Surface Temperatures*

The in-situ preheating temperature evolution over the build-up process of the specimens is depicted in three different diagrams (Figures 4–6), each showing the preheating temperature over the layer number at a fixed ILT level and different VED levels. In addition, Figure 7 displays the same plots for the basis VED at different ILT levels within one diagram for easier comparison. The captured IR signals were not exploitable for every parameter combination over the entire part due to the narrow band of the set calibration ranges of the IR camera as described in [35]. Only exploitable signals were converted into real temperatures and plotted in the diagrams. Hence, there are some missing parts within some of the curves. Especially, the lower temperature regions were often not resolved within the set calibration ranges. Therefore, considerable shares of the specimens produced with intermediate ILT and long ILT could not be resolved properly in their lower sections.

**Figure 4.** Temperature-layer-number-plots for short ILT. The orange sections highlight the layers of the specimen volumes used for deeper analysis as depicted in Figure 1. The colored bars show the IR calibration ranges (IR-CB) used in the respective layers. Missing parts of the curves (e.g., in the low VED specimen) are due to the narrow bands of the calibration ranges of the IR camera.

**Figure 5.** Temperature-layer-number-plots for intermediate ILT. The orange sections highlight the layers of the specimen volumes used for deeper analysis as depicted in Figure 1. The colored bars show the IR calibration ranges (IR-CB) used in the respective layers.

**Figure 6.** Temperature-layer-number-plots for long ILT. The orange sections highlight the layers of the specimen volumes used for deeper analysis as depicted in Figure 1. The colored bars show the IR calibration ranges (IR-CB) used in the respective layers.

**Figure 7.** Temperature-layer-number-plots for basis VED. The orange sections highlight the layers of the specimen volumes used for deeper analysis as depicted in Figure 1. Missing parts of the curves are due to the narrow bands of the calibration ranges of the IR camera.

#### *3.2. Grain Size Analysis*

The EBSD measurements revealed differences in HAGB grain sizes and LAGB subgrain sizes between the sections of the window of investigations. The mean LAGB sub-grain sizes and the mean HAGB grain sizes are depicted in Figures 8 and 9 for each combination of ILT and VED (see Table 3) and of the upper part and lower part volumes of investigation (see Figure 1). The corresponding inverse pole figure maps for the specimens' sections marked with capital letters in Figure 8 are shown in Figure 10.

**Figure 8.** Comparison of sub-grain sizes (LAGB 5◦) for each parameter combination. The capital letters correspond to the respective inverse pole figure maps in Figure 10.

**Figure 9.** Comparison of grain sizes (HAGB 15◦) for each parameter combination.

**Figure 10.** Inverse pole figure maps comparison with crystallographic orientation related to direction normal to the map plane. The capital letters correspond to the respective sub-grain sizes in Figure 8.

The measured grain size distribution is not Gaussian but follows a log-normal distribution. Hence, the mean and the standard deviation were calculated from logarithmic transformed measuring data. When retransformed, the standard deviation has to be considered multiplicatively, which results in asymmetric error bars with pronounced overlapping upper parts for the individual measuring points. Despite significant overlapping, the changes in the mean values are to be discussed. The mean values and standard deviations of the individual data points presented in Figures 8 and 9 are additionally given in Tables 5 and 6.


**Table 5.** LAGB sub-grain sizes.


**Table 6.** HAGB grain sizes.

#### *3.3. Cellular Substructure*

The SEM images revealed a cellular growth mode for all examined parameter combinations. The intersection counts as well as the calculated average cell size are depicted in Figure 11. Although there are huge overlapping areas of the deviation bars, two trends can be recognized from the results, as they appear consistently. First, the cellular size appears to be increased at the upper part of the specimens manufactured at short ILT for all VED levels. At the same time, no differences can be noticed between upper and lower part at longer ILT and standard VED. Second, the cell size increases with increasing VED (decreasing scanning velocity *v*s) irrespective of the build height. This can only be reported for the short ILT level, as for the other ILT levels only the standard VED was considered in this measurement. The average cell size within this investigation is between 0.52 μm and 0.76 μm.

**Figure 11.** Comparison of cell spacing intersection counts for different parameter combinations. The right y-axis corresponds to the calculation of the cell spacing.

#### *3.4. Chemical Composition*

The EBSD measurements showed no hint for phases other than austenite. The measured chemical composition of the examined specimens is depicted in Table 7.


**Table 7.** Chemical composition of selected specimens in weight %.

The measured chemical composition of the examined specimens was compared to the material specification listed in Table 1. In all cases, the chemical composition meets the specifications. The chemical composition of the lower part was compared to the chemical composition of the upper part for each specimen and for each chemical element. Considering the measurement uncertainty, no significant differences between the upper and lower part of each specimen can be recognized. In addition, no significant differences to the chemical composition of the powder can be recognized.

The results of the measurement of the oxygen content conducted at two separate specimens are depicted in Table 8.

**Table 8.** Oxygen content in weight %.


#### **4. Discussion**

*4.1. Surface Temperatures*

The preheating temperature plots reveal three clear trends. First, the preheating temperature increases over the entire build height of the specimens. This confirms similar results from previous work [5] and the work of Williams et al. [34]. As long as the preheating temperature rises over the build height, there is no equilibrium between the rate of heat input and the rate of heat dissipation [34]. Heat dissipates mainly by thermal conduction into the build and the base plate due to strong insulating effects of the surrounding powder [22]. Therefore, the heat dissipation is mainly governed by thermal conductivity and the geometry of the build. For a constant geometry and a given material, the heat dissipation via heat conduction can be shortened by reducing the time before the next energy input, i.e., by reducing the ILT.

This directly leads to the second trend observed in the plots: the increase of preheating temperature is significantly affected by a change of the time for heat dissipation through varying ILT. Shorter ILTs allow for a shorter time for heat dissipation resulting in increasing preheating temperatures. A massive heat accumulation is observable in the most extreme case (short ILT and high VED) of the parameter matrix, leading to temperatures of up to approximately 600 ◦C. In contrast, the preheating temperature in the least extreme case (long ILT and low VED) level was up to approximately 140 ◦C. The magnitude of this intrinsic preheating effect is material-specific due to material-specific thermal conductivity. It would be expected to be reduced for materials with higher thermal conductivity.

Third, the increase of preheating temperature also depends significantly on the energy input varied by the distinct processing parameters. This results in increased temperatures at a reduced scanning velocity. It is well known that the energy input is higher at slower scanning velocities resulting in higher specimen temperatures [40,41].

Oxidation layers may drastically change the emissivity of metallic surfaces, which is a well-known phenomenon [42]. Oxidation phenomena were argued to be responsible for drastic changes in emissivity values at temperatures above 580 ◦C in the previously conducted experiments for the determination of emissivities [35]. Furthermore, oxidationdriven tempering colors could be noticed for short ILT specimens, especially for those at basis VED and high VED [5]. Therefore, the interpretation of calculated temperatures above 580 ◦C should be considered very carefully in this study. However, there are two aspects that back the reliability of the measured temperature values despite oxidation of the specimen's bulk surface. First, oxidation thickness growth depends always on atmosphere, temperature and time [35]. The atmosphere can be assumed to be the same for all individual specimens of the different ILT levels, as they were produced within the same build process with a low oxygen content (below 0.1% [5]). The suspect temperatures are not far beyond the revealed detrimental temperature threshold of 580 ◦C. The time for oxidation of the recoated powder layer before the measurement signal extraction is comparably short, i.e., below 15 s in the case of the L-PBF process with short ILT. In comparison, Janssen [43] studied oxidation processes at austenitic stainless steel AISI 304 in air and noticed the start of slight yellow annealing colors by eye at 550 ◦C at 5 min holding time. In addition, the new recoated powder layer did not undergo the temperature cycle of the L-PBF bulk material. Therefore, it did not face very high temperatures prone to oxidation. Second, the relative comparison of the preheating temperatures of the distinct VED levels shows a constant ratio irrespective of the individual ILT. Hence, within the light of the given measurement uncertainty, the presented temperature values can be directly used for comparison. Potential oxidation is assumed to not have affected the emissivity of the powder surface significantly before the recording of the extracted IR signal.

#### *4.2. Grain Size Analysis*

Three clear trends can be derived from the measurements: First, HAGB grain sizes and LAGB sub-grain sizes show the same qualitative differences regarding VED, ILT and build height. Second, the grain sizes and, respectively, the sub-grain sizes increased with increasing VED for every ILT. Third, for every parameter combination, the upper part sections exhibit a higher grain size and sub-grain size as compared to the lower sections. However, this increase is small for long ILT and intermediate ILT compared to short ILT specimens. For the short ILT specimens, the difference in mean grain sizes, respectively, mean sub-grain sizes, can be higher than a factor of two, as can be seen for basis VED and high VED. The measured mean HAGB grain sizes as well as mean LAGB grain sizes are in the same order of magnitude as examined elsewhere.

In the previous publication [5], no significant difference in mean values of the subgrain sizes of the lower part sections and upper part sections of the short ILT specimens could be examined by the applied manual measurement via line interception of light microscopy images. This was obviously due to a very high degree of measurement uncertainty. An in-situ heat treatment during the process was proposed as a potential explanation. However, this proposition can now be clearly disproven by the EBSD results, as clear differences in the mean grain size and the mean sub-grain size between upper and lower part can be seen whenever the preheating temperature was also increased strongly. The average

preheating temperature of each specimen between layer 2140 and layer 2200, which is within the upper part sections, and the LAGB sub-grain sizes are depicted within the same diagram in Figure 12. This visualizes the high degree of correlation between the preheating temperature as a boundary condition for solidification and grain size development. The noticeable discrepancy between a comparatively high preheating temperature and still small mean grain size in the specimen of short ILT and low VED as compared to, e.g., the specimen of long ILT and high VED, should not be considered without referring to changes in melt pool depth as presented in [5]. The preheating temperature shows an effect on the development of the microstructure. The latter is also known to be strongly affected by the melt pool dimensions [3], which are comparatively small for the low VED value due to the higher scanning velocity [5]. Therefore, the temperature influence should be rather considered within the individual VED levels for direct comparison.

**Figure 12.** Comparison of LAGB sub-grain sizes and preheating temperatures for each parameter combination in the upper part sections. The preheating temperature values depict the average of the measured preheating temperature of the respective specimen between layer 2140 and 2200.

#### *4.3. Cellular Substructure*

The calculated average cell size is in the same order of magnitude as reported in other literature, where cell sizes in the range of 0.5 μm to 1 μm or 1.5 μm, depending on processing parameters, were measured [15,39,44,45]. Leicht et al. [46] presented slightly smaller cell sizes in a range of 0.36 μm to 0.58 μm.

Roehling et al. [30] described the propagation rate of the solid liquid interface being linked with the scanning velocity by its product with the cosine of the angle between the laser scanning direction and the solidification direction. Typical values are in the range of 0.012 m·s−<sup>1</sup> to 0.12 m·s−<sup>1</sup> and, therefore, significantly smaller than the scanning velocity *<sup>v</sup>*<sup>s</sup> [9]. These values can be estimated for scanning velocities of about 700 mm·s−<sup>1</sup> assuming an angle between the direction of the maximum heat flow and the build direction between 0◦ and 10◦, as supposed by DebRoy et al. [3]. Thermal gradients *G* are reported in the range from 104 <sup>K</sup>·m−<sup>1</sup> to 107 <sup>K</sup>·m−<sup>1</sup> and being rather at the top of this range in the case of L-PBF as compared to direct energy deposition [9]. Pinomaa et al. [9] conducted a phase field simulation of the rapid directional solidification of 316L and measured the cell sizes for different local melt pool solidification rates *R* and different thermal gradients *G*. They examined a clear cellular growth mode of solidification over a broad range of the typically reported thermal gradient ranges and solidification rates [9].

In the case of cellular growth mode, which also appeared in the examined specimens of the present study, a general trend of a decrease of the cellular size with increasing solidification rate as well as increasing thermal gradients could be revealed from the work of Pinomaa et al. [9]. Their 2D phase field model brought up cell sizes in the range of 0.64 μm to 4.1 μm for the pure cellular growth mode. When comparing the values of Figure 11 to their simulation results, the figures are again in the same order of magnitude for their higher *R* and different thermal gradients *G*. Qualitatively, the relationship between increasing cell size with decreasing thermal gradients tends to appear for the short ILT, suggesting that the increased preheating temperature (see Figure 4) decreased the thermal gradient of cooling. Additionally, at lower scanning velocities *v*s (higher VED) the cell size increased accordingly.

The good agreement to the simulation results, published in [9], seems to be surprising since the melt pool geometry is reported to have a huge impact on the heat and mass transfer within the melt pool [47,48]. Differences in melt pool depth were examined for the varying processing conditions in the previous study [5]. In addition, the solidification rate *R* as well as the local thermal gradient *G* vary over the cross section of the melt pool [30,47,48]. Yadroitsev et al. [49] have shown the sensitivity of the cell spacing to the scanning velocity and the location of measurement within single track melt pools. At a first glance, this would appear to complicate valid comparisons of cell size measurements as the selection of the measurement region within the cross sections might affect the result strongly. In fact, the measurement regions in the SEM images of the same cross section subjectively appeared to show huge variation in the cell size. This is assumed to be the reason for the comparably huge deviation bars in Figure 11, as similarly concluded by Leicht et al. [46]. However, the potential melt pool cross section areas to be investigated within the bulk of the specimens are limited to fragments of the lower part of the melt pool in this study. This is due the layer-wise remelting and overlapping of melt pools. Yadroitsev et al. [49] measured gradual increasing differences in cell spacing of up to a factor of 2 between upper and lower part of the melt pool. A comparison of the lower part and the middle section of the melt pool showed only a difference of a factor of 1.3. Therefore, it can be assumed that the variations in the measurable cell spacings are reduced due to remelting. Additionally, it is assumed that the primary solidification structures remain stable and are not affected significantly in any secondary heat cycle. This was also one of the critical model assumptions of the phase field simulation by Pinomaa et al. [9].

Deng et al. [39] conducted recently very fundamental investigations on the thermal stability of the cellular substructure which consists of dislocations. They hold 316L L-PBF specimens at elevated temperatures of 500 ◦C, 600 ◦C, and 700 ◦C for up to 150 h. No recrystallization was observed at these temperatures. They eliminated a lack of knowledge about the behavior of the dislocation network at elevated temperatures below the oftenreported dislocation dissolution temperatures above 850 ◦C [16]. The cellular substructure remains stable at 600 ◦C for up to 100 h. At 700 ◦C, the decomposition of the dislocation cells was already visible after a 10 h annealing. The dislocation cells showed a uniform growth along all directions at this heating condition. This growth was related to a rearrangement and coarsening of dislocation structures. It did not occur homogeneously over the entire cross section areas that were investigated. The growth proceeded very slightly when increasing the annealing time up to 150 h. The findings of Deng et al. [39] exclude a potential in-situ annealing effect as a reason for the measured differences in the cell spacing in this study. This was suggested as a potential reason for differences in hardness values in the previous study [5]. However, this does not apply since the measured preheating temperatures are well below the threshold of 700 ◦C. Therefore, the differences in the feature size of the cellular substructure of this study are assumed to completely develop during solidification. This also supports the consideration of differences of *G* and *R* for being the main cause of the differences in feature size as discussed above.

#### *4.4. Chemical Composition*

No significant differences between the upper and lower part of each specimen or to the chemical composition of the powder can be recognized. However, small differences in the oxygen content of the "short ILT, high VED" specimen and the "intermediate ILT, basis VED" specimen are detected. Although these differences (0.003 weight % to 0.005 weight %) barely exceed the measurement uncertainty, a closer look into these differences seems to be reasonable.

At the first glance, this would even correlate well with the different preheating temperatures (see Figures 4 and 5) of the parts examined here and with the different annealing colors at the outer surfaces of the specimens observed in [5]. However, looking in more detail, such a perceived view cannot explain the difference between the lower part of the short ILT specimen and the upper part of the intermediate ILT specimen. Both face similar preheating conditions as shown in Section 3.1. It cannot explain a perceived slightly higher oxygen content in the lower part of the short ILT specimen compared to its upper part, although oxidation of the L-PBF surface in its upper part was clearly visible. In addition, the preheating temperatures were in a temperature range prone to surface oxidation. Surface oxides were not measured in the oxygen analysis since hydrochloric acid etching was conducted before the measurement. Hence, only the oxygen intake in the bulk material was measured.

However, short ILT and intermediate ILT specimens were manufactured in two different processes. Therefore, the logging data of the internal oxygen lambda probes of the L-PBF system have to be examined. As the experienced L-PBF user of this specific machine knows, the process starts when the residual oxygen concentration in the process chamber is below 0.1%. For the working principle of the gas flushing regarding the maintenance of a low oxygen content, one is referred to the detailed explanation given by Pauzon et al. [50] for another L-PBF machine with a similar principle. After reaching 0.1%, the concentration measured at the lambda probes usually levels down in the beginning of the process to approximately 0.02%. Figures 13 and 14 depict the oxygen concentration in the atmosphere of the process chamber during the first 300 min of the short ILT process and intermediate ILT process respectively. The upper x-axis of these plots shows the respective build height, which must be substantially higher within the same process time for short ILT. It can be derived from the two diagrams that the residual oxygen content during manufacturing of the lower ex-situ volumes of analysis (build height between 2.5 mm and 12.5 mm, see Figure 1) was higher for the short ILT process compared to the intermediate ILT process. Therefore, this can be presumed to cause the higher weight % of oxygen in the lower part of the short ILT specimen measured by chemical analysis, as listed in Table 8. This can be supported by findings of similar magnitude by Dietrich et al. [51]. They reported an increase in oxygen content by 0.0188 weight % in L-PBF Ti6Al4V bulk material manufactured in a process chamber atmosphere of 0.0977 weight % oxygen concentration compared to a process with 0.0002 weight % oxygen concentration.

The reason for the difference in the time span until the oxygen content in the process chamber leveled down cannot be clarified within the frame of the experimental set-up of this study. Potentially, the residual oxygen consumption in the process chamber is affected by the number of parts or (more precisely) the ratio of area exploitation. While only the three specimens, which were in the field of view of the IR camera, were manufactured in the short ILT process, additional 15 specimens of the same size were manufactured in the intermediate ILT process. Hence, the faster decrease of residual oxygen concentration during the build-up could be related to a bigger surface area available for oxygen intake in the intermediate ILT process.

**Figure 13.** Oxygen concentration in the process chamber during the first 300 min of the short ILT process.

**Figure 14.** Oxygen concentration in the process chamber during the first 300 min of the intermediate ILT process.

After leveling down of the oxygen concentration in the process chamber to approximately 0.02%, these values kept constant over the rest of each build process. Hence, the small differences in the upper part of the two specimens, which are smaller than the measurement uncertainty, could be a result of higher oxygen intake into the L-PBF

bulk due to different preheating temperatures. The specimens with shorter ILT showed slightly higher oxygen content than specimens with longer ILT. This suggestion can be supported by recent findings of Pauzon et al. [52]. They reported that a reduced ILT can lead to increased oxygen pick-up during L-PBF manufacturing of Ti6Al4V specimens. They measured differences in oxygen pick-up of approximately 0.05 weight % for specimens at 70 mm build height manufactured with different ILT, when the oxygen concentration in the process atmosphere was below 0.1 weight %. However, as the measurement uncertainty is high in comparison to the discussed difference, further examinations should be done in future work.

The measured quantities of oxygen content are well within the range of published values in the literature for the same material and process. A recent study from Pauzon et al. [50], dedicated to process gas influence during L-PBF processing of 316L, revealed oxygen concentrations of approximately 0.0424 weight % in the bulk of their specimens. This is not only in good agreement in terms of magnitude but also quite close to the values examined here. Lou et al. [23] measured an oxygen content of about 0.0384 weight % at 316L L-PBF specimens. Pauzon [53] also highlighted the solubility limit of oxygen in austenite being estimated by Kitchener et al. [54] at about 0.003 weight % +/− 0.003 weight %. Oxygen content above this value is expected to be connected to secondary phase oxide inclusions, mainly with elements such as Cr, Mn, or Si [53]. Hints about the existence of such nanosized precipitations in 316L can be found, e.g., in the work of Liverani et al. [17], Saedi et al. [55], and Sun et al. [18]. Krakhmalev et al. [16] described the size of these particles in the range of 15 nm to 100 nm. Detrimental influences on impact toughness were discussed by Lou et al. [23].

#### *4.5. Subsumption of the Results with Regard to Hardness*

In this section, the variations of the analyzed features are discussed with regard to hardness values obtained in the previous study [5]. A significant hardness drop in the upper part sections of the short ILT specimens as compared to the lower part sections was revealed [5], despite relatively low defect densities. At intermediate ILT, only a slight decrease in hardness over the build height was recognized. The range of hardness values was at a similar level in the upper and the lower part sections at long ILT. The hardness values in the upper part sections are transcribed from [5] into a diagram that again shows the sub-grain sizes of the respective upper parts, see Figure 15. The hardness values are discussed in the following as representative for material strength. The strength of metallic materials is the sum of the following contributions: contributions from dislocations, from grain boundaries, from solid solutions, and from precipitations [56]. Hence, the identified differences in grain sizes as well as in cell spacing should be discussed with respect to hardness.

An inverse relationship between hardness values and LAGB sub-grain sizes can be seen in the direct comparison diagram in Figure 15. The same relationship would be visible also for the HAGB grain sizes, as a comparison between the results in Section 3.2 indicates (see Figures 8 and 9). Both microstructural feature sizes seem to obey a Hall-Petch type relationship between grain sizes and material strength. However, as reported at many places the high dislocation density of the cellular substructure within the sub-grains plays an additional and very important role in strengthening of 316L material produced by L-PBF [9,15,39,57]. Besides the measured grain sizes, the measured cell spacing also shows an inverse relationship regarding hardness. For the most extreme parameter combination (short ILT, high VED, and upper part), a contribution of keyhole porosity to the hardness drop cannot be excluded entirely [5]. However, for all other specimens the defect density was low enough for not being assumed to affect hardness.

**Figure 15.** Comparison of LAGB sub-grain sizes of the upper part sections and the respective hardness values (Adapted from ref. [5]) for each parameter combination.

Deng et al. [39] conducted very fundamental annealing experiments. They showed that a decrease in hardness already appears before the onset of any recrystallization as a matter of changes in dislocation cell size. Under the assumption of changes in dislocation cell size only, the cell size is allowed to be used for a direct correlation to strength based on a Hall-Petch relationship as proofed valid by Deng et al. [39]. However, they also showed that the correlation factor *k*, which is normally assumed to be a constant factor in a Hall-Petch type relationship, can change non-linearly due to different dislocation annihilation behavior depending, e.g., on the annealing time. This is already relevant below the starting temperature of a complete annihilation of dislocations, below 800 ◦C. In simplified terms, not only the cell size of the dislocation structure but also the dislocation density within the cell boundaries contribute to the material strength. However, this can only be studied by intense use of transmission electron microscopy.

A direct transfer from the annealing experiments of Deng et al. [39] to the results of the present study does not work since it can be assumed that the differences in microstructural features of the specimens of this study are not caused by annealing but by differences in the initial conditions of solidification. This assumption is supported by differences in grain sizes between upper part and lower part sections of the same specimens as discussed in Section 4.2. This cannot be the result of any recrystallization or annealing grain growth, as otherwise the cellular substructure would have been dissolved. Therefore, the primary cause of the differences in the feature size of the cellular structure as well as in the LAGB and HAGB grain sizes is assumed to be related to the differences in solidification rate and thermal gradients. Both are affected by the interplay of VED and ILT variations as well as by the build height. The evolution of the preheating conditions over the build height for the different parameter combinations clearly indicates a change of the initial thermal conditions of solidification. An increase of grain size with decreasing cooling rates was already reported by Zitelli et al. [1] and Keshavarzkermani et al. [14].

Interestingly, Bang et al. [58] recently investigated changes in microstructure and hardness i.a. of small 10 mm cubic L-PBF specimens of 316L over a broad range of parameter combinations of laser power (80 W to 480 W) and scanning velocity (493 mm·s−<sup>1</sup> to 2958 mm·s<sup>−</sup>1). For all parameter combinations with resulting high density, their microstructural characterization revealed an increase of cell size and grain size in proportion to the applied VED except for one outlier at the highest VED condition. A decrease in hardness from approximately 220 HV0.5 to approximately 180 HV0.5 was exhibited with increasing VED, which they related to the inverse relationship between hardness and grain sizes. As mentioned elsewhere, a direct comparison of VED values is not acceptable in its entirety and has to be done very carefully, see, e.g., [59,60]. However, when considering a comparison of the hardness values of Bang et al. [58] with the values of the present study—its pre-study [5]—it becomes clear that Bang et al. [58] used a much broader range of processing parameters (laser power and scanning velocity) than in the present study. Thereby, they provoked similar conditions in terms of resulting hardness and trends of increasing microstructural feature size at their 10 mm cubic specimens. These conditions were induced by a relatively narrow variation of the VED in combination with an application relevant build height of over 100 mm and decreasing ILTs in the present study.

This in total emphasizes the importance of ILT in combination with build height on the development of the microstructure and the resulting mechanical properties in L-PBF, as together they seem to be able to drastically shift the processing window, gained from typical process parameter studies.

#### **5. Conclusions**

An in-depth analysis of the microstructural feature sizes of 316L specimens produced at different VED levels and different ILT levels has been conducted. Furthermore, the evolution of the intrinsic preheating temperature over the complete build-up of specimens was monitored by use of a thermographic in-situ monitoring set-up.

Several influencing factors and their implications have been identified.


Furthermore, there was a slight tendency of increasing oxygen intake in regions of high preheating temperature. However, the basis for these oxygen measurements is quite limited, and further investigations in this field are required. This will also include better control of the boundary conditions of oxygen content within the L-PBF process.

The findings of this study are strongly linked to intrinsic changes in preheating temperature during the L-PBF process. The causes of these significant changes were

identified to be related to processing parameters such as scanning velocity (affecting VED) but also to build height and ILT, which are overlooked in many other cases in the literature. When considering real part geometries and current trends in the development of new L-PBF machines (e.g., multi laser machines), a decrease in ILT can be expected during manufacturing. This will make the issue of differences in microstructure and mechanical properties due to intrinsic preheating temperature changes more severe. Therefore, the authors want to close with the recommendation to always include the ILT into the process documentation to enhance the comparability of measurement results of L-PBF products.

**Author Contributions:** Conceptualization, G.M.; methodology, G.M., K.S. and T.K.; software, G.M. and T.K.; validation, G.M., K.S. and T.K.; formal analysis, G.M., K.S., T.K. and S.R.; investigation, G.M., K.S., T.K. and S.R.; resources, S.J.A., K.H.; data curation, G.M., K.S. and T.K.; writing—original draft preparation, G.M., T.K.; writing—review and editing, G.M., K.S., T.K., S.J.A., S.R., D.B. and K.H,.; visualization, G.M.; supervision, K.H.; project administration, S.J.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by BAM within the focus area materials.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would like to thank M. Ostermann for XRF measurements, A. Meckelburg for determination of non-metals, J. Roik for ICP-OES measurements, R. Saliwan Neumann for SEM images, and A. Charmi for support in generating IPF maps.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyzes, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

#### **References**


### *Article* **Can Potential Defects in LPBF Be Healed from the Laser Exposure of Subsequent Layers? A Quantitative Study**

**Alexander Ulbricht 1,\*, Gunther Mohr 1,2, Simon J. Altenburg 1, Simon Oster 1, Christiane Maierhofer <sup>1</sup> and Giovanni Bruno 1,3**


**Abstract:** Additive manufacturing (AM) of metals and in particular laser powder bed fusion (LPBF) enables a degree of freedom in design unparalleled by conventional subtractive methods. To ensure that the designed precision is matched by the produced LPBF parts, a full understanding of the interaction between the laser and the feedstock powder is needed. It has been shown that the laser also melts subjacent layers of material underneath. This effect plays a key role when designing small cavities or overhanging structures, because, in these cases, the material underneath is feed-stock powder. In this study, we quantify the extension of the melt pool during laser illumination of powder layers and the defect spatial distribution in a cylindrical specimen. During the LPBF process, several layers were intentionally not exposed to the laser beam at various locations, while the build process was monitored by thermography and optical tomography. The cylinder was finally scanned by X-ray computed tomography (XCT). To correlate the positions of the unmolten layers in the part, a staircase was manufactured around the cylinder for easier registration. The results show that healing among layers occurs if a scan strategy is applied, where the orientation of the hatches is changed for each subsequent layer. They also show that small pores and surface roughness of solidified material below a thick layer of unmolten material (>200 μm) serve as seeding points for larger voids. The orientation of the first two layers fully exposed after a thick layer of unmolten powder shapes the orientation of these voids, created by a lack of fusion.

**Keywords:** selective laser melting (SLM); additive manufacturing (AM); process monitoring; infrared thermography; optical tomography; X-ray computed tomography (XCT); healing; in situ monitoring

#### **1. Introduction**

Additive manufacturing (AM) of metals has evolved from a method for rapid prototyping to a production process applied in many industries including automotive, aerospace, and railway [1]. Among the AM methods established for metals, laser powder bed fusion (LPBF) is the most widely used, as it can produce net-shaped parts, which do not necessarily need additional surface treatments. To design LPBF parts, it is necessary to understand how the laser interacts with the layers of molten and unmolten powder. Previous studies have shown that the laser also melts, in addition to the current layer of powder, subjacent layers [2,3]. This effect is actually needed for a strong bonding between the layers and to prevent lack-of-fusion (LoF) defects [4,5]. If the volumetric energy density is high enough, the melt pool may not only re-melt solidified material, but also entrap keyhole pores into the bulk material up to several hundred of μm below the currently illuminated surface [6].

**Citation:** Ulbricht, A.; Mohr, G.; Altenburg, S.J.; Oster, S.; Maierhofer, C.; Bruno, G. Can Potential Defects in LPBF Be Healed from the Laser Exposure of Subsequent Layers? A Quantitative Study. *Metals* **2021**, *11*, 1012. https://doi.org/10.3390/ met11071012

Academic Editors: Tomasz Czujko and Matteo Benedetti

Received: 11 May 2021 Accepted: 17 June 2021 Published: 24 June 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Therefore, the melting process of subjacent layers needs to be kept in mind when designing parts with cavities or overhanging structures [7]. To address this issue, LPBF machine manufacturers provide specialized downskin process parameters [8,9]. Many studies have been focussed on the determination of the part quality from in-situ monitored process signals of the build process [6,10–13]. In situ monitoring techniques based on thermographic cameras usually aim at the quantification of thermal inhomogeneities (within the current built surface or a stack of surfaces) to predict the formation of voids in the final part. The main drawback of thermographic techniques is the inability to observe the effect of the melt pool in the underlying, previously exposed layers.

To predict the existence of defects in the final part (i.e., voids whose forms, positions, and sizes might be a threat to the service life of the component) from in situ surface temperature data, it is necessary to understand the influence of the melt pool penetration depth on unmolten powder. Thus, several studies reported results from simulations [14,15] and experiments [16,17] on the interaction between melt pool and powder.

Based on these results, this study aimed to evaluate how the laser exposure of superjacent layers affects void formation in previously non-exposed areas of different heights in an LPBF specimen. A particular question is, if and how the laser exposure of superjacent layers can heal or close voids by successive melting of material in these areas.

In an LPBF specimen made of AISI 316L austenitic stainless-steel, a few consecutive layers were not directly exposed to the laser at nine different locations along the height of a cylindrical specimen. A scan strategy that rotates the orientation of a stripe scan pattern for each layer was applied to correlate the shape of detected voids to the scan pattern of distinct layers.

The build process was in situ monitored using thermographic cameras and optical tomography (the same LPBF machine and a similar optical setup as in [6]). The results from optical tomography (OT) enabled the extraction of the deployed orientations of hatches in each layer. OT was also used to study the integral intensity of the emitted thermal radiation of each built layer.

To analyse the final component, X-ray computed tomography (XCT) was used. This widely accepted non-destructive 3D measuring method enables quantitative characterisation of internal structures and volumetric irregularities; it also allows the evaluation of the geometrical precision of the built part compared with its planned design [6,18].

Additionally, we also used XCT data to capture the influence of the shape of internal surfaces and roughness on the formation of voids.

#### **2. Materials and Methods**

#### *2.1. Material and Machine*

Gas atomized powder of AISI 316L austenitic stainless steel was used as feedstock material on a commercial LPBF system SLM280 HL (SLM Solutions Group AG, Lübeck, Germany). The machine was equipped with a single 400 W continuous wave ytterbium fiber laser. In the focal position, a spot size of 80 μm at an emitted wavelength of 1070 nm was used [6]. The standard process parameters for 316L provided by the machine's manufacturer were applied for the build process: laser power P = 275 W, scan velocity vs. = 700 mm/s, layer thickness t = 50 μm, and hatching distance h = 120 μm. Sky writing was used during the build job to prevent changes in the volumetric energy density at the end of scan tracks, where the laser guiding system needed to be aligned to the orientation of the next scan track. The powder specifications given by its supplier are listed in Table 1. Argon was used as shielding gas during the build job with a resulting oxygen content of less than 0.1%.

**Table 1.** Powder characteristics (AISI 316L).


#### *2.2. Specimen Design*

A cylindrical specimen with a height of 12 mm and a diameter of 7 mm was designed. This resulted in a total of 240 layers based on a layer thickness of 50 μm. At nine specific heights, one quarter of the cylinder's circular surface was not exposed by the laser (see Table 2). To prevent heat accumulation during the build job, owing to possible voids in the non-exposed quarters, the quarters were distributed clockwise over the four quadrants of the cylinder and the build height. A 67◦ rotation of a meandering stripe scan strategy for each layer in the bulk was applied to minimize porosity [19]. A border scan and a fill contour scan were additionally applied to ensure smooth surfaces and precise part dimensions. In the layers of the non-exposed quarters, the contour scans followed the actual three-quarter shape of the exposed section. Hence, potentially unmolten powder particles could be removed through these gaps in the surface. An ultrasonic bath of the specimen was used to remove as much unmolten powder as possible from the non-exposed quarters of the manufactured specimen.

**Table 2.** Overview of the position and characteristics of the non-exposed quarters. The height to be exposed included the height of the non-exposed quarter plus the height of the first fully exposed layer above (50 μm).


To analyse the ability of the laser exposure of subsequent layers to fully melt subjacent layers of powder, a precise registration of the XCT results as well as of the in situ monitoring results was needed. Hence, a (helical) staircase was designed to be manufactured around the cylinder. This design was derived from Gobert et al. [20], who introduced additional staircases to enable a better registration of observable features to a distinct layer. Here, every step of the staircase represented the starting height of a non-exposed quarter of the inner cylinder. A small gap was introduced between the staircase and cylinder to enable an easy removal of the staircase and enable high resolution XCT scans. In order to improve the registration of a rotational symmetric specimen, an embossed T-shaped mark was added to the top surface (see Figure 1).

**Figure 1.** (**a**) CAD file of the specimen including the staircase; (**b**) Photograph of the produced specimen (top view, including the trigger pins) (**c**) Photograph of the produced specimen (side view) (**d**) Photograph of the specimen after the removal of the staircase. The yellow ellipse marks an open porosity of a non-exposed quarter.

#### *2.3. Optical Tomography and Thermography*

The build process was monitored in situ by optical tomography (OT, bulb exposure of each layer exposition [21]) and thermography. In comparison with the optical setup within the LPBF machine's build chamber previously reported in [6], the external optical setup was modified. Beam splitters divided the radiation into an OT CMOS camera (M4020, Teledyne Digital Imaging Inc., Billerica, MA, USA) and a short wave infrared (SWIR) camera (Goldeye CL-033 TEC1, Allied Vision Technology GmbH, Stadtroda, Germany). The OT camera system was sensitive to light emission in the near infrared spectral range (880 nm ± 25 nm). A spatial resolution of 40 μm per pixel was achieved, enabling visualisation of the hatching pattern with a hatching distance of 120 μm. The image data acquired by in situ OT show a map of intensity values that are proportional to the spectral radiosity of the part surface integrated in the spectral range of the used filter and over the whole layer illumination time. As the radiosity in a fixed spectral window strongly increases in the near infrared at the involved temperatures of molten steel, these intensity values are well suited as a measure for the maximum temperature reached at each point. However, as the time integral over the spectral radiosity is recorded, reduced cooling rates can also cause high OT intensities. Thus, data interpretation must be performed carefully. A comparison with the time resolved thermography data may help to clarify the origin of possible deviations in the OT intensity, despite the lower spatial resolution (factor of three).

#### *2.4. Micro Computed Tomography*

Micro computed tomography (XCT) was performed in two steps. An overview scan of the whole part was performed using the commercial CT-scanner GE v|tome|x 180/300 (GE Sensing & Inspection Technologies GmbH, Wunstorf, Germany) at a voltage of 222 kV and a current of 45 μA applied with an aluminium pre-filter of 1.0 mm thickness. A reconstructed voxel size of (10 μm)<sup>3</sup> was achieved. After the removal of the staircase, the inner cylinder was scanned again using a custom-made industrial 3D micro CT scanner, which was equipped based on a 225 kV micro focus X-Ray source (X-Ray WorX GmbH, Garbsen, Germany) [22]. A voltage of 210 kV and a current of 60 μA in combination with a metal pre-filter of 1 mm copper and 0.25 mm aluminium were used. A voxel size of (5 μm)3 was achieved by combining the results from two measurements taken at two heights. The combined (5 μm)3 data were filtered using the plugin "non-local means denoise" [23,24] in the open-source imaging software Fiji [25]. For further analysis, the higher resolution—(5 μm)3 voxel size—data were registered onto the lower resolution— (10 μm)<sup>3</sup> voxel size—data using the commercial software VG Studio MAX version 3.3.3 (Volume Graphics GmbH, Heidelberg, Germany). The same software was used for all XCT data analyses. The (5 μm)3 voxel size data enabled the quantitative analysis of voids with size above (10 μm)3. The analysis was performed in a virtual cylindrical cut-out (Ø = 6.87 mm, L = 11 mm) of the inner cylinder (Ø = 7 mm, L = 11.86 mm) to prevent surface roughness from influencing the size determination of open voids. The volumetric porosity was analysed using VG Studio MAX's built-in porosity analysis modules. A lower threshold for void detection was set to 8 voxels. To correlate the main orientation of the voids with the orientation of the stripe scan pattern, virtual lines were fitted onto the voids of virtual cuts in the VG Studio MAX software. The built-in dimensioning tool was used to calculate the angles of the LoF voids from a set 0◦ reference line.

#### **3. Results**

#### *3.1. In Situ Monitoring*

The OT results from layer 200 (last fully exposed layer before the beginning of Q8, see Table 1) and layer 209 (first fully exposed layer after Q8) are exemplarily depicted in Figure 2. From the OT data, the rotation angle α of the meandering stripe pattern was extracted. Exemplarily, the rotation angles of these two layers are indicated, α(layer 200) = 75◦ and α(layer 209) = 13◦. The comparison of the OT data revealed lower intensities in the quarter of layer 209, which covered the unexposed quadrant I. A comparison with time

resolved thermography results shows that the spectral radiosity in the wavelength window of the SWIR camera was reduced in this quadrant as well. Thus, the maximum temperature reached in this quadrant was indeed lower than in the other quadrants. Ghost images appeared in the OT data, caused by the optical set-up, adding some blur to the images. The resulting offset intensity error in the superposed areas is in the range of approximately +8% related to peak intensity.

**Figure 2.** Optical tomography (OT) images showing the orientation of the hatches for (**a**) layer 200 (last complete layer below Q8) and (**b**) layer 209 (first complete layer above Q8).

#### *3.2. XCT*

The XCT results showed that, in all of the nine quarters, most of the powder was molten by the laser exposure (see Figure 3 and Table 3). Figure 3 shows the 3D rendering of the segmented voids in the whole cylindrical specimen. Figures 4 and 5 show the segmented voids in a virtual cut of the XCT data as well as the 3D rendered void segmentation. As shown in Figure 5e,f and Table 3, at a height of 450 μm (+50 μm of the superjacent fully exposed layer) of unmolten powder, a porosity of 5.56% was observed. This was surprisingly low as the unexposed volume was expected to contain many unmolten powder particles. Instead, solid material with LoF voids was observed.

**Figure 3.** (**a**) Sideview of the combined rendering of the (10 μm)3 data and the (5 μm)3 data showing segmented voids in the high-resolution data; (**b**) top view of the rendering of the (5 μm)3 data of the cylinder showing a projection of all segmented voids.

**Table 3.** Porosity of the non-exposed quarters.

**Figure 4.** Void distribution at the positions of the unexposed quarters. Slice images taken at 10% of the quarter's height. (**a**) Q4: four layers unexposed; (**b**) projection of the void distribution in the unexposed layers containing Q4; (**c**) Q5: five layers unexposed; (**d**) projection of the void distribution in the unexposed layers containing Q5; (**e**) Q6: six layers unexposed; (**f**) projection of the void distribution in the unexposed layers containing Q6.

**Figure 5.** Void distribution at the positions of the unexposed quarters. Slice images taken at 10% of the quarter's height. (**a**) Q7: seven layers (350 μm) unexposed; (**b**) projection of the void distribution in the unexposed layers containing Q7; (**c**) Q8: eight layers unexposed; (**d**) projection of the void distribution in the unexposed layers containing Q8; (**e**) Q9: nine layers unexposed; (**f**) projection of the void distribution in the unexposed layers containing Q9.

> At up to a thickness of 200 μm of unmolten powder, almost no additional porosity due to the underexposure by the laser was observed (see Figure 4a,b for 200 μm of unmolten powder in Q4). In these quarters, only pores at the interface between bulk and contour scan could be detected. This observation correlates well with the results from the literature [26]. The porosity value is directly linked to the number of pores occurring inside the quarters,

not to the explicitly unmolten layer thickness. At a non-exposed thickness of 250 μm of unmolten powder (Q5), voids were detected at the positions where the outlines of the quarter intersect the perimeter of the cylinder (see Figure 4c,d). Voids at the quarters' inner perimeter were detected only above a non-exposed thickness of 300 μm (i.e., six layers, Q6, see Figure 4e,f and Figure 5a,b). At a thickness of 400 and 450 μm of unexposed powder, areal voids were detected (see Figure 5c–f, Q8 and Q9). Figure 5f shows the rendered defects; they seem to correspond to hatches of the scan pattern. As the orientation of the stripe scan pattern rotated by 67◦ with each layer, it was possible for Q6–Q9 to assign the orientation of LoF voids to distinct layers. As listed in Table 4, the main orientation of the LoF voids corresponds to the orientation of the first fully exposed layer above the quarter. For Q8 and Q9, a secondary orientation of LoF voids was also detected. Figure 7 combines the 3D rendering of the segmented voids with OT images of the first and second exposed layer above the quarter. The figure emphasises how the hatch orientation of these layers determined the shape of the segmented LoF voids.

**Table 4.** Comparison between the observed lack-of-fusion (LoF) pattern and the scan hatch orientation. OT, optical tomography.


Figure 6a shows a magnified virtual cut of a large defect at the centre of Q9 obtained from the high-resolution XCT data. Figure 6b revealed that voids were mainly found at the bottom of Q9 and large voids could be observed towards the perimeter of Q9. In contrast to the remaining quarters in Q9, a larger void could be observed in the centre of the quarter (see yellow highlighting in Figure 6a,b).

**Figure 6.** (**a**) Magnified sideview of the large defect at the centre of Q9 obtained from the high-resolution X-ray computed tomography (XCT) data. The largest void in Q9 is highlighted; (**b**) 3D rendering of the voids in Q9. The yellow mark highlights the position of the largest void from (**a**).

#### **4. Discussion**

The aim of this study was to analyse the effect of healing of successive laser passes during LPBF manufacturing. We thus investigate how (and how many) unmolten layers of powder were molten to form a solid with dense connection to the underlying bulk material. Although standard machine parameters of the LPBF machine based on 50 μm thick layers of powder were applied, XCT data revealed that the melt pool was deep enough to partially

melt 10 layers of powder (500 μm), thereby creating lower than expected porosity values (5.6%). The lack of unmolten powder particles found in the non-exposed quarters illustrates the ability of the laser to transfer heat to powder layers below the surface. This result corresponds to the results from the in situ monitoring.

Figure 2b reveals that the thermal radiosity in quadrant I of the first fully exposed layer above Q8 seems to be lower than for the regions that have solid material below. This might be surprising at a first glance, as powder can be regarded as a heat insulator [27]. Therefore, one would expect to observe a higher radiosity owing to heat accumulation above the insulating powder. To explain the observed radiosity, the ability of the laser to transfer a sufficient amount of heat to layers below the current surface should be invoked. Foroozmehr et al. [15] had simulated the optical penetration of the laser radiation into a powder bed of AISI 316L. In agreement with previous studies [14,17], they assumed, in addition to absorption, multiple reflections of the laser radiation at the surfaces of the powder particles. Therefore, the laser–powder interaction seems to be a complex combination of transmission, scattering, and absorption of the laser energy by the powder particles. The laser radiation is not only absorbed at the surface of the powder layer, but also *within* the layer. At Q9, the missing layer thickness was 10 times higher than the single layer thickness of 50 μm. This led to a higher optical penetration depth, and thus to a lower volume energy density as in the areas with the single layer thickness. Consequently, the maximum temperature and thus the radiosity detected by the OT camera of the first solidified layer is lower.

Figure 6 and Figure 9 show that the voids created by the missing illumination of the layers were mainly found at the bottom of the quarters where the melt pool could not melt powder particles [28]. As shown in Figure 7, the melt pools of the first (and, above seven unmolten layers, also the second) fully exposed layer above the non-exposed quarter shaped the detected LoF voids. At these deeper regions, the melt pool is expected to be narrower. Therefore, in such regions, melt pools from neighbouring scan tracks did not seem to overlap each other. The combination of solidification shrinkage and surface tension effects of the melt pool (e.g., Marangoni effect [29–31]), which could draw neighbouring powder particles into the melt pool, appears to have created voids between scan tracks. Further in-depth analysis of the energy limits that form LoF voids in LPBF parts has been discussed by Biffo et al. [32–34]. In Q4 to Q7, these LoF voids between scan tracks were only observed close to the perimeter of the quarter. In Q8 and Q9, these LoF voids were also observed in the bulk of the quarters. This indicates that, up to a depth of 350 μm (below the current layer surface), neighbouring scan tracks overlap in such a way to cover the gap between them (120 μm).

Figure 7a–d shows that the orientation of the LoF voids observed in the quarters Q6–Q9 mainly corresponded to the orientation of the scan pattern of the first fully exposed layer above. This indicated that, at a depth of 350 μm and below, the melt pool widths of neighbouring scan tracks do not overlap sufficiently to prevent LoF defects. Because, in Q6 and Q7, this observation was made only at positions close to the edge of the quarters, the melt pool width seemed to vary during the laser exposure. In Q8 and Q9, a secondary orientation of LoF voids was also observed. This showed that the melt pool depth of the first solidified layer was lower than the powder layer thickness, leaving some unmolten power at the bottom of Q8 and Q9. The penetration depth of the melt pool did not seem to be constant, because, up to Q8 (powder height of 400 μm), only small voids (height < 100 μm) at the bottom of the quarter were detected. In Q9 (quarter height of 450 μm), a network of large voids with a height of up to 300 μm was observed (see highlighted void in Figure 6b). The lack of large voids in quarters Q1–Q5 indicates that the laser energy density was sufficient to melt several layers of powder in the non-exposed quarters.

**Figure 7.** Combination of optical tomography images of the first fully exposed layers above the quarters and the orientation of LoF voids, as detected by XCT. (**a**) Void distribution of Q6 combined with the OT of the first layer above; (**b**) void distribution of Q7 combined with the OT of the first layer above; (**c**) void distribution of Q8 combined with the OT of the first layer above; (**d**) void distribution of Q9 combined with the OT of the first layer above; (**e**) void segmentation of Q8 combined with the OT of the second layer above; (**f**) void distribution of Q9 combined with the OT of the second layer above.

Figure 8 shows a third orientation of LoF voids close to the bottom surface of Q8 and Q9. The combination of XCT and OT data revealed that their orientation corresponds to the orientation of layer numbers 200 (in the case of Q8) and 220 (in the case of Q9). These layers were the last fully exposed layers below the non-exposed quarters. The virtual cuts presented in Figure 8 were taken 60 μm above the bottom of Q8 and 10 μm below the bottom of Q9. Still, at that height, the orientation of the underlying solidified surface seemed to influence the orientation of LoF voids. It can be assumed that the surface roughness of these layers served as seeding points for the larger LoF voids in the quarters.

**Figure 8.** (**a**) Virtual cut taken at 60 μm above the bottom of Q8 combined with an optical tomography image showing the hatch orientation of layer number 200 (last completely exposed layer before Q8). The latter seems to dictate the orientation of the voids more than the layers above. (**b**) Virtual cut taken at 10 μm below the bottom of Q9 combined with an optical tomography image showing the hatch orientation of layer number 220 (last completely exposed layer before Q9). The latter seems to have formed the first voids in the bulk of Q9.

In Figure 9, the top yellow line was drawn from the shape of the cylinder's top surface. This profile was also applied to the internal surfaces of Q9 and Q8. The correspondence between this template and inner surfaces could indicate that this uneven surface was present throughout the whole build process. This indicates that the height difference between the centre and perimeter of the cylinder also existed at lower built heights. The slope explains why the imperfections of layer number 220 were visible in both images of Figure 8. During the build job of the specimen, sky writing was used to ensure a constant scan speed for the whole hatch length. To achieve a constant speed, the laser was turned off at the end of the scan track before repositioning the guiding mirrors. Hence, deceleration and acceleration effects could be avoided. Suddenly turning off the laser resulted in the reported elevated end-sections of scan tracks, followed by a dent as reported by Yeung et al. [35], and corresponds to simulations of the melt flow by Khairallah et al. [31]. According to them, these dents could form pores at the end of scan tracks and might explain the observation of pores at the intersection of the bulk and contour scan in this study. A ring of elevated end-sections of scan tracks has formed throughout the build height of the specimen owing to the 67◦ rotation of the applied stripe pattern in the bulk (see Figure 9).

**Figure 9.** Cross section taken in the middle of the core cylinder showing voids at the bottom edges of Q8 (blue marked area at the bottom of the right side) and Q9 (blue marked area at the left side). The blue lines represent the nominal size taken from the CAD file. Yellow lines emphasize the structure of the internal surface.

#### **5. Conclusions**

In this study, we investigated the effect of unmolten powder layers on the defect formation in LPBF AISI 316L. In particular, we determined how many laser-unexposed layers of AISI 316L powder could be molten using a set of basis parameters provided by the LPBF machine's manufacturer. We found that, up to a thickness of 200 μm of unexposed powder (i.e., four powder layers), no additional porosity was observed, aside from pores between the bulk and contour scan. Therefore, we conclude that the heat input from the melt pool could sufficiently melt an amount of powder of four layers. We presume that this occurs because of a sufficient melt pool penetration depth, which allows fusion to the underlying solid material, and by being able to allow gas bubbles entrapped between powder particles to escape from the melt.

Further process parameter optimization (not within the scope of this study) might be able to make the process more efficient by, e.g., a slight increase of the scanning velocity. However, for large components, a slightly excessive melting depth can render the build process less prone to process irregularities (e.g., heterogeneities of the powder recoating process).

The present results will enable the interpretation of the signals acquired by in situ monitoring systems, allowing the LPBF users to decide whether or not an irregularly observed signal during the build process will be locked as a defect in the final part.

Our results also suggest that healing among layers occurs only if a scan strategy is applied, where the orientation of the hatches is changed for each subsequent layer. In fact, the porosity observed between the bulk and border scan indicates that healing does not occur if the subsequent layers are applied using the same hatching orientation.

Finally, the present study shows that small pores and surface roughness of solidified material below a thick layer of unmolten material (>200 μm) could serve as seeding points for larger voids. The orientation of the first two layers that are fully exposed after a thick layer of unmolten powder shapes the orientation of these voids, created by a lack of fusion.

**Author Contributions:** Conceptualization, A.U., G.M. and S.J.A.; methodology, A.U., S.J.A. and S.O.; formal analysis, A.U., S.J.A. and S.O.; investigation, A.U., S.J.A. and S.O.; writing—original draft preparation, A.U., G.M., S.J.A., S.O. and C.M.; writing—review and editing, A.U., G.M., S.J.A., S.O., C.M. and G.B.; visualization, A.U. and S.O.; supervision, S.J.A. and G.B.; project administration, S.J.A. and C.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** This work has been funded by the BAM Focus Area Materials project ProMoAM "Process monitoring of Additive Manufacturing". We are thankful for the financial support and the fruitful cooperation with all partners.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **Radiographic Visibility Limit of Pores in Metal Powder for Additive Manufacturing**

#### **Gerd-Rüdiger Jaenisch 1, Uwe Ewert 2, Anja Waske <sup>1</sup> and Alexander Funk 1,\***


Received: 11 November 2020; Accepted: 30 November 2020; Published: 4 December 2020

**Abstract:** The quality of additively manufactured (AM) parts is determined by the applied process parameters used and the properties of the feedstock powder. The influence of inner gas pores in feedstock particles on the final AM product is a phenomenon which is difficult to investigate since very few non-destructive measurement techniques are accurate enough to resolve the micropores. 3D X-ray computed tomography (XCT) is increasingly applied during the process chain of AM parts as a non-destructive monitoring and quality control tool and it is able to detect most of the pores. However, XCT is time-consuming and limited to small amounts of feedstock powder, typically a few milligrams. The aim of the presented approach is to investigate digital radiography of AM feedstock particles as a simple and fast quality check with high throughput. 2D digital radiographs were simulated in order to predict the visibility of pores inside metallic particles for different pore and particle diameters. An experimental validation was performed. It was demonstrated numerically and experimentally that typical gas pores above a certain size (here: 3 to 4.4 μm for the selected X-ray setup), which could be found in metallic microparticles, were reliably detected by digital radiography.

**Keywords:** additive manufacturing; feedstock powder; porosity; radiography; digital detector array; numerical simulation; detectability

#### **1. Introduction**

The reliability of additively manufactured (AM) parts depends to a large degree on the defects and irregularities they contain [1]. Typical flaws in AM parts include delaminations, cracks, inclusions, and pores. For the laser powder bed fusion (LPBF) process, most defects are formed during the dynamic melting process, when the laser interacts with the solid and the melt pool [2,3]. The AM community distinguishes between lack of fusion pores, which are flat and irregular pores (voids) between non-fused powder layers, keyhole pores, which are irregular pores (voids) created by the laser and a high energy input, and gas pores, which are mostly spherical pores formed by adding gas to the melt pool [2,4–8]. A detailed review of pores and voids created during the AM build process was recently published by Sola et al. [2].

Another possible source for gas pores in AM parts is pores already present in the feedstock powder [6,9–12]. Due to the fast heating and cooling rate of the melt pool up to 106 K/s [13] during the LPBF process, gas pores in the powder become bubbles in the melt pool, which under certain circumstances do not have sufficient time to reach the surface of the melt by convection [2,14]. Hence, it is important to check the quality of the feedstock powders, for instance, by determining its overall porosity and pore size distribution [6,15,16]. However, determining the porosity of powders experimentally, e.g., by pycnometry or metallography, is a challenging task [16]. For standard AM materials like steels, aluminum, magnesium, titanium, and nickel alloys, typical porosities of the feedstock powder are below 1 vol.% [10,16]. In particular, high feedstock powder porosities and single particles with large

pores influence the melting behavior of the powder and are likely to merge and solidify together with the melt pool and may become a defect in the final part [2,6]. Several testing methods for the characterization of AM feedstock powders are standardized [17,18]. However, since currently no common quality requirements or certification for AM powders exist, there is the uncertainty that the quality of the powder might vary between different manufacturers and batches. This is particularly true for non-standard AM powder materials, for instance, functional materials like shape-memory alloys [19], permanent magnets [20], or magnetic refrigerants [21], that are now being adapted to AM. For non-standard powders, the production of the feedstock powder is particularly challenging, as the atomization parameters need to be optimized. Large overall porosities up to 24 vol.%, large pore sizes, and shape irregularities leading to a poor powder flowability are also reported for standard AM materials [6,9,12], which require quality control of every powder batch before using them for AM [1].

Feedstock powders for AM are usually checked for their size and shape distribution using sieve-based, light scattering, or direct imaging methods [15,22]. Since these rely on the outer contour of the geometry or optical imaging, internal defects of metal powders, like gas-filled pores, are not accessible. Very accurate determination of internal defects, as well as size and shape distributions of a powder, can be carried out using 3D X-ray computed tomography (XCT) [6,9,16,23]. However, the scan time for a typical powder sample with a commercial XCT device is rarely below one hour [16]. Depending on the size of the powder, the system magnification, and the detector size, only about 1000 to 1,000,000 particles can be imaged during one scan when the highest resolution is required, since the field of view of XCT is limited. This number of particles is equivalent to a few milligrams of metal powder. When considering that several hundred grams and up to several kilograms of powder are needed to manufacture AM parts, milligram samples are not representative for the evaluation of feedstock powder batches and hence for meaningful quality assurance. A technology capable of screening larger amounts of particles in a shorter time is needed for this task.

In-line digital radiography of products and goods is already used, e.g., in fine casting inspection in industry, weld inspections, the food industry, and for luggage inspection at airports [24]. Correspondingly, 2D X-ray inspection was developed for speed and high throughput. In this paper, the potential and requirements of digital radiography for the quality assurance of metal powder by detecting spherical gas-filled pores in metal particles are evaluated. Nowadays, commercially available laboratory XCT scanners are used for measurements, which are available in most AM laboratories worldwide to inspect the final parts produced. However, in the present article, instead of collecting projections from different angles of the powder sample for a reconstruction of a 3D tomographic dataset, 2D radiographs of single layers of the powder are used for inspection. In practice, this would later require that, e.g., a conveyor belt-like or particle stream apparatus is used for moving the particles into the inspection region, similar to the ones used in light scattering devices or direct imaging devices for powder, like a commercial Camsizer® (Microtrac Retsch GmbH, Haan, Germany) [22,25,26]. For the study presented here, a metal alloy is used, but the pore imaging principle applies to other materials, as well. In this paper, a criterion based on a minimal contrast to noise ratio and a basic spatial image resolution is applied, which must be fulfilled in order to detect pores of certain sizes in a metallic particle by digital radiography.

#### **2. Materials and Methods**

#### *2.1. Experimental Sample Preparation*

The tested spherical gas-atomized powder material is a MnFePSi-based alloy [27], with a nominal particle size range of diameters between 100 μm and 150 μm. Note, the particle size range for numerical simulations is broader (see Section 2.5). The experimentally investigated powder represents the geometrical constitution of powders used in AM processes [1]. Both a multi-particle and single-particle sample were radiographed. For sample preparation, one side of a double-sided adhesive tape was placed on a polymer substrate to ensure mechanical stiffness, whereas the other side was covered with particles. The multi-particle sample was fixed on a sample rod.

After testing the multi-particle sample, a single particle containing several pores was identified and isolated from the multi-particle sample using a micro-manipulation tool, radiography, tomography, and light microscopy. The isolated particle was fixed again on a sample rod.

#### *2.2. Experimental Acquisition of Radiographic Images and Tomograms*

Radiographic images were acquired employing a commercial X-ray computed tomography (XCT) device, GE nanotom m 180, and using the image acquisition software datos|x 2.2 acquisition (Waygate Technologies (Baker Hughes Digital Solutions GmbH), Wunstorf, Germany) [28]. A set of radiographic projections, taken at discrete angular positions of the observed sample, served as input data for a subsequent volume reconstruction using the image reconstruction software datos|x 2.2 reconstruction (Waygate Technologies, Wunstorf, Germany) [28]. For the experiments, a phoenix|X-ray micro-focus tube (Waygate Technologies, Wunstorf, Germany) with a tungsten transmission target on a diamond window and a digital detector array (DDA) of type DXR500L (Waygate Technologies, Wunstorf, Germany) was used [28]. The X-ray radiation was not filtered at the source side in order to achieve the highest possible intensity. The X-ray tube can be operated in different operation modes, varying the size of the focal spot. For the selected tube current and acceleration voltage range, nominal spot size of *f* = 5 μm in mode 0 and *f* = 1.3 μm in mode 2 are provided. In this work, mode 2 was used.

Both samples, the multi-particle sample (a) and the single-particle sample (b), were imaged using similar X-ray system parameters, as summarized in Table 1. For sample size reasons, the source to object distance (SOD) and the source to detector distance (SDD) were chosen to be 3 mm/600 mm (a) and 2 mm/400 mm (b), respectively. As a result, the effective pixel size of the radiographs and the voxel size of the volume reconstruction are 0.5 μm. For the tomographic reconstruction, 1700 projections (a) and 800 projections (b) were recorded while rotating the sample. An acquisition time of about 45 min is required for medium image quality for sample (a). To improve the image quality of the XCT projections (noise reduction), a skip of two projections and a frame averaging of five projections on each angular position were selected, which prolonged the total acquisition time by a factor of seven to about 5 h.


**Table 1.** Summary of experiments and their image acquisition parameters.

For the analysis of 3D volumes and the particle and pore size distributions, as well as for visualization, Thermo Fisher Scientific Avizo 9.2 software (Waltham, MA, USA) [29] was applied. The used analysis approaches to detect particles and pores in volumetric datasets can be found in [16].

#### *2.3. Prediction of Pore Detectability by Human Observers*

The basics for detecting small holes in objects, examined by human observers using radiography, were published in [30]. Here, a minimal contrast to noise ratio CNRmin is derived as a criterion to determine the detection limit of hole plate image quality indicators at a magnification of one, depending on the basic spatial resolution of the detector SRdetector <sup>b</sup> and the hole diameter *d*hole given by the equation:

$$\text{CNR}\_{\text{min}} = \frac{10 \cdot \text{SR}\_{\text{b}}^{\text{detector}}}{d\_{\text{hole}}} \tag{1}$$

This concept was extended considering the magnification *M*, spot size *f*, and the pore geometry [31]

$$\text{CNR}\_{\text{min}} = \frac{10}{M} \cdot \frac{2}{\pi d\_{\text{Pore}}} \sqrt{\left((M-1)f\right)^2 + \left(2\text{SR}\_{\text{b}}^{\text{detector}}\right)^2} \tag{2}$$

with *d*pore—pore diameter. Note, the equation is independent of the material tested.

#### *2.4. Image Analysis of Radiographs Based on the Contrast to Noise Ratio*

The digital image analysis was carried out using the software ISee! version 1.11.1 (BAM, Berlin, Germany) [32] for the measurement of the contrast to noise ratio (CNR) in simulated and measured radiographs. The profile was drawn over the center of the powder particle pore to measure the contrast in the radiograph (see Figure 1). The noise was measured in a region of interest in the free beam area. The procedure for the noise measurement implemented in ISee! is described in [33]. The resulting CNR was compared to the theoretical minimal required CNRmin for pore detection (see Section 2.3). The pore is visible to human observers if the determined CNR exceeds CNRmin, as calculated by Equation (2).

**Figure 1.** Scheme for measuring the contrast to noise ratio (CNR): the position of the line profile for the CNR measurement (**a**) and representation of the corresponding profile with and without noise to measure the CNR (**b**).

#### *2.5. Numerical Simulation of Radiographic Images*

The radiographic simulation software *aRTist* (BAM, Berlin, Germany) [34–36] was used to model different inspection scenes of the feedstock powders, using physical models for the production, interaction, and detection of X-rays. The graphical user interface of *aRTist* allows for setting up experimental scenes with different components like the radiation source, different detectors, and geometries of the object under investigation, as shown in Figure 2a. The software combines analytical and Monte Carlo methods to efficiently model the interaction of X-rays with matter. Hence, the way in which X-rays are absorbed and scattered in an object can be simulated and the resulting radiographic image at the detector can be calculated.

For simulation, mode 2 of the XCT scanner (see Section 2.2) with a nominal focal spot size of *f* = 1.3 μm was applied, together with an acceleration voltage of 130 kV and maximum gray values of GVmax = 4200, in accordance with the available experiments, and GVmax = 10,000 to examine the influence of the exposure time on the detectability of the pores.

The following parameters were used for the simulation with *aRTist*:

	- Tungsten transmission target with a thickness of 5 μm;
	- Diamond window with a thickness of 200 μm;
	- Focal spot size of *f* = 1.3 μm;
	- Tube voltage of 130 kV and spectrum resolution of 1 keV, no external filtering on tube side (for resulting spectrum, see Figure 2b).
	- Powder particles: MnFePSi alloy, density of 6.4 g/cm3;
	- Pores: air: N2 0.755, O2 0.231, Ar 0.013 (in mass percent), density of 0.001293 g/cm3.
	- Pixel size of 100 μm;
	- Basic spatial resolution of the detector: SRdetector <sup>b</sup> = 130 μm;
	- Covered by a 750 μm thick carbon fiber-reinforced plastic plate;
	- Maximum gray value of (a) GVmax = 4200 and (b) GVmax = 10,000;
	- Internal scatter ratio of 15%, internal scatter ratio correlation length of 10 mm, gray response of 1000 GV/mGy, maximal signal-to-noise ratio (SNR) of 1400, efficiency of 500 SNRN/mGy1/2.
	- SDD = 400 mm;
	- SOD = 2 mm;
	- *M* = 200.

**Figure 2.** Schematic representation of the radiographic setup with source, object, and detector in (**a**), and the 130 kV spectrum plot used in the simulation in (**b**).

For the numerical simulation, an idealized geometrical description was used to represent the feedstock particles in a size range between 10 μm and 150 μm, to cover the full range of commonly used AM feedstock powders [1]. The particles were assumed to be spherical and arranged in a single layer. The pores are described as spheres filled with air and positioned in the center of the powder particle, which yields the minimum achievable contrast in the radiographic images. Figure 3 shows an example of the geometric arrangement and the radiographic image of 441 particles with internal pores

used for simulation. The high number of spheres was selected to permit a more accurate evaluation of pore visibility. To determine the minimum detectable pore sizes, the actual pore diameter was reduced stepwise by 0.1 μm. Simulated radiographic images were analyzed after each step, as described in Section 2.4.

**Figure 3.** Representation of a single layer of a 21 × 21 arrangement of metallic particles of 50 μm in diameter and with 5 μm air-filled pores inside, taken from the *aRTist* simulation scene (**a**). Radiographic image of the identical geometry with the profile (yellow inset) to investigate the visibility as function of CNR (**b**). The pores are the light gray areas in the center of the spheres.

#### **3. Results and Discussion**

#### *3.1. Minimal Visible Pore Size*

Figure 4 shows the CNRmin according to Equation (2) for two different focal spot sizes and SRdetector <sup>b</sup> = 130 μm. For *f* = 5 μm (Figure 4a), the minimum required CNRmin is almost independent of the magnification in the selected range, while for *f* = 1.3 μm (Figure 4b) for small pores and microor nano-focus tubes, the CNRmin depends significantly on the magnification. Additionally, the CNRmin for *f* = 5 μm is generally higher than the smaller focal spot size of *f* = 1.3 μm, meaning that for a real experimental setup with known SRdetector <sup>b</sup> and proper exposure, small pores are more difficult to detect with a big focal spot size (Figure 4).

**Figure 4.** Minimal contrast to noise ratio CNRmin for pore visibility according to Equation (2) with SRdetector <sup>b</sup> = 130 μm, different magnifications *M* and the focal spot sizes: *f* = 5 μm (**a**) and *f* = 1.3 μm (**b**).

*Metals* **2020**, *10*, 1634

The diameter of a just visible pore, *d*pore\_min, in a radiograph of spherical particles can be predicted as function of the radiographic setup and the exposure parameters as follows:

$$d\_{\text{pore\\_min}} = \frac{10}{M} \cdot \frac{2}{\pi \cdot \text{CNR}\_{\text{min}}} \sqrt{\left((M-1)f\right)^2 + \left(2\text{SR}\_{\text{b}}^{\text{detector}}\right)^2} \tag{3}$$

The magnification *M*, the focal spot size *f*, and the basic spatial detector resolution SRdetector b depend on the radiographic setup. The detectable pore size decreases if the focal spot size and the basic spatial resolution of the detector are selected to be as small as possible.

Furthermore, the detectable pore size also decreases if the CNR can be increased by the exposure conditions and *M* is optimized. The operator controls the pore contrast and noise by the selection of the X-ray energy and exposure parameters. The contrast is increased when the selected tube voltage is decreased. The CNR is increased if the noise is reduced. This requires increasing the tube current and the exposure time (for DDAs, increase frame time and frame averaging number). Generally, it is concluded that the CNR increases with the square root of exposure time and tube current. This requires an effective calibration of the digital detector array (DDA) to avoid an additional noise contribution by fixed pattern noise, which appears typically due to the sensitivity differences of the detector elements (pixels) and bad pixels. An increase in the tube voltage reduces the contrast and the noise, which influences the CNR depending on the attenuation process, typically the photo absorption or the Compton attenuation. At a higher tube voltage, where the Compton effect dominates, the contrast shows a low dependence on the selected tube voltage, but the exposure time is reduced significantly since the SNR increases proportionally to the tube voltage.

The ratio of particle diameter *d*particle to pore diameter *d*pore, referred to as DPP, influences the measured pore contrast slightly due to the measurement procedure, as shown in Figure 1. Figure 5 shows the surface curvature changes, as seen in the profile, if the DPP is changed from 2 to 10. The pore contrast is slightly reduced with decreasing DPP depending on the particle surface curvature and corresponding line profile change. For large particle diameters, compared to the pore diameters, the pore contrast does not change any more with increasing particle diameter.

**Figure 5.** Contrast change as a function of the overlaid profiles of the pore and particle for different particle diameters. C1 is smaller than C2 for the same pore diameter, since the line profile of the larger particle (50 μm) is almost a flat plateau in contrast to the smaller particle.

A significant hardening of the spectrum is observed with increasing particle diameter for transmission microfocus tubes with diamond window and no prefiltering on the source side. Furthermore, the noise in the pore image increases due to the attenuation of larger particles. Consequently, the CNR is slightly reduced.

#### *3.2. Simulation Results*

By varying the size of the particles and the pores and determining whether the CNR of the pore signal in the radiographic image exceeds CNRmin, it can be determined whether a pore can be detected or not. The CNRmin value of Equation (2) as the visibility limit was verified by three operators for the simulated pores in the particles and accepted as a valid approach within a precision of about ±15% of the determined CNR, which was measured as shown in Figure 1 of the modeled images. In total, about 100 images were created and analyzed. As a result, the CNRmin obtained from Equation (2) was considered as valid limit by the three human observers. For the given simulation setup with *f* = 1.3 μm, a CNRmin for just visible pores of about 3, corresponding to pore diameters of about 4 μm, was determined. Bigger pores can be detected reliably, as the CNR will always exceed the CNRmin.

Based on this, Figure 6 shows the minimum pore size required in order to detect pores in metallic powder particles between 10 μm and 150 μm in diameter by means of digital radiography for the implemented X-ray setup. For the smallest particles with a diameter of 10 μm, the detectable pore diameter is equivalent to 35% of the particle diameter, while for the largest particles of 150 μm in diameter, the detectable pore has a diameter of 3% of the particle diameter (see Figure 6). The detectable minimum pore size increases slightly for very large and very small particles, with a local minimum at a particle diameter of about 70 μm. This is explained due to effects discussed in Section 3.1, e.g., the change of the X-ray spectrum (hardening) with increasing particle diameter on the right side of the graph in Figure 6 and the line profile shape (particle surface curvature), which yields a bias in the contrast measurement, for the left side of the graph in Figure 6.

**Figure 6.** Diameter of the minimum pore sizes detectable by digital radiography in metal powder particles with diameters between 10 μm and 150 μm. The schematic insets are not to scale.

The minimum detectable pore sizes differ only slightly dependent on the selected exposure time of the detector with gray values of GVmax = 4200 and GVmax = 10,000 due to the limitation by the detector calibration (remaining detector fixed pattern noise) and internal backscatter in the detector (see Figure 6). The more highly illuminated image with GVmax = 10,000 demonstrates slightly smaller detected pores. This indicates that experimental exposure parameters leading to GVmax = 4200 are sufficient to detect the smallest pores according to Equation (2) for the present X-ray setup (SRdetector <sup>b</sup> , detector efficiency, magnification, focal spot size, and exposure parameters).

For GVmax = 4200, the smallest detectable pore sizes for three different particle diameters are summarized in Table 2, together with an additional example for a large particle with a large pore. The corresponding simulated images are shown in Figure 7. The additional example with a large pore is in accordance with a particle and pore size which are examined in the experimental results section (see Section 3.3).

**Table 2.** Detectable pore size diameters for different particle sizes (at a maximum gray value of GVmax = 4200).


<sup>1</sup> Smallest detectable pore for the corresponding particle diameter. <sup>2</sup> Large pore and particle size, which was found in the experiment (see Section 3.3).

**Figure 7.** Simulated radiographs (GVmax = 4200) of different particle and pore diameters. The images were filtered, and the contrast was optimized for printed paper. (**a**–**c**) The smallest detectable pores for a particle diameter of (**a**) 10 μm, (**b**) 70 μm, and (**c**) 150 μm. Image (**d**) covers a particle diameter of 135 μm and a pore diameter of 40 μm, which is in the range of the particle and pore sizes found in the experiment (see Section 3.3). White arrows in (**b**,**c**) point to the centered pore. All images are in correspondence with the values listed in Table 2.

The smallest detectable pore sizes were found to be very similar in the range between 3.0 μm to 4.4 μm for the variety of particle sizes and GVmax = 4200. This can be explained by Equation (3) using a small focal spot size of *f* = 1.3 μm and a high magnification of *M* = 200 as well as the constant unsharpness of the system, which does not require the particle diameter.

Consequently, an almost constant pore diameter as a visibility limit, independent of the particle diameter, is expected. Due to the magnification of 200, the object's scattered radiation does not contribute to the image formation process. Therefore, only the attenuation differences in the materials (pores inside the powder particles) are essential for the contrast in the radiographic image. Basically, as it is measured here (Figure 1), the contrast can be approximated as proportional to the pore diameter, which applies to small pores. The noise is independent of the pore diameter, when measured in the free beam area. This approximation was applied since the noise could not be measured accurately behind the spheres and the noise changes only slightly for low contrast indications. The simulation did confirm that the visibility limit is just between 3.0 μm and 4.4 μm pore diameter for GVmax = 4200, for a sphere diameter range of 10 μm to 150 μm and for the selected setup.

It is shown in Figure 6 that the detectable pore size does vary by about a factor of 1.5 if the particle size varies by a factor of 15. The volume of a sphere increases with the third power of its diameter. Because of this geometrical relationship, the minimal detectable pore volume percentage of a particle of a certain size decreases significantly with the particle size. Figure 8 shows the previous results (Figure 6) on detectable pores expressed as the volume percent of the particles. For GVmax = 4200, it can be concluded that for the smallest powder particles of 10 μm, the smallest visible pore volume amounts to about 5.1 vol.%. For powder particles of 25 μm, the pore volume fraction decreases to 0.25 vol.% and, for the largest powder particles studied with a diameter of 150 μm, the detectable pore volume is equivalent to only 0.0025 vol.% of the particle volume. With increased exposure time and higher magnification, even smaller percentages of pore volume in relation to the particle volume can be detected.

**Figure 8.** Minimum volume of pores detectable by digital radiography in metallic powder particles with diameters between 10 μm and 150 μm expressed as the pore volume fraction of the powder particles. The fraction of the detectable pore volume decreases rapidly with particle size. The schematic insets are not to scale.

This indicates that the contribution of the smallest detectable pore size in large powder particles to the overall porosity of the AM part is low and most likely does not affect the mechanical properties of the AM part. This is true if the volume fraction of the feedstock porosity is negligible and pore healing strategies in the AM fabrication process are applied [6,37]. A powder porosity of 5.1 vol.% is most likely critical for small particles with a diameter of 10 μm. The criticality of pore sizes in AM parts is discussed carefully in the literature, as many authors use very different materials, powder fractions, melting devices, and process parameters [1,2]. There is no strict rule for which amounts, sizes, and distributions of porosity in AM parts need to be avoided. In general, the porosity of an AM part should be as low as possible. However, it makes a difference if a single big pore or multiple very small pores create the total porosity of the AM part, as from mechanical testing it is known that the parts commonly crack at the biggest pores present [38]. Filigree and delicate AM parts, e.g., lattice structures, are especially endangered [26]. Whether a certain pore size or defect distribution is critical or not may also depend on the material, heat treatment, number of defects, arrangement of defects, location of the pores (close to surface or not), part geometry, and mechanical load. Most likely, very small pores and low total porosities are assumed to not be harmful. However, most potential harmful powder pores and large total feedstock porosities, e.g., hollow spheres or multiple medium-sized pores, can be detected by radiography for the examined particle diameters. Hence, it can be concluded that digital

radiography can reliably detect the important pores (in particles with diameters ranging from 10 μm to 150 μm), which potentially have an impact on the AM product.

#### *3.3. Experimental Results and Comparison to Simulation*

Figure 9a shows a radiograph and Figure 9b a tomogram of the multi-particle monolayer-like sample. The tomogram is used here as a basic information standard. From the images, it is obvious that the radiograph already contains most information of the powder particles, e.g., the diameters, positions, and shapes of the particles (gray regions), as well as the diameters, positions, and shapes of the pores (light gray regions). This is due to the prepared monolayer-like sample, which is optimized for 2D radiography. Most of the particles are located individually. However, in the experiment, it is difficult to prepare an exact monolayer of powder particles, and hence overlapping of particles may be observed, leading to dark gray regions. The particles are not ideally arranged and do not cover the complete detector area. Therefore, the maximum possible number of particles per image is not reached. Small satellites attached to the surfaces of the particles are visible, which originate from the atomization process. The shape of several particles deviates from a sphere and they form ellipsoidal-shaped particles. The imaged sample region contains about 70 particles in the size range of about 100 μm to 150 μm known from the 3D volume analysis. Pores of very different sizes are frequently observed in this powder sample specimen, which enhances the chance to find very small pores in this sample. Even multiple pores located in one particle are visible if they do not overlap significantly. The smallest visible pore diameter found in the radiographic image (see Figure 9a) is about 10 μm. The biggest visible pore diameters are about 80 μm. Pores with a diameter above 10 μm are directly visible without any image contrast optimization, as they show a large CNR, which is discussed in detail later. Smaller pores are more difficult to detect in big particles by human observers, as the total contrast and CNR of a small pore is low, which was described earlier (see Section 3.1, Figure 5). The detection of very small pores is difficult, as there is only one sample orientation imaged. The overlap of particles and pores present here disturbs the analysis. This applies even if the exact position of the pores is known from the tomogram (see Figure 9b). Therefore, a single particle was investigated in more detail (see Figure 10 and red arrows in Figure 9). In particular, here, a higher exposure time of the detector, leading to GVmax = 4200, was used.

**Figure 9.** Experimental verification of the simulation results. A monolayer-like multi-particle sample with diameters in between 100 μm and 150 μm and severe porosity inside was prepared and analyzed: (**a**) radiography and (**b**) rendering of the tomogram. A single particle from this monolayer-like sample was picked (red arrows) and was investigated in more detail (see Figure 10).

*Metals* **2020**, *10*, 1634

**Figure 10.** A rendered tomographic image and one radiographic projection of the single-particle sample with nine pores are shown in (**a**) and (**b**), respectively. In (**a**), the pores are numbered in correspondence to the index of the pores in Table 3. The contrast and brightness of (**b**) were enhanced based on filtering and a histogram correction, as presented in (**c**,**d**). In image (**b**), two red lines mark the profiles which belong to big pore no. 1 (**e**) and small pore no. 9 (**f**), respectively. Small pore no. 9 is highlighted by an arrow in (**d**,**f**).


**Table 3.** Measured CNR of pores in the single-particle sample.

<sup>1</sup> Pore no. 8 was detected in the tomogram, but not in the radiograph, since it was overlapped by pore no. 2 at the selected projection angle (see Figure 10a).

The single particle covers an equivalent diameter of 137 μm. The equivalent diameter of an irregular shaped volume object (pore, particle) is the diameter of a perfect sphere of equivalent volume [39,40]. From the tomogram of the single-particle sample (Figure 10a), it is known that nine individual pores of different sizes are present (see Table 3). However, to detect all pores in the radiographic image, one must turn the particle to its optimal projection direction to ensure the projected pores are visible separately. From different projection angles, the CNR was measured for the nine pores (Table 3) when the contrast sensitivity was optimal for the observer. Two-line profile plots of a big (profile plot 1) and a small (profile plot 2) pore are shown exemplarily together with radiographic images in Figure 10b–f. The contrast of the radiographs was optimized and filtered for the observed regions in Figure 10b,d to enhance the visibility on printed paper. Larger pores above 10 μm in diameter show a CNR above 8, whereas small pores down to 4 μm in diameter are close to the detectability limit of CNRmin according to Equation (2) (see Section 2.3). In some cases, the determined pore diameters from the radiography were found to be slightly smaller than the calculated volume equivalent pore diameters [39,40] from the corresponding tomogram. This can be explained by the orientation of irregularly shaped pores in the 2D projection and the usage of an equivalent pore diameter from the 3D analysis.

The presented numerical simulations show that it is feasible to detect pores down to a diameter of 3.0 μm to 4.4 μm in metallic microparticles of 10 μm to 150 μm in diameter by radiographic imaging, depending on the exposure parameters and the available setup (see Section 2.5). When comparing the experimental and simulated results, it is obvious that the numerical model is an idealized approximation of centered pores but gives valuable estimates of the detectable pore sizes. In practice, an optimal projection direction is important to identify individual pores if multiple pores per particle occur. In addition, pores are rarely placed exactly in the center of a particle. Pores located out of the center and close to the surface tend to be more difficult to detect, as they are placed within a strong signal gradient originating from the particle shape. Real feedstock powders may show satellites, irregular shapes, rough surfaces, or irregularly shaped pores, which have an orientation that is not known in any case when doing radiography. This potentially modifies the detectability. The low CNR of small pores occurring in the experiment may also originate from a variation of the device parameters. According to Equation (2), this would influence the required CNRmin to detect a pore of a certain size and may explain the difficulties to find pores close to the detectability limit in the experimental radiographs. The smallest detectable pores have a diameter of 4 μm and a CNR of about 2.5 (see Table 3), and therefore the simulated results are confirmed by the experiment within the measurement precision. As mentioned before, small pores in large particles have a negligible contribution to the total porosity of the final AM part. In contrast, large pores with a significant impact on the AM process are detected reliably.

In a final step, the pore size distribution of the metallic particles found experimentally by means of XCT (see Figure 9b) and 3D image analysis was compared with the visibility limit calculated by the simulation. Figure 11 shows the histogram of all equivalent pore diameters found in the multi-particle sample. The theoretical visibility limit from the simulation was found to be 3.0 μm to 4.4 μm for the used device and exposure conditions and is indicated as a red line. It is concluded from Figure 11 that more than 99 vol.% of the pore volume present in this powder sample can be detected using digital radiography within the 95% confidence bound.

#### *3.4. The Potential of Digital Radiography in Comparison to Other Methods for Powder Analysis*

AM powders are usually characterized by their shape and size distribution using methods like sieving, laser diffraction, or light microscopy (Camsizer® [22,25]) methods. However, as highlighted in this article, the investigation of internal powder defects, e.g., pores, is not necessarily in the scope of standard investigations. However, the density of a powder is an independent quality characteristic. To access the density or the pore size distribution of a powder, typically pycnometry, metallography, or XCT are used.

**Figure 11.** Histogram of the pore size distribution found in the metal powder by means of 3D X-ray computed tomography (XCT). Digital radiography was able to detect pores down to about 5 μm considering the 95% confidence bound at the selected setup (blue line). The predicted value for centered pores is 3 μm to 4.4 μm (red line). More than 99 vol.% of the pores volume present in this sample were detected experimentally.

All of the named methods have their benefits and drawbacks. An AM powder customized radiography technique comprises the potential to combine the best benefits of the discussed methods while minimizing the drawbacks. Sieving, laser diffraction, and light microscopy methods can screen large amounts of powder in a short time, but internal defects are not accessible. Pycnometry can also characterize large quantities of powder for its density, but not for its pore size distribution. Metallography or XCT can investigate the density and pore size distribution simultaneously. Still, both methods screen only small amounts of powder and need special attention, e.g., sample preparation or image analysis. For metallography, the sample preparation including polymer embedding, grinding, and polishing, is time-consuming. In addition, the imaging and image analysis takes time. When metallography is compared to high resolution XCT, it potentially investigates more particles, since XCT is a volume-based method and its quality of information can be treated as a "gold standard" for AM powders. However, XCT is a time-consuming method as well, including an optimal sample preparation, scanning, reconstruction, and image analysis. High throughputs of large powder batches are difficult to achieve by means of XCT.

As XCT takes projections from various angles of a sample, the data basis for the reconstructed volume and correspondingly the information content of internal sample features are much larger compared to digital radiography. However, considering the important information for AM powders, that pores are present or not, and that the actual position of the pores is not relevant per se, a radiographic imaging setup should be sufficient. The particle throughput of a radiographic setup compared to XCT is larger, even when radiography and XCT employ the same X-ray device setup. XCT needs a set of hundreds of projections from the sample for one scan. At the same time, radiography can image more particles. This is due to a geometrical relationship between the powder particle sizes and the X-ray device detector. One XCT scan can cover a cylindrical sample full of particles fitting the detector size. Imaging monolayer-like arranged powder particles fitting the complete detector by radiography leads to a larger throughput, when the XCT scan time or the amount of XCT projections is used as a time equivalent. The radiographic setup needs to be optimized for throughput, sensitivity, and resolution.

Therefore, digital radiography potentially combines the benefits of the methods, e.g., a high throughput and detailed internal powder information (pores). Drawbacks exist, as a complex sample preparation and image analysis need to be replaced by an automatic powder supply apparatus and dynamic and automated image analysis software, respectively, similar to the already employed techniques in light imaging and laser diffraction methods.

#### **4. Summary and Outlook**

The potential of digital radiography for the quality control of metal feedstock powders for AM in comparison to XCT was investigated in this work. It was shown numerically that for AM feedstock powder particles in the size range of 10 μm to 150 μm, pores down to 3.0 μm to 4.4 μm can be detected by X-ray radiography for the used commercial device in a typical setup and relevant exposure conditions. In most cases, the detectable pore size is sufficient for a quality control of the AM powder before it is processed. The numerical results were confirmed by the experiments. However, the selected X-ray setup is essential to detect smallest pores in particles. It can be improved by using a smaller focal spot size, higher magnification, longer exposure time, and a detector with smaller inherent detector unsharpness (lower SRdetector <sup>b</sup> value). Experimentally, it turned out that the orientation of the particles and pores relative to the radiographic projection direction influences the detectability, e.g., when pores or particles overlap in the radiograph. The minimal detectable pore volume amounts to around 5.1 vol.% of the particle volume for the smallest particle size studied in this work (10 μm). For the largest particle size (150 μm), this value decreases down to 0.0025 vol.%. Relevant particle pores, e.g., pores with a large pore to particle diameter ratio or large total feedstock powder porosities (multiple pores), with a potential negative impact on the AM process, are detected with high reliability by digital radiography.

As an outlook, an advanced digital radiography device can be designed to detect pores in AM powders. The powder would need to be moved on a conveyor belt or in a free-falling setup in order to achieve a high throughput. In addition, to speed up the imaging process, short exposure times are required, which can be achieved by faster and more efficient detectors and X-ray sources with high power and small focal spots, e.g., flash tubes. Such an advanced radiographic imaging setup would outrange competitive techniques and enable the opportunity to become a standard route for the quality assurance of AM powders.

**Author Contributions:** Conceptualization, G.-R.J. and A.W.; methodology, G.-R.J., A.F., and U.E.; software, G.-R.J., and A.F.; validation, G.-R.J., A.F., and U.E.; formal analysis, G.-R.J., A.F., and U.E.; investigation, G.-R.J., A.F., and U.E.; resources, A.W.; data curation, G.-R.J., A.F., and U.E.; writing—original draft preparation, G.-R.J., A.F., U.E., and A.W.; writing—review and editing, G.-R.J., A.F., U.E., and A.W.; visualization, G.-R.J., A.F., and U.E.; supervision, A.W.; project administration, A.W.; funding acquisition, none. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors gratefully thank Uwe Zscherpel, Jörg Beckmann, David Schumacher, Alexander Ulbricht, Lina Pavasaryte, and Tobias Gustmann for fruitful discussions and proofreading of the manuscript. BASF is acknowledged for providing testing material.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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## **Experimental Determination of the Emissivity of Powder Layers and Bulk Material in Laser Powder Bed Fusion Using Infrared Thermography and Thermocouples**

#### **Gunther Mohr 1,2,\*, Susanna Nowakowski 3, Simon J. Altenburg 1, Christiane Maierhofer <sup>1</sup> and Kai Hilgenberg 1,2**


Received: 29 October 2020; Accepted: 18 November 2020; Published: 20 November 2020

**Abstract:** Recording the temperature distribution of the layer under construction during laser powder bed fusion (L-PBF) is of utmost interest for a deep process understanding as well as for quality assurance and in situ monitoring means. While having a notable number of thermal monitoring approaches in additive manufacturing (AM), attempts at temperature calibration and emissivity determination are relatively rare. This study aims for the experimental temperature adjustment of an off-axis infrared (IR) thermography setup used for in situ thermal data acquisition in L-PBF processes. The temperature adjustment was conducted by means of the so-called contact method using thermocouples at two different surface conditions and two different materials: AISI 316L L-PBF bulk surface, AISI 316L powder surface, and IN718 powder surface. The apparent emissivity values for the particular setup were determined. For the first time, also corrected, closer to real emissivity values of the bulk or powder surface condition are published. In the temperature region from approximately 150 ◦C to 580 ◦C, the corrected emissivity was determined in a range from 0.2 to 0.25 for a 316L L-PBF bulk surface, in a range from 0.37 to 0.45 for 316L powder layer, and in a range from 0.37 to 0.4 for IN718 powder layer.

**Keywords:** laser powder bed fusion (L-PBF); selective laser melting (SLM); laser beam melting (LBM); thermography; emissivity; calibration; thermocouples; 316L; IN718; process monitoring

#### **1. Introduction**

Additive manufacturing (AM) technologies comprise several different modern manufacturing methods. Within metallic production routes, laser powder bed fusion (L-PBF) is of outstanding interest [1]. Due to the layer-wise nature of the process, L-PBF offers unique opportunities to monitor the complete production of a part layer by layer. Numerous monitoring approaches using various technologies and diverse methodologies can be found in the relevant literature [2,3]. They are used to monitor several different objects in L-PBF, e.g., powder bed compaction [4], particle gas emissions [5], laser power [6], and thermal emissions [7].

In this introductory section, a brief overview is given on thermal monitoring in L-PBF and the theoretical background about emissivity of real metallic surfaces. Furthermore, a brief review on temperature adjustment attempts for thermography in AM and a short survey on oxidation and its influence on emissivity are given. In Section 1.5, the calibration approach of this study is introduced.

#### *1.1. Thermal Monitoring in L-PBF*

As melting, solidification and cooling are essential for L-PBF, thermal aspects of the component during manufacturing are of utmost interest. Transient heat flux and thermal history directly affect part quality and properties of L-PBF components. Therefore, the most applied monitoring approaches deal with the spatial and temporal monitoring of heat radiation of the built-up [8]. Among the approaches of thermal condition monitoring, contactless measurement techniques are most common. Passive infrared (IR) thermography is a technology which was used by several groups of authors for thermal in situ process monitoring means [7,9–14]. IR thermography can acquire data of thermal emissions of the process layer by layer with variations in spatial and temporal resolutions, depending on the particular equipment and setup [12]. Compared to highly localized pyrometric measurements, IR cameras allow for a relatively large field of view, as well as for the capability to capture different build parts or different sections of one part at the same time without the need for an implementation that is coaxial to the laser path.

However, without appropriate calibration or adjustment of the signal of the IR camera used in the particular conditions of a specific setup, the acquired data provide information on absolute or relative radiation intensity or apparent temperatures, but not on real surface temperature values. It is interesting to note that there are currently no standardized procedures and reference standards for the calibration of infrared cameras in additive manufacturing setups. Therefore, in the following, temperature adjustment and temperature calibration are used as synonyms. This is due to the fact that the computation of temperature from data recorded with an IR camera is not only based on measured radiation intensity but highly depends on the emissivity of the target object [15]. IR cameras deliver either calculated IR signal values or apparent temperature values [13] (in the case of a previous black body calibration of the camera itself), or they deliver IR signals proportional to the radiant flux absorbed by the camera detector [16] (in the case of no previous black body calibrations or no computational considerations of such a forgone calibration). Commercial IR thermography cameras are often calibrated for black body radiation by their manufacturer. In these cases, the IR signal values, delivered by the camera, are sometimes referred as apparent temperatures, as done by the authors in other work [12]. These apparent temperatures are well below the actual temperatures of the regarded surfaces. The discrepancy between real temperatures and these apparent temperatures is mainly a result of differences in emissivity of real surfaces and black body radiators [15] on the one hand, and additional attenuation effects by optical elements in the optical path between camera and object in the particular scenery on the other hand [9,12].

Depending on the monitoring goal, the use of IR thermography without determination of real temperatures due to a missing calibration of the setup can still be very valuable, as for many issues the relative comparison of apparent temperatures or cooling rates can already provide enough informative value for particular conclusions, e.g., defect detection [7,12,16] or detection of areas of heat accumulation [7,13,17]. Therefore, the knowledge of an absolute temperature is not always necessary, especially when IR thermography is used as comparative mean against a kind of standard condition. However, there are also several research questions in which the knowledge of a calibrated absolute temperature or at least a reliable approximation of the absolute temperature would be desirable, e.g., in the field of validations of numerical modelling [18] or for considerations and classifications of in situ heat treatments during the L-PBF process [13]. Hence, a calibration of an installed IR camera at a L-PBF machine is considered to be very useful.

#### *1.2. Theoretical Background about Emissivity or Real Metallic Surfaces*

According to Usamentiaga et al. [15], the most important calibration parameter for temperature measurement using IR thermography is emissivity. They reported a general procedure to measure emissivity, i.e., the so-called contact method. This method uses a thermocouple to acquire a reference temperature of the target object, which is heated up to a temperature of real working conditions. At these conditions, the apparent temperature of the IR camera can be calibrated against the temperature of the thermocouple.

Hereafter, a brief excursus into the theoretical background and definition of emissivity is given and the introduced equations will be used in subsequent sections: The radiosity *W*λ*<sup>b</sup>* of a black body (a black body is defined by transmittance τ = 0 and reflectance ρ = 0; hence, absorptance α = 1, and thus its radiosity equals its radiant exitance) is a function of temperature *T* and wavelength λ and can be described by Planck's law, where *c*<sup>1</sup> and *c*<sup>2</sup> are radiation constants [15,19]. The peak intensities for higher temperatures are shifted towards smaller wavelengths. The shift can be explained by Wien's displacement law. Both is graphically illustrated in Figure 1.

$$\mathcal{W}\_{\lambda b}(\lambda, T) = \frac{c\_1}{\lambda^5} \frac{1}{\exp\left(\frac{c\_2}{\lambda^T T}\right) - 1} \tag{1}$$

**Figure 1.** Planck's law and Wien's displacement law graphically expressed. The visible spectrum (VIS) and the mid-wavelength infrared (MWIR) region of the camera of this study are highlighted.

It is worth noticing from Figure 1 that the most relevant temperature regions of solidified surface temperatures of L-PBF parts during cooling down after laser exposure as well as in the pre-heating condition prior to laser exposure have their maximum intensity in the mid-wavelength infrared (MWIR) region. As also summarized by Usamentiaga et al. [15], the integration of Planck's law through all

wavelengths leads to the radiant exitance of a blackbody and can be defined as in Equation (2), where σ is the Stefan-Boltzmann constant (<sup>σ</sup> <sup>=</sup> 5.6704 ... <sup>×</sup> <sup>10</sup>−<sup>8</sup> <sup>W</sup>/(m2 K4)).

$$\mathcal{W}\_{b,total} = \sigma T^4 \tag{2}$$

For the determination of the spectral emissivity, a computation of the spectral exitance is required. An integration over all wavelengths, leading to Equation (2), would be an ineligible simplification in the case of the restricted spectrum of wavelengths in thermographic applications. As IR sensors are always sensitive in a restricted spectral range only, an integration of Planck's law over the appropriate wavelengths is required. Figure 2 shows the difference in calculations for an integration over 2 μm to 5.7 μm (comparable to the spectral range of the sensor used in this study) compared to the Stefan-Boltzmann approach. This demonstrates clearly that the use of Stefan-Boltzmann would lead to significant errors.

**Figure 2.** Theoretical calculations of radiant exitance *Wb* using the Stefan-Boltzmann approach and an integration through a limited spectrum of wavelengths.

Real surfaces do not fulfill the definition of a black body. They always emit less energy than a black body. The ratio of the spectral exitance of a real body *W*λ*<sup>r</sup>* to that of a black body *W*λ*<sup>b</sup>* at the same temperature is defined as spectral emissivity ελ, see Equation (3).

$$
\varepsilon\_{\lambda}(\lambda) = \frac{\mathcal{W}\_{\lambda r}(\lambda)}{\mathcal{W}\_{\lambda b}(\lambda)}\tag{3}
$$

The emissivity of a black body is ε = 1, the emissivity of real bodies is smaller (ε < 1). For simplification reasons, the emissivity ε of solid objects is often treated as a constant and independent of the wavelength within short intervals, in which IR sensors work [15]. In doing so, real bodies are assumed to be grey bodies [15].

In the case of unknown transmission losses of the optical path between sensor and target object in a specific experimental setup, a calculation of the emissivity based on measured reference temperatures and apparent temperatures of an IR camera would result in an apparent emissivity ε*app* of the target object in the particular scenery which is smaller than the actual emissivity of the target object ε*real*.

As the aim of this work was the temperature adjustment of a specific MWIR camera setup used as thermal monitoring device at a particular L-PBF system, thereafter, ε*app* was used in the further considerations in a first stage. This simplified the analysis, as the transmission losses of the optical elements were neglected under the assumption of being constant over the respective temperature regions. These have often been referred to as being influential factors on emissivity, e.g., by Lane et al. [9]. In a second stage, a correction of transmission losses and a consideration of radiation of the ambient temperature were conducted to calculate an approximation of the real emissivity of the target object ε*corr*, although still within the grey body approximation.

The emissivity of a real target object depends on several factors: material, surface condition (surface roughness and oxidation state), viewing angle, temperature and wavelength [20]. The published reference values of emissivity of different materials in data sheets are usually considered as being captured perpendicular to the surface of the target object [21]. Metals and their alloys have considerably low emissivity values and undergo heavy variations due to their surface conditions [22], e.g., polished steel sheets have ε = 0.1 at a temperature of *T* = 310 ◦C, but in aged and oxidized condition, they show an emissivity of up to ε = 0.8. For stainless steel AISI 316 in polished condition, one can find emissivity values between 0.24 and 0.31 in a temperature range of 200 ◦C to 1040 ◦C [21].

#### *1.3. Calibration Attempts for Thermography in Additive Manufacturing*

Within the scope of IR thermography in AM, some work has been published that includes attempts to calibrate a particular IR camera setup or to evaluate emissivities for particular process conditions. The differences of the cooling rate of the transition between liquidus and solidus in the melt pool can be used as a kind of single-point calibration in cases where the temporal or spatial resolution of the camera allows for reliable capturing of this condition. This was done by Doubenskaia et al. [23] for laser metal deposition (LMD) using TiAl6V4. They used an IR camera sensitive in a spectral range from 3 μm to 5 μm and calculated an emissivity of ε = 0.201 at the transition temperature. Yadroitsev et al. [24] also used the liquidus solidus transition during a L-PBF process using TiAl6V4. They used a CCD camera setup coaxial to the laser path and measured at a wavelength of 0.8 μm. They calculated an emissivity of ε = 0.35 at the transition temperature. Heigel and Whitenton [25] determined the liquidus-solidus transition for the calibration of a SWIR camera monitoring the L-PBF process of the nickel-based alloy IN625. Additionally, they calculated the effective emissivity of a L-PBF IN625 surface as ε = 0.168, based on the transition temperatures [25]. Other work by Lane et al. [9] argued for using assumption-based estimations of uniform emissivity values of ε = 0.5 as long as no measured emissivity values are available and in order to still use temperature values instead of IR signal values.

As mentioned above, a possible approach for transforming IR signals or apparent temperatures of IR cameras into real temperatures is the synchronous use of a second but already calibrated temperature measuring technique during IR capturing, which measures the temperature of the object of investigation directly as a reference. The classic approach for this is the contact method, using thermocouples (TC) for reference temperature measurement. There is only limited work published on this for L-PBF. Heigel et al. [26] and Williams et al. [14] presented calibration results of the contact method for their specific camera setups.

Williams et al. [14] installed an IR camera of type A 35 (FLIR Systems Inc., Wilsonville, OR, USA) in the build chamber of a commercial L-PBF system of type AM250 (Renishaw plc, Wotton-under-Edge, UK) using an observation angle of 24◦ (detector plane to build plane). The resulting resolution of their setup was approximately 1 mm<sup>2</sup> per pixel, captured at a framerate of 60 Hz. They used a heated AM calibration component manufactured by L-PBF using 316L with and without powder on top of it. The real surface temperature was measured by one TC. The results were directly used for a determination of in-process surface temperatures of built parts, which were monitored afterwards in the same study. They abstained from any calculation of apparent or real emissivity values.

Heigel et al. [26] calibrated an IR camera sensitive in a reduced spectral range of 1.35 μm to 1.6 μm by using a purposely built calibration setup outside of a L-PBF system. Their calibration setup ensured similar conditions to their monitoring setup at a L-PBF system of type M270 (EOS GmbH, Krailing, Germany) presented by Lane et al. [9], i.e., using an observation angle of 45◦ to 43.7◦. They used a heated AM calibration component manufactured by L-PBF using IN625. They calculated an emissivity ε = 0.680 of a rather smooth surface (Sa approximately 12 μm) and an emissivity ε = 0.761 of a rather rough surface (Sa approximately 27 μm). Oxidation of IN625 was also considered, but resulted in being negligible as a factor of emissivity in their study. However, the question as to whether the not purposely oxidized specimens (post process oxidation was conducted for some specimens) might have already been oxidized during the built process remained unclear.

#### *1.4. Oxidation and Its Influence on Emissivity*

In the frame of this study, knowledge regarding oxidation growth at steel surfaces and its effect on emissivity in general is needed for the discussion section. Hence, a brief excursus is given hereafter, based on the relevant literature, summarizing published results on oxide layer thickness of steels and its influence on emissivity. Thickness growth of material dependent oxide layers depends on atmosphere, temperature and time. When assuming a constant atmosphere, temperature and time play important roles in the evolution of an oxide layer.

Hakiki et al. [27] measured the oxide film thickness of austenitic stainless steel AISI 304 (1.4301) tempered in the temperature range between 50 ◦C and 450 ◦C in air for 2 h. The film thickness varied between 8 nm (50 ◦C) and 30 nm (450 ◦C) [27].

Kämmerer [28] measured the thickness of oxide layers of cold-rolled plates of the ferritic steel AISI 441 (1.4509) tempered in air. She showed the exponential relationship between tempering temperature and oxide layer thickness. She examined a change in oxide layer growth rate between 400 ◦C and 500 ◦C towards higher growth rates for higher temperatures, at a tempering time of 10 h. At a tempering temperature of 400 ◦C, no significant change of oxidation thickness could be revealed between holding times of 1 h and 10 h. The measured oxide layer thickness was between 3 nm and 3.5 nm at a tempering temperature of 400 ◦C and approximately 4 nm at 500 ◦C (holding time 10 h). However, repeated tempering with interim cooling down (10 times 1 h at 400 ◦C) resulted in doubling of the oxidation layer thickness [28].

According to Janssen [29], who studied oxidation of austenitic stainless steel AISI 304 (1.4301) in air, the literature values about the thickness of a passive oxidation layer of steels varied between 1.5 nm and 8 nm (mostly in the area 2 nm +/− 0.6 nm). During his oxidation experiments, a slight yellow annealing color started to be visible by eye at 550 ◦C (5 min holding time) changing to gold-yellow at 600 ◦C (9 min holding time) and darkened after a subsequent 10 min holding time at 595 ◦C. During the temperature rise from 410 ◦C to 550 ◦C, he observed a distinct increase in oxidation of chromium and iron. From approximately 580 ◦C and especially from 600 ◦C, the oxidation rate of iron increased strongly, while the chromium oxidation rate increased slightly. This was in accordance with his measurements of the oxidation layer thickness: A first distinct growth of the oxidation layer was measurable after a temperature rise from 410 ◦C to 550 ◦C, followed by a strong increase in the temperature region from 550 ◦C to 600 ◦C. At 900 ◦C, the oxidation layer thickness was around 35 nm to 65 nm with an additional 2 μm to 3 μm thick scale layer.

Iuchi et al. [30] investigated the modelling of an emissivity change during the growth of oxide layers for a wavelength of λ = 1.5 μm at cold rolled steel tempered at 500 ◦C. They found that the emissivity behavior of oxide films thinner than 5.8 nm was almost identical to that of non-oxidized surfaces. For oxide films thicker than 39.1 nm, the emissivity behavior changed drastically from approximately ε = 0.3 (at 5.8 nm) to approximately ε = 0.7 (at 39.1 nm); ε = 0.8 (at 54.2 nm); ε = 0.87 (at 82.7 nm) [30].

According to Zauner et al. [31], the change of emissivity of steel surfaces due to the growth of an oxide layer reached a first maximum above ε > 0.8 for an oxide film thickness of about 100 nm. While the emissivity fluctuated in the beginning of the growth phase, it started to stabilize after reaching approximately 500 nm film thickness at a value of ε = 0.85. These results were based on theoretical calculations. The fluctuations stem from interference phenomena of reflectance at oxide films at metallic surfaces which depended on oxide film thickness [31].

Del Campo et al. [32] studied the oxidation kinetics of iron below 570 ◦C and conducted emissivity measurements at four different temperatures: 415 ◦C, 480 ◦C, 535 ◦C, 570 ◦C. Their results for thin oxide films were not contradicting to the afore mentioned. However, they had a stronger focus on various spectral wavelengths and on thicker oxide layers resulting from longer holding times.

#### *1.5. Calibration Approach of This Study*

The literature basis regarding emissivity determination and IR camera calibration for L-PBF is limited, also due to the requirement of specificity of each setup. Thus, this study aimed for the experimental temperature adjustment of an off-axis MWIR thermography setup, which was used for in situ thermal data acquisition of L-PBF processes in other studies of the authors [13,17]. The contact method was applied for this purpose. Furthermore, a correction of apparent emissivity values of the specific setup was pursued in in order to receive setup independent emissivity values of L-PBF bulk material and powder layers, which might be useful for, e.g., numerical simulations. A third goal of this work was the transferability of the technical equipment used during the calibration for the later use in other specific setups.

#### **2. Materials and Methods**

This section describes the experimental setup, the used equipment and materials, as well as the experimental variations.

#### *2.1. Thermographic Measurement Setup and L-PBF System*

A MWIR thermographic camera of type ImageIR8300 (InfraTec GmbH, Dresden, Germany) was mounted on top of a commercial L-PBF system of type SLM280HL (SLM Solutions Group AG, Lübeck, Germany). It had optical access to the build chamber through a purposely installed sapphire window in the ceiling of the chamber. The optical path was deflected by two gold mirrors to shift the observation field in the direction of the center of the build plate while keeping the angle of observation at approximately 0◦ (angle between detector plane and build plate plane). Compared to similar off-axis IR camera setups used as thermal monitoring device in L-PBF (cf. Krauss et al. [33], Lane et al. [9]), the nearly perpendicular view onto the build plane is beneficial in terms of having a large focus area. Tilted systems are always faced with very limited areas which are in focus and usually have large defocused areas. A schematic and two photographs illustrate the setup in Figure 3. The same setup was also used in other work of the authors [13,17] in the same configuration for in situ process monitoring means. The schematic also includes the heating device, which is described in Section 2.2.

**Figure 3.** MWIR camera setup: installed camera on top of L-PBF machine ((**a**) side view, dimensions of the process chamber: (280 <sup>×</sup> 280 <sup>×</sup> 360) mm3; (**b**) top view, dimensions of the camera body; (244 <sup>×</sup> <sup>120</sup> <sup>×</sup> 160) mm3; (**c**) schematic, not to scale).

The camera used a cooled InSb-focal-plane-array of size 640 pixel × 512 pixel and a bit resolution of 14 bits was used. A 25 mm objective lens was used, resulting in a spatial resolution of the setup of approximately 420 μm per pixel length. No additional external filters were used. The camera was sensitive in a spectral range from 2 μm to 5.7 μm. The optical path outside of the build chamber was shielded by blackened metallic tubes, it could be interrupted manually by a shutter. According to the manufacturer's specifications, the reflectivity of the gold mirrors was above 99% in the spectral range of the camera, the transmissivity of the window above 83%. Typical spectral reflectivity (mirrors), transmissivity (window, objective, camera internal filters) and sensitivity (camera detector) were known to be at least in the relevant spectral range between 2 μm and 5.7 μm and were used for the emissivity calculation in Section 3.3.

The camera was calibrated using a black body radiator by the manufacturer in different calibration ranges that could be chosen for the specific experiment. The following camera calibration ranges were used:


Frame capturing of the camera was conducted at 100 Hz. To reduce the amount of data, a subframe was used for capturing a size of 224 pixel × 160 pixel, similar to the cited in situ measurements.

#### *2.2. Heated Reference Device*

A specimen was manufactured by L-PBF using 316L, which was used as the heated AM reference part. The manufacturing parameters were in accordance with the standard parameters used in [13] (laser power of 275 W; scanning velocity of 700 mm/s; hatch distance of 0.12 mm; layer thickness of 0.05 mm; bi-directional scanning parallel to the edges of the specimen). No additional up-skin parameter was applied. The surface area roughness of the top surface was approximately Sa = 7 μm, determined at two areas of 0.8 mm × 10 mm using a coherence scanning interferometry profilometer of the type Nexview (Zygo Corp., Middlefield, CT, USA). The cuboid specimen had the dimensions 13 mm × 20 mm × 140 mm. In the middle of the upper surface of the specimen, a cross-like artefact with a depth of 0.5 mm was manufactured to help finding the focus level during the calibration experiments. The rim of the specimen was elevated by 0.5 mm at a width of 1 mm.

A fixture was constructed that ensured the upright standing of the specimen, as well as thermal insulation between the specimen and the fixture by ceramic plates. A heating mat and a heating inverter of type ST11 (Sokol-Therm Deutschland GmbH, Eisenhüttenstadt, Germany) were used to heat up the specimen. The specimen was wrapped by the heating mat and placed within a sheet metal enclosure. For insulation reasons, an insulation wool was placed between the heating mat and the enclosure. To shield heat radiation towards the camera which did not come from the heated AM specimen, high-temperature fiberboard was used to cover the top of the heating device. Four K-type thermocouples (TC, TC1 to TC4) of 0.127 mm diameter were spot welded at the four sides of the specimen approximately 1 mm below the upper surface of the rim. At one side, an additional TC (TC Inv.) was installed to act as target measuring point for the heating inverter. The responses from the thermocouples were acquired through a measuring amplifier device of type MX1609 (HBM GmbH, Darmstadt, Germany) at a sampling rate of 10 Hz. The heating device was positioned by lowering the build plate lift of the machine in such a way that the surface of the reference specimen was in the usual build plane of the L-PBF setup. A schematic of the specimen surface and the clamping are shown in Figure 4. This also includes the positioning of the thermocouples. Figure 5 shows photographs of the heating device. Two separate TCs were spot welded at the sheet metal and the substrate, respectively, in order to monitor the heat development at the device.

**Figure 4.** (**a**) schematic of heating device without outer insulation; (**b**) schematic of specimen surface indicating TC positions.

**Figure 5.** Photographs of mounted heating device: L-PBF reference specimen (**1**); heating mat (**2**); insulation wool (**3**); sheet metal enclosure (**4**); high-temperature fiberboard on top of the device (**5**); the heating device is placed at its measuring position (position 1, as described in Section 2.4.3).

#### *2.3. Examination Methodology*

Recording of MWIR camera data and TC data was started synchronously by the experimental conductors at different times during the heating cycle. The apparent temperature data of the MWIR camera were gained by using the software IRBIS3 professional (InfraTech GmbH, Dresden, Germany). Four regions of interest (ROIs) were defined across the top surface of the specimen, excluding the cross in the middle of the surface as well as the rim in order to exclude additional surface property effects, cf. Figure 6. The mean temperatures of these four ROIs were exported as ASCII files. Subsequent analysiswas conducted using the software Origin 2019 (OriginLab Corporation, Northampton, MA, USA). The total mean of all pixels within the four ROIs was taken as apparent temperature value of the camera. Considerations of standard deviations and fluctuations are discussed in Section 3.5. The TC temperature data were also analyzed using Origin 2019.

**Figure 6.** Schematic of the ROIs (purple color) for data capture.

#### *2.4. Experimental Measurment Variations*

The temperature calibration experiments were conducted at different conditions, which are introduced in this section. Unless stated otherwise, all experiments were conducted under typical L-PBF working conditions. Thus, the experiments were conducted inside the build chamber and under argon gas atmosphere at a gas flow velocity of approximately 21.5 m/s (measuring sensor in the gas circulation pipes), with a gas flow flushing the chamber from the right to the left. A one-point nonuniformity correction (NUC) was always conducted before the beginning of any new capturing of the MWIR camera. This was done by placing a shutter in the optical path outside of the build chamber and using the NUC function of the camera. The optical shutter was at room temperature. A manual refocusing of the objective lens was conducted whenever a blackbody calibration range of the camera was changed. This was necessary, since the additional camera internal filters A and B in the calibration ranges 200–400 and 300–600 changed the optical path length.

The following experimental variations were investigated using different camera calibration ranges:


The individual experiments are explained in detail in the respective sections.

#### 2.4.1. Temperature Variations at a Non-Oxidized L-PBF Surface (316L)

During the temperature variation experiments, the virgin 316L L-PBF specimen was heated up to a temperature of 750 ◦C in several stages in the L-PBF build chamber. Data couples of TC temperatures and apparent temperatures were acquired. The heat up was paused at different temperature stages to reach temperature plateaus. Different camera calibration ranges were used during the data acquisition (see Section 2.1). The sheet metal enclosure of the heating device reached a maximum temperature of approximately 350 ◦C and the substrate of the fixture a maximum temperature of approximately 375 ◦C during the heating experiments. All temperatures measured by the temperature sensors of the L-PBF system stayed within the narrow rage of the specifications of the manufacturer during the experiments, e.g., the build chamber temperature was between 31 ◦C and 36 ◦C.

#### 2.4.2. Temperature Variations at Powder Surface (316L and IN718)

Two different powder materials were spread on top of the specimen in two separate experiments before the heating up. The powder was manually placed using a spatula in the middle of the top surface of the specimen and then spread manually over its entire surface by using a razor blade. Thereby, a powder bed of approximately 500 μm thickness was generated according to the dimensions of the rim. Table 1 contains information of the powder properties according to supplier's information (SLM Solutions Group AG, Lübeck, Germany). The heating device with the powder bed on top was heated up to 650 ◦C in several stages.


**Table 1.** Powder properties according to supplier's information.

#### 2.4.3. Positioning

To evaluate a potential influence of the x-y position of the target object within the build chamber, measurements were conducted at three different positions as illustrated in Figure 7. The heating device was placed manually. The measurements were carried out at a specimen surface temperature of around 400 ◦C. The center of the specimen was approximately located at the following coordinates (reference 0 as in Figure 7, coordinates in mm): x140, y66 (Position 1); x113, y81 (Position 2); x143, y140 (Position 3). Position 1 and position 2 are approximately at the positions where two of the in situ monitored specimens of [13,17] were located. Position 3 was representative of a specimen in the center of the L-PBF substrate plate. The tilt of the gold mirrors as well as the focus of the camera had to be adjusted to capture position 3. Position 1 and position 2 were located within the same chosen field of view. These measurements were conducted using an oxidized specimen, which was oxidized in pre-tests of the heating device up to a temperature of 600 ◦C outside of the L-PBF machine at ambient atmosphere beforehand. Apart from the position shifts described here, all other experiments were conducted at approximately position 1.

**Figure 7.** Positioning of the heated specimen on top of the (lowered) build plate.

#### *2.5. Determination of Emissivity Values*

Two different ways of determining emissivity values were implemented, resulting in non-corrected, so-called apparent emissivity values and corrected, closer-to-real emissivity values. The values were calculated for the distinct measurement points, which comprised the temperature of the thermocouples *TTC*, the apparent temperature of the MWIR camera *Tapp*, and the temperature in the build chamber *T*0.

#### 2.5.1. Determination of Apparent Emissivity Values

The computation of emissivity values without consideration of transmission losses and thermal stray radiation leads to the so-called apparent emissivity ε*app*. The apparent emissivity ε*app* can be computed using Equation (3) (neglecting the wavelength dependency, grey body approximation). Thereby, an integration of Equation (1) (Planck's law) in the spectral range of the MWIR camera (λ<sup>1</sup> = 2 μm to λ<sup>2</sup> = 5.7 μm) for the reference TC temperature (*W*λ*b*) and for the apparent temperature of the camera of the respective calibration range (*W*λ*r*) must be conducted:

$$\varepsilon\_{\lambda}(T = T\_{TC}) = \frac{\int\_{\lambda\_2}^{\lambda\_1} \mathcal{W}\_{\lambda r}(\lambda\_\prime T\_{app}) d\lambda}{\int\_{\lambda\_2}^{\lambda\_1} \mathcal{W}\_{\lambda b}(\lambda\_\prime T\_{TC}) d\lambda} \tag{4}$$

This simplified analysis was performed, since it is a widely used way to estimate emissivity values.

#### 2.5.2. Determination of Corrected Emissivity Values

The calculation of the apparent emissivity by Equation (4) is a rough estimate. This analysis neglects the radiation that was reflected from the surroundings at the surface as well as all the spectral characteristics of all optical elements and the camera detector. Assuming a homogeneous thermal background radiation of a black body at temperature *T*0, the emitted spectral radiosity of a grey body is:

$$\mathcal{W}\_{\lambda r}(\lambda, T, \varepsilon, T\_0) = \varepsilon(T) \cdot \mathcal{W}\_{\lambda b}(\lambda, T) + (1 - \varepsilon(T)) \cdot \mathcal{W}\_{\lambda b}(\lambda, T\_0) \tag{5}$$

Here, the spectral and angular dependence of ε are still neglected; thus, the determined values are still effective values for the spectral range of the camera. To better estimate the surface emissivity, first, the total irradiance measured by the camera during calibration at a black body was calculated, considering the spectral transmissivity of the optics present during the calibration τ*opt*,*cal*(λ) and the spectral responsivity of the detector *S*(λ):

$$E\_{\rm call}(T) = \int\_{-\infty}^{\infty} \mathcal{W}\_{\lambda b}(\lambda, T) \cdot \tau\_{\rm opt, call}(\lambda) \cdot \mathcal{S}(\lambda) \cdot d\lambda \tag{6}$$

Please note that the influence of the atmosphere (absorption and emission) is neglected here as well. Knowing the needed optical properties (at least typical values), *Ecal*(*Tapp*) can be calculated for all measured apparent temperatures *Tapp*, using Equation (6). Then, in a next step, the radiance of the surface that was measured during the experiment by the camera can be calculated as follows:

$$E\_{\rm max}(T,\varepsilon,T\_0) = \int\_{-\infty}^{\infty} \mathcal{W}\_{\rm Jr}(\lambda, T, \varepsilon, T\_0) \cdot \pi\_{\rm opt,rms}(\lambda) \cdot \mathcal{S}(\lambda) \cdot d\lambda \tag{7}$$

For each measurement point above, the temperature of the inner ceiling of the build chamber was monitored by the L-PBF system's sensors. This temperature was used as surroundings temperature *T*<sup>0</sup> here. Please note that the experimental transmissivity τ*opt*,*meas*(λ) was dependent on the selected calibration range of the camera, since the camera internal absorptive filters differed.

As the camera outputs the same values at the same irradiance rather than at the same temperature of the object observed by the camera, the emissivity can be reconstructed by setting:

$$E\_{\rm cal}(T\_{app}) = E\_{\rm mens}(T\_{TC}, \varepsilon, T\_0) \tag{8}$$

for each measurement point (*TTC*, *Tapp*, *T*0), where ε was the only unknown variable. Thus, ε*corr* was determined by:

$$\kappa\_{\rm corr} = \underset{0 < x < 1}{\text{arg min}} \left| E\_{\text{meas}}(T\_{\text{TC}}, \varepsilon, T\_0) - E\_{\text{cal}}(T\_{\text{app}}) \right| \tag{9}$$

#### **3. Results and Discussion**

#### *3.1. Selection of Thermocouples*

The TCs showed temperature deviations depending on their position with respect to the sample surface and the gas flow, as shown in Figure 4. Figure 8 shows exemplarily a sequence of TC measurements during a cooling down phase of the specimen. While deviations of the measured temperature were small between TC1, TC3 and TC4, the temperature measured at TC2 was remarkably lower than at the other TCs. TC2 was directly placed in the gas flow. This deviation could be associated with the gas flow, as the difference decreased when reducing the gas flow velocity at the times of 103.5 s (21.5 m/s before 103.5 s), 217 s (reduction to 14.9 m/s until 217 s), 330 s (reduction to 8.9 m/s until 330 s) and 344 s (reduction to 0 m/s until 344 s, no gas flow after 344 s) in the presented example. Thus, TC2 values were excluded from further examinations. The mean of TC1, TC3 and TC4 was taken as surface reference temperature in all subsequent considerations. A constant surface temperature was assumed. A consideration of measurement uncertainty is given in Section 3.5.

**Figure 8.** Effect of gas flow on TC temperature. The gas flow velocity decreases at the highlighted times.

#### *3.2. Apparent Emissivity*

The apparent emissivity values are presented in the following subsections for the 316L L-PBF surface, the 316L powder layer and the IN718 powder layer.

#### 3.2.1. Apparent Emissivity of the 316L L-PBF Surface

The comparison of the reference temperature values of the 316L L-PBF surface, the mean value of three TCs (see Section 3.1), and the respective apparent temperature values, calculated as the mean apparent temperature of the four ROIs (see Section 2.3) of the MWIR camera data, clearly indicated that the apparent temperature values of the black body calibrated MWIR camera underestimated the reference temperatures. The difference between reference temperature and apparent temperature increased from approximately 64 ◦C to 181 ◦C at reference temperatures of approximately 134 ◦C and 579 ◦C, respectively. This underestimation was not surprising, as the emissivity of the real L-PBF surface was expected to be much smaller than unity, which was assumed by the apparent temperature computation of the camera. Figure 9 displays data couples of TC reference temperatures and apparent temperatures of the MWIR camera (black hollow symbols). Three different calibration ranges of the camera were used to measure the large variance of surface temperatures during the experiment (see Section 2.1). The measured data for each calibration range are distinguished by the distinct symbols (circle, square, triangle) in the plot. The connected data points of the calibration ranges 60–200 and 200–400 follow a linear trend, whereas a non-linear trend is revealed for the calibration range 300–600. In addition, steps between the curves of the distinct calibration ranges are noticeable. Both are discussed in the course of the emissivity determination, below.

**Figure 9.** Apparent temperature (black hollow symbols) and apparent emissivity (blue full symbols) of 316L L-PBF bulk surface over measured TC temperature. In the camera calibration range 300–600, measurements were conducted before the onset of increased oxidation (star symbols) and after oxidation (circle symbols).

The apparent emissivity ε*app* of the 316L L-PBF surface was computed using Equation (4) (neglecting the wavelength dependency, grey body approximation) for all data couples presented in Figure 9 (reference temperatures between 134 ◦C and 700 ◦C). In addition to the temperature data couples (black hollow symbols), Figure 9 displays the respective apparent emissivity ε*app* (blue full symbols).

The apparent emissivity ε*app* of the surface of the L-PBF specimen in the particular setup showed a decrease in the camera calibration range 60–200 with increasing temperature, starting at ε*app* = 0.25 at a temperature of 134 ◦C, leveling off to ε*app* = 0.18 at temperatures above 300 ◦C. However, the radiation of the ambient temperature was not considered for this calculation of the apparent emissivity. Especially for lower temperatures, which were of a similar magnitude as the ambient temperature, the radiation of ambient temperature is expected to lead to significant falsifications if not considered. A correction analysis including data of measured ambient temperatures of the build chamber of around 33 ◦C is presented in Section 3.3.

When switching the calibration range from 60–200 to 200–400 at constant TC temperature, there was a jump in the apparent temperature of more than 25 K. This led to an increased apparent emissivity of the surface of the L-PBF specimen of approximately ε*app* = 0.28 at temperatures between 350 ◦C and 580 ◦C. To examine this peculiar effect, additional experiments were conducted outside of the L-PBF setup: Firstly, experiments were performed using a black body radiator (Fluke 4181, Fluke Corporation, Norwich, UK) set to a temperature of 200 ◦C. Changes of the camera calibration range between 60–200 and 200–400 showed only a small deviation of the measured temperature by the camera of below 1 K, indicating a correct black body calibration. Secondly, further investigations using 316L samples produced in the described L-PBF machine, heated on a hot plate to 200 ◦C were conducted. Here, the jump in the apparent temperature observed in the calibration experiment at the L-PBF setup was reproduced. Thus, this effect was in fact caused by the non-unity emissivity of the material. A consultation of the camera manufacturer revealed that the absorptive filter elements that were introduced to the optical path within the camera in the calibration ranges at elevated

temperatures (200–400, 300–600) have a transmissivity that strongly depends on the wavelength. Therefore, their spectral transmissivity had to be considered for a correct emissivity determination and correction. A further analysis is presented in Section 3.3. The big step between the apparent emissivity values of distinct calibration ranges obtained by the simple analysis approach can be seen as an imposing example of the risk of data misinterpretation when using commercial thermography cameras with various calibration ranges. Unless clearly stated by the vendor, one has to be very careful when transferring experimentally determined values to slightly other conditions of the setup, in this case to another camera calibration range.

#### 3.2.2. Oxidation Effects on the Apparent Emissivity of the 316L L-PBF Surface

At TC temperatures above approximately 500 ◦C, tempering colors could be recognized by the human eye, beginning with a slightly brownish appearance, which darkened until approximately 580 ◦C and then turned into a bluish appearance, inspected through the green UV protection window of the process chamber door. Thus, despite the low oxygen content in the build chamber during the experiments, oxidation of the heated surface was still occurring. Oxidation layers can drastically change emissivity values. This effect is well known in the literature [20], and an excursus into this matter is therefore given in the introduction Section 1.4.

Such an oxidation-driven change of emissivity values was clearly revealed at temperatures above 580 ◦C (compare Figure 9). Additionally, a slight increase in apparent emissivity could be seen for temperatures above 500 ◦C (increase from 0.28 to 0.29), which might be attributed to the onset of oxidation as visually noticed during the heat up. While the apparent emissivity change between 500 ◦C and 580 ◦C was very small, the emissivity values changed drastically above 580 ◦C. The oxidation of the surface got too strong to present reliable emissivity values of an unoxidized or only slightly oxidized 316L L-PBF surface above 580 ◦C. The measurement data which are displayed transparent in Figure 9 and their respective computations of emissivity values were heavily influenced by a change of emissivity due to oxidation. This was in good agreement with the visually noticeable tempering colors and the literature review. For example, apparent emissivity values of 0.58 were determined using the same camera in the laser metal deposition of AISI 316L, where stronger oxidation is expected to occur due to a less efficient shielding of oxygen by a local shielding gas flow in surrounding air conditions [34].

Remarkably, there are measurement points between 500 ◦C and 580 ◦C TC temperature, which were obtained at different times and different camera calibration ranges, i.e., calibration ranges 200–400 and 300–600, showing huge differences in apparent emissivity for the same temperatures. The measurement of the data points symbolized by full circles (calibration range 300–600) was conducted approximately 70 min after the measurement series symbolized by triangles (calibration range 200–400). The temperature of the specimen in between these two measurement series was constantly higher than 530 ◦C, most of the time around 600 ◦C. Apparently, the oxidation layer thickness was still very small during the measurements in the calibration range 200–400, but had enough time and temperature to grow before the measurements at a calibration range of 300–600 were conducted. This would explain the discrepancy between apparent emissivity for the same TC temperatures. Interestingly, the apparent emissivity step in Figure 9 between the calibration ranges 200–400 and 300–600 can be explained by oxidation without further correction for the change of the internal filter of the camera: The measurement of the extra dot (star symbol) was taken using the calibration range 300–600 during the measurement series represented by triangles (200–400), and thus before the strong oxidation started. It shows a very similar apparent emissivity to the results obtained in the 200–400 calibration range. This observation might be explained by a similar spectral dependence of the transmissivity of filter A and B (at lower amplitudes for filter B). This is important to know, for any later use of these calibration ranges, which were identified as most relevant for in situ L-PBF monitoring means (cf. [13]).

#### 3.2.3. Apparent Emissivity of the 316L Powder Layer

The determination of the apparent emissivity and the comparison of TC reference temperatures and thermographically acquired apparent temperatures of the 316L powder layer followed the same procedure as for the solid 316L L-PBF surface, described and discussed in the previous section. Figure 10 displays the respective temperature data couples and computed apparent emissivity values of the 316L powder for the three different camera calibration ranges. For comparison reasons, it also contains the respective values of the L-PBF 316L surface at similar conditions in transparent colors.

The non-corrected emissivity values of the powder layer leveled to approximately ε*app* = 0.33 in the camera calibration range 60–200. Before the onset of increased oxidation above 580 ◦C, apparent emissivity was calculated to approximately ε*app* = 0.43 for the camera calibration ranges 200–400 and 300–600. In comparison to the solid L-PBF surface of the same material, the 316L powder layer showed significantly increased emissivity values. This was already mentioned in the literature, e.g., in [14], and originates from the strongly increased surface roughness of a powder layer compared to a solid L-PBF surface. It also explains the potential occurrence of apparent temperatures of new recoated powder layers which could be higher than the apparent temperatures at the same position prior to recoating in L-PBF real manufacturing, monitored by in situ thermography, as in [17].

**Figure 10.** Apparent temperature (black hollow symbols) and apparent emissivity (green full symbols) of the 316L powder layer over measured TC temperature. For comparison, apparent temperature (gray hollow symbols) and apparent emissivity (blue full symbols) of the 316L L-PBF bulk surface over TC temperature are also depicted.

#### 3.2.4. Apparent Emissivity of the IN718 Powder Layer

The determination of the apparent emissivity and the comparison of TC reference temperatures and thermographically acquired apparent temperatures of the IN718 powder layer followed the same procedure as for the 316L L-PBF surface, described and discussed in Section 3.2.1. The results are plotted in Figure 11. The non-corrected emissivity values of the IN718 powder layer leveled to approximately ε*app* = 0.34 in the camera calibration range 60–200. The apparent emissivity was calculated to approximately ε*app* = 0.41 to 0.42 for the camera calibration ranges 200–400 and 300–600. The determined apparent emissivity values of the IN718 powder layer were at a similar level as the values of the 316L powder layer, depicted in Figure 12. In contrast to the 316L powder, the rise of apparent emissivity values above 580 ◦C is significantly smaller, which is assumed to be attributed to other oxidation kinetics for the nickel-based IN718 as compared to the stainless steel 316L. This is in

good agreement with experiments by del Campo et al. [35], who showed a rather small influence of short-term oxidation at 700 ◦C of IN718 on emissivity.

**Figure 11.** Apparent temperature (black hollow symbols) and apparent emissivity (brown full symbols) of IN718 powder layer over measured TC temperature.

**Figure 12.** Comparison of apparent emissivity results of IN718 powder layer (brown full symbols) and 316L powder layer (green symbols) over measured TC temperature.

#### *3.3. Determination of Corrected Emissivity*

The corrected emissivity values ε*corr* are presented in the following subsections for the 316L L-PBF surface, the 316L powder layer and the IN718 powder layer. The correction analysis is described in Section 2.5.2.

#### 3.3.1. Corrected Emissivity of 316L L-PBF Surface

When considering the radiation that was reflected from the surroundings at the surface as well as all the spectral characteristics of the optical elements including the different internal filters as described above, some fundamental changes of the corrected emissivity curves compared to the apparent emissivity curves (discussed in Section 3.2.1) can be observed. Figure 13 compares the corrected emissivity values with the non-corrected apparent emissivity values. The following discussion focuses on the emissivity values of the non-oxidized surface, i.e., below 580 ◦C.

**Figure 13.** Comparison of corrected (blue symbols) and non-corrected apparent (black hollow symbols) emissivity values of 316L L-PBF bulk surface over measured TC temperatures.

First of all, the significant effect of apparently increasing emissivity values in the lower temperature region decreased drastically. The radiation of the surroundings (build chamber temperature around 33 ◦C) had a strong influence at relatively low temperatures of the target object, which resulted in the apparent increase of the non-corrected emissivity values with decreasing TC temperatures. Therefore, the corrective analysis flattened the curve in this region. However, there is still a slight increase below a TC temperature of 250 ◦C. This was assumed to be a result of the position of the TC of the L-PBF system within the build chamber, which was located toward the front of the chamber ceiling, rather than close to the optical path of the IR camera. As a result of the TC position, a slight underestimation of the radiation of the surroundings *T*<sup>0</sup> could be assumed to be responsible for this, as, e.g., a value of *T*<sup>0</sup> = 38 ◦C leads to a complete flattening of the curve.

Secondly, the huge jump of the apparent emissivity values connected to the change of the calibration range of the camera from 60–200 to 200–400 almost disappeared by the correction analysis as a result of the consideration of the distinct spectral transmissivities of the respective internal filters, which changed with the changing calibration ranges. The small remaining jump between the real emissivity values of the different calibration ranges is assumed to be attributed to possible slightly differing optical parameters of the actual optical elements from the typical values used for the calculations (see Section 3.5).

It was revealed that the emissivity of the L-PBF bulk surface used in this experimental setup increased with increasing temperatures. The computed emissivity of 316L L-PBF bulk surface varied between ε*corr* = 0.2 and ε*corr* = 0.23 in the temperature region from 200 ◦C to 500 ◦C and between ε*corr* = 0.23 and ε*corr* = 0.25 in the temperature region between 500 ◦C and 580 ◦C, where slight oxidation effects could not be excluded, as discussed in Section 3.2.1. These values are in good agreement with literature values of stainless steel [36], as presented in Figure 14.

**Figure 14.** Corrected emissivity of 316L L-PBF bulk surface (blue symbols) over measured TC temperature. For comparison, temperature depend literature values of emissivity of stainless steel in different conditions (black hollow symbols) are added from [36].

#### 3.3.2. Corrected Emissivity of Powder Layers

The same general changes between corrected emissivity values and apparent emissivity values, as discussed in the previous section for a 316L L-PBF bulk surface, also applied to the corrective analysis of the emissivity values of the two different powders. Figure 15 contains a comparison of the corrected emissivity values of 316L powder layer, IN718 powder layer and 316L L-PBF bulk surface.

**Figure 15.** Corrected emissivity of 316L powder layer (green symbols) and of IN718 powder layer (brown symbols) and of 316L L-PBF bulk (blue symbols) over measured TC temperature.

The computed corrected emissivity of the 316L powder layer varied between ε*corr* = 0.37 and ε*corr* = 0.4 in the temperature region from 200 ◦C to 500 ◦C and between ε*corr* = 0.4 and ε*corr* = 0.45 in the temperature region between 500 ◦C and 600 ◦C. The increase at higher temperatures was attributed to oxidation effects.

The computed corrected emissivity of the IN718 powder layer varied between ε*corr* = 0.37 and ε*corr* = 0.38 in the temperature region from 200 ◦C to 500 ◦C and between ε*corr* = 0.38 and ε*corr* = 0.4 in the temperature region between 500 ◦C and 600 ◦C.

#### *3.4. Influence of Measurement Position*

No significant differences between the three positions of the heated sample could be found, as can be seen in Figure 16, which shows single temperature couples and the respective apparent emissivity values at a similar temperature, determined for the same calibration range. A comparison of the different positions was conducted using the camera calibration 200–400 measuring around a reference temperature of about 400 ◦C. Please note that the calculated emissivity values did not contain any corrections, as discussed in Section 3.3, since a correction was not necessary for this relative comparison. It is also interesting to note that these measurements were conducted at a specimen which was heated up to 604 ◦C in air outside of the build chamber prior to these measurements. The surface temperature was above 570 ◦C for about 480 s. Therefore, the presented measurements stem from a slightly oxidized surface condition. The apparent emissivities under these conditions were: at position 1 ε*app* = 0.28; at position 2 ε*app* = 0.28; at position 3 ε*app* = 0.29. The deviations of the emissivity values with regard to the different positions were within the measurement accuracy of the camera (see Section 3.5). According to published results on the angular dependence of emissivity [20,35], this result was not surprising, as the angular tilt between the particular measurement sceneries for the different positions was small. However, the confirmation of comparable results irrespective of the position of the target object was important for further monitoring tasks.

**Figure 16.** Apparent temperature and apparent emissivity of a 316L L-PBF bulk surface at three different positions within the build chamber according to the positions shown in Figure 7.

#### *3.5. Measurement Uncertainty*

As discussed above, unnoticed changes of the surface condition of the target object, e.g., an onset of oxidation layer growth, could lead to inaccuracies or misinterpretation. In addition, potential systematic measurement errors of the applied setup contributed to the measurement uncertainty. A rough quantification of the main contributing factors is given hereafter. The main factors contributing to the measurement uncertainty were identified as follows: accuracy of thermocouples, accuracy of MWIR camera, temperature heterogeneities over the target surface (with respect to TC and to IR camera values).

**Accuracy of thermocouples:** The standard limit of error of the used thermocouples was specified according to DIN EN 60594-1: +/−2.5 ◦C or +/−0.75% [37].

**Accuracy of the camera:** The manufacturers' specifications of the MWIR camera allow for a deviation of up to 1% in the determination of apparent temperature in ◦C or 1 ◦C, whichever is larger.

**Temperature heterogeneities over the target surface:** Figure 8 shows a temperature plot of the single thermocouples over a short period of time at temperatures between 520 ◦C and 560 ◦C. It was proposed to define the mean of TC1, TC3 and TC4 as the surface temperature. This mean was taken in the discussion section without consideration of its standard deviation. The standard deviation of the temperatures of the three thermocouples was either smaller than 2.5 ◦C or smaller than 0.75% of the measured temperature over the entire region of examined temperatures (130 ◦C–700 ◦C). Only in the temperature region between 300 ◦C and 470 ◦C were the standard deviations slightly higher, resulting in standard deviations of up to 1.1%. To compare the temperature of the top surface and the temperature at the described positions TC1-TC4, one test specimen was heated up outside of the build chamber, which had two TCs on top of the upper surface, replacing TC2 and TC4. The temperature differences between these two TCs on top and TC1 and TC2 at the side surface were below the measuring errors mentioned above.

For a conservative estimation of the measuring error of the apparent temperature, the standard deviations of the max. and min. apparent temperature values of the four ROIs (see Figure 6) were calculated for the L-PBF bulk surface. They were up to 7.9% of the respective mean value in the calibration range 60–200; up to 4.2% in the calibration range 200–400; and up to 6.5% in the calibration range 300-600. It was interesting to note that the standard deviation decreased drastically above an apparent temperature of approximately 500 ◦C to 2% in the measuring data of the calibration range 300–600. This corresponds well with the onset of oxidation and thus an increase of the emissivity above this value. Table 2 summarizes the resulting deviations per temperature regime. This results in a potential uncertainty of the emissivity determination of approximately 0.05. Apart from these mentioned potential measuring errors, the separate measurements at three different positions (Sections 2.4.3 and 3.4) without significant deviations in apparent emissivity results demonstrate the good repeatability of the conducted measurements.


**Table 2.** Measurement uncertainties of temperature determination.

Soldan [38] (p. 26) pointed out that potential measurement errors of thermographic measurements can occur due to incorrect focusing of the camera with regard to the target object. This is problematic in the context of unknown target objects, as there is no absolute measure for image sharpness [38]. In the frame of the thermographic setup of this study, the focusing of the IR camera was conducted by manual adjustment of the objective lens until the operator had the subjective impression of a sharp image in the live view mode of the software. This procedure had to be repeated when a calibration range of the camera was changed. Although the camera had a nearly perpendicular view of the target object and, therefore, a large lateral area at the same focus position, deviations from the ideal focus plane could not be completely precluded. However, the effect of defocused measurements is negligible when the region of interest does not contain edges, i.e., large temperature gradients. Here, only a plane surface area was taken into account for the measurements (compare Figure 6). A step-wise change of the z-position of the heating device of up to 10 mm difference in z-height revealed no differences in the mean apparent temperature. Thus, the manual focusing seemed to be reliable for the measuring procedure of this study.

#### **4. Conclusions**

An experimental temperature adjustment of an off-axis MWIR thermography setup, which was installed at a L-PBF machine, was conducted using the usual L-PBF working conditions. The apparent emissivity values for the specific setup were determined for two materials at two different conditions using the contact method: 316L L-PBF bulk material, 316L powder layer and IN718 powder layer. For this purpose, a heated reference device was placed inside a L-PBF build chamber. A corrective analysis considering transmission losses due to optical elements within the optical path as well as the affecting radiation of the surroundings revealed corrected emissivity values for the spectral range of 2 μm to 5.7 μm. In the temperature region from approximately 150 ◦C to 580 ◦C, where oxidation did not strongly effect the measurements, the corrected emissivity is in a range from 0.2 to 0.25 for a 316L L-PBF bulk surface, in a range from 0.37 to 0.45 for 316L powder layer, and in a range from 0.37 to 0.4 for IN718 powder layer. With the knowledge of these emissivity values, a real temperature determination for in situ thermographic measurements can be conducted. The findings will also

be very useful for numerical simulations. Additionally, the heated reference device can be used for temperature adjustments of other thermographic setups that show differences, e.g., in the spectral sensitivity of the camera.

**Author Contributions:** Conceptualization, G.M.; methodology, G.M., S.N., and S.J.A.; validation, G.M., S.N., and S.J.A.; formal analysis, G.M., S.N. and S.J.A.; investigation, G.M., S.N., and S.J.A.; data curation, G.M., S.N.; writing—original draft preparation, G.M.; writing—review and editing, G.M., S.N., S.J.A., C.M. and K.H.; visualization, G.M., S.N.; supervision, K.H.; project administration, S.J.A., C.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by BAM within the focus area Materials.

**Acknowledgments:** The authors would like to thank Mathias Röllig for his support in the verification of the camera calibration ranges against a black body radiator. The authors would also like to thank Matthias Weise for the measurement of the surface roughness.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**


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