**2. Methodology**

In this work, in situ tensile tests were carried out on specially prepared specimens inside the SEM chamber in a deformation stage. The local EBSD data from the same specimen were used to run a full phase crystal, plasticity-based numerical simulation model. The material's local deformation and damage behavior, especially around an MnS inclusion, was analyzed and compared with the numerical simulation results. This section

contains a complete methodology of the in situ tensile tests, EBSD data collection, and data processing that was carried out.

#### *2.1. In Situ Test Setup and Data Collection*

For in situ investigations, a specialized method was adopted based on previously published work by other researchers [35–39]. For in situ testing, tensile specimens according to DIN EN ISO 6892-1 with a length of 50 mm and a thickness of 0.6 mm with notches for strain concentration were prepared as shown in Figure 1c. The samples were cut from the discs using a water jet cutting machine to avoid material wastage and residual stress accumulation on the surfaces during conventional machining. The prepared samples were finely milled to obtain a better edge finish and produce small u-shaped notches in the middle of the neck, as shown in Figure 1c. They were prepared by metallographic polishing. Since the specimens were very thin, a special embedding compound was used during the polishing process that could be dissolved in acetone when heated to 30 ◦C after the polishing process was complete. As the test specimens' deformed surface was later to be analyzed with digital image correlation software, the test specimens were etched for 5 s in a 3% Nital solution to achieve the required surface contrast. The visual inspection of specimens before testing revealed that only non-deformed inclusions were found on the surface of the specimens, and a few MnS inclusions with an elongated shape were present in the middle of the specimen. Further details about specimen preparation and the achievement of the correct contrast of micrographs using image processing techniques are provided in Appendix A for interested readers.

**Figure 1.** (**a**) ZEISS Gemini SEM 450 scanning electron microscope used (**b**) and the in situ tensile model. (**c**) Geometry of the in situ specimens with notches for the stress concentration, where all the dimensions are in mm.

The overall chemical composition of the current material is shown in Table 1 in comparison with the standard chemical composition of the alloy. It is modified 16MnCrS5 with 50% lower carbon content and 20% more sulfur. Therefore, the strength of this modified material is slightly lower; due to higher sulfur content and less carbon, it contains more MnS inclusions, with some being predominantly large (as discussed later in Sections 2.3 and 2.4).


**Table 1.** Chemical composition of the investigated modified 16MnCrS5 steel in weight percentage in comparison with standard non-modified 16MnCrS5 steel.

The in situ tensile tests were carried out with a ZEISS Gemini SEM 450 scanning electron microscope using a Kammrath and Weiss tensile test stage, as shown in Figure 1a,b. This module allows in situ data collection during tensile or compressive loading using SE, EBSD, and EDS in the Gemini SEM450 of Carl Zeiss AG. For the experiments, different points on the tensile stress–strain curve were targeted at a forming speed of 8 μm/s, and the specimen was held at various values of stress and strain. At the same time, analyses of the microstructure and chemistry were performed. A series of images was taken during tensile testing. All images were taken with a resolution of 2048 × 1536 pixels. In addition, all photos in the area of interest were taken with a magnification of 11k and WD (working distance) of 16.6 mm with the "InLens" module.

#### *2.2. Selection of Area for Full Phase Simulations*

For the crystal structure analysis, the specimens were placed in the Gemini SEM450 from Carl Zeiss AG. The EBSD analysis was performed with an accelerating voltage of 20 kV, a working distance of 11 mm, and a specimen holder pre-tilted by 70◦. The magnification was 10,000<sup>×</sup>. For the EBSD analysis, the Symmetry S2 detector from Oxford Instruments PLC was used. The analysis area was 95.4 μm × 71.8 μm, with a step size of 0.2 μm. The advanced Symmetry S2 EBSD detector utilizes a unique combination of speed (4500 pixels/second), sensitivity (CMOS technology sensor), and diffraction pattern details (1244 × 1024 pixel resolution) to efficiently produce high-quality EBSD data for the selected area, which can then be post-processed to obtain information in the desired format. Modified 16MnCrS5 steel contains inclusions that are quantitatively analyzed and recoded using EDS Ultim MaxX from Oxford Instruments PLC.

The multi-phase steel material Representative Volume Element (RVE) was obtained after EBSD analysis. The data were initially raw and required cleaning for unindexed points due to crystallographic noise at the grain boundaries. This noise was reduced using an intelligent algorithm implemented on the MTEX toolbox with MATLAB [40]. The procedural details of the EBSD data cleaning and the developed algorithm are published elsewhere [41]. Therefore, readers are encouraged to refer to that work for further details.

The ferrite matrix distribution is shown in Figure 2a, and the distributions of alumina (Al2O3), cementite (Fe3C), and manganese sulfide (MnS) concerning the grain boundaries are displayed in Figure 2b. Most of the inclusions detected in this area of the specimens are present on the grain boundaries. This kind of microstructure with appropriately large second phase particles distributed homogeneously on the grain boundaries of adequately large ferrite grains appears to be due to the adopted manufacturing strategy.

#### *2.3. Statistical Analysis of the EBSD Data*

A quantitative comparison of the grain shape (aspect ratio) and particle size of the ferrite matrix and inclusions is presented in Figures 3 and 4, respectively. In Figure 3, the aspect ratio of 1 corresponds to almost perfectly round shapes, whereas the higher aspect ratio corresponds to the adequately elongated grain or inclusion. Considering this criterion, the aspect ratio of ferrite grains in Figure 3a predominantly lies between 1–2, except for some grains with a high degree of elongation of >4, which is the normal ferrite microstructure reported in previous literature [42,43]. On the other hand, the inclusions in Figure 3b–d are largely round (aspect ratio = 1), with some particles slightly elongated. There can be two reasons why the manufacturing process yields such inclusion shapes, as reported previously [44], or it can be due to the limitations of the measurement

and magnification chosen in this work. During EBSD analysis, only these slightly large inclusions with round profiles were detected due to the chosen magnification and the set step size. In contrast, very thin and long inclusions were missed.

**Figure 2.** Multi-phase steel specimen. (**a**) IPF for ferrite matrix with BCC crystal structure, with different colors showing different crystallographic orientations. (**b**) Three types of inclusions spread all over the ferrite matrix and (**c**) the mesh resolution showing the grid size for calculation points. (**d**) IPF figure showing orientations of ferrite grain orientations with reference directions.

**Figure 3.** Distribution of aspect ratios of (**a**) ferrite grains, which are relatively larger and have a wider spread; (**b**) cementite inclusions, which are close to 1, with few inclusions at 1.3 and 1.7; (**c**) MnS inclusions are also usually round, with a few with a spread of 2.8; (**d**) Al2O3 inclusions are also usually round with an aspect ratio of 1, with some inclusions reaching up to 2.3.

**Figure 4.** Distribution of grain size in terms of equivalent radius (ER) for (**a**) ferrite, which is biased towards small grains but being widespread reaches up to 8 μm; (**b**) cementite inclusions, which are generally small with sizes close to 0.1 μm, with a few inclusions up to 0.18 μm ER; (**c**) MnS inclusions, which although usually small are in a large number with 0.16 μm ER and a few as large as 0.23 μm. (**d**) The Al2O3 inclusions have a large spread with many having sizes close to 0.1 μm and then having a downslope spread up to 0.25 μm ER.

The grain size in Figure 4 is measured in terms of the mean sphere diameter. A significant number of ferrite grains in the selected area for EBSD analysis are below 4 μm, as observed in Figure 4a, and some grains are larger than 6 μm. As shown in Figure 4b–d, the inclusions are comparatively very small. Most inclusions are around 0.1 μm in size, whereas very few are larger than 0.2 μm. Even smaller inclusions may be present within the microstructure but were not detected due to the selected magnification and EBSD measurement step size. This lack of smaller inclusions negligibly alters the material chemistry or local phase distribution and hence is assumed to have almost no effect on the simulation results.

Second phase inclusions have been talked about a grea<sup>t</sup> deal in this section. The elemental analysis of an MnS inclusion using EDS analysis is presented in Figure 5 for reference. All the other inclusions—i.e., Al2O3 and Fe3C—have also been identified using the same process.

#### *2.4. Selection of Area, Tools Used, and Methodology Adopted for In Situ Strain Measurement*

During the in situ tensile tests, a large, elongated sulfide inclusion (MnS) was analyzed. The inclusion, along with the chemical analysis confirming it to be MnS, is shown in Table 2. The length of the inclusion together with the cavity is about 42.5 μm. The elongated inclusion aligned with the tensile loading axis (horizontal to the shown micrograph) was expected to be prone to severe fracture and was therefore of grea<sup>t</sup> interest.

**Figure 5.** Elemental analysis of the modified 16MnCrS5 steel specimen using EDS to identify the inclusions (the red dotted line represents the line of measurement). The inclusion shows a major concentration of Mn and S; therefore, it is classified as an MnS inclusion.

**Table 2.** Chemical analysis of inclusion at different points, confirming MnS. The units of the measurement are in mass, %.


The in situ tests come with their own challenge of image acquisition [35–37]. The images taken during the test should have a specific contrast and clear feature identification possibility [45]. To ensure that the images taken during the current tests are of acceptable quality and grayscale distribution, an analysis was performed that has not been included in the main part of the body but is presented in Appendix A. The effect of different settings and attributes is discussed and can be interesting for readers interested in performing such tests themselves. Appendix A also contains detailed information about the local and global strain measurement during experimentation.

The digital image correlation software VEDDAC from Chemnitzer Werkstoffmechanik GmbH was used to process the captured image series. When processing the images, images with strong contrast or sharpness fluctuations were removed from the calculations, and the final set contained images. Two calculation areas were selected during DIC. The first calculation area is shown in Figure 6a, which consists of the matrix around the inclusions and the cavities. The second calculation is the inclusion area and cavities around it, as shown in Figure 6b. The optimal grid sizes for a particular series of images were 9 × 9 pixels (coarse) for the matrix and 5 × 5 pixels for the inclusion (fine). More information about the local strain measurement methodology is provided in Appendix B.

(a) (b) 

**Figure 6.** Calculation network for digital image correlation (**a**) around non-metallic inclusions (**b**) in non-metallic inclusions and cavity area. In this work, a grid of 9 × 9 pixels (coarse) for the matrix and 5 × 5 pixels for the inclusion (fine) was chosen to ge<sup>t</sup> accurate and fully resolved results.

#### **3. Numerical Simulation Model Setup**

The EBSD data and the information of each phase's chemical and crystallographic structure were used to model and run a full phase crystal plasticity-based numerical model with calibrated material models. These simulations were used to provide detailed information about the local deformation and damage behavior of this material and how different inclusions, morphologies, and distributions affect the local deformation and damage behaviors. This insight is useful to understand the data from limited in situ tests.

First developed by Hutchinson [46] and later extended by Kalidindi [47], the phenomenological model implemented in the DAMASK framework [33] calculates the plastic deformation by slip planes based on the initial and saturated slip resistance—*S*0, *Ss*, respectively (refer to Table 3). This resistance value for slip systems = 1,2,3 ... Nslip increases from the initial to saturation value depending on the crystal structure specifications and the critical shear value on the slip plane during deformation.

This model uses a mathematical description to correlate the initial deformation gradient (*F*) with the resulting first Piola–Kirchoff stress tensor (*P*), as shown in Equations (1) and (2). The elastic part is simplified in the form of the generalized Hook's law, and for the plastic part, it is given with the help of the plastic velocity gradient given in Equation (3).

$$\begin{aligned} \dot{F}\_{ij} &= \begin{bmatrix} 1 & 0 & 0 \\ 0 & \* & 0 \\ 0 & 0 & \* \end{bmatrix} \times 10^{-3} \text{s}^{-1} \\ \mathcal{P}\_{ij} &= \begin{bmatrix} \* & \* & \* \\ \* & 0 & \* \\ \* & \* & 0 \end{bmatrix} Pa \\ \mathcal{S} &= CE^{\epsilon} \end{aligned} \tag{1}$$
 
$$\mathcal{S} = CE^{\epsilon} \tag{2}$$

where

> *S* = second Piola–Kirchoff stress tensor;

*C* = fourth-order elastic stiffness Tensor;

*Ee* = second-order Langrangian strain tensor.

$$L\_p = \sum\_{\alpha=1}^{\text{Nslup}} \dot{\mathbf{y}}^{\alpha} \left( \mathbf{m}^{\alpha} \odot \mathbf{n}^{\alpha} \right) \tag{3}$$

The value of the velocity plasticity gradient *Lp* is dependent on the shear strain γ (Equation (4)), which is a function of the resolved shear stress τ<sup>α</sup> and slip-resistance on the α slip plane S<sup>α</sup>.

$$\dot{\boldsymbol{\gamma}}^{\alpha} = \dot{\boldsymbol{\gamma}}\_{0} \left| \frac{\boldsymbol{\pi}^{\alpha}}{\mathbf{S}^{\alpha}} \right|^{\alpha} \text{sgn}(\boldsymbol{\pi}^{\alpha}) \tag{4}$$

and

α= 1, 2, 3 ··· , Nslip (For BCC Ferrite Nslip = 24)

A non-conserved damage field *ϕ* is governed by the continuous release of the stored mechanical energy density from undamaged to fully damaged conditions in a region; i.e., *ϕ* = 1 to *ϕ* = 0. In the ductile damage criterion implemented in DAMASK, plastic energy dissipation at a material point is the driving force here for damage flux *fϕ.* Therefore, plastic energy dissipation in the form of the following equation is used:

$$w\_{plastic} = \frac{1}{2} \varrho^2 \int M\_p \, L\_p dt. \tag{5}$$

Consequently, the minimization of the total free energy density is responsible for force to drive damage, and it is given as follows:

$$f\_{\Psi} = -\left[\frac{\partial w\_{\text{plastic}}}{\partial \rho} + \frac{\partial w\_{\text{surface}}}{\partial \rho}\right] = \frac{G}{l\_c} - \varrho \int M\_{\text{P}} L\_{\text{p}} dt.\tag{6}$$

where

> *G* = surface tension of the newly generated damage surface;

*lc* = length scale of the diffused surface;

*Lp* = plastic velocity gradient.

The plastic governing law changes to the following when damage evolution is coupled with dissipated plastic energy:

$$L\_p = f\left(\frac{M\_p}{\varphi^2}\right) \tag{7}$$

Readers are encouraged to read the pioneering work by the developers of DAMASK for further details and understanding of the model [33,34,48,49]. For instance, a strategy was published recently by Qayyum et al. [50] by choosing an optimal RVE that behaves isotopically ye<sup>t</sup> is small enough to produce fast results for the calibration of the material model parameters of single-phase materials. The strategy comprises a 10 × 10 × 10 size RVE containing 1000 grains, where each point represents a different grain. The RVE adopted from that published methodology is shown in Figure 7a. This RVE was used to calibrate the fitting parameters in the material model by comparing simulation outcomes with the experimental observations, and the results are shown in Figure 7b.

It is observed that the simulation results match well with the experimental observations globally. The dips in the experimental data are positions where the test was stopped and pictorial data were recorded. The adopted and calibrated material model parameters used in this study are shown in Table 3. This set of parameters was used to run full phase simulations and then analyze the local material deformation and damage behavior.

The DAMASK framework is designed to ge<sup>t</sup> all the inputs in the form of specifically structured text files with a complete microstructural description of RVE with geometrical details, material behavior attributes, and boundary values. Elastic and plastic phase parameters for ferrite and only elastic parameters of all the inclusions are defined to observe the micromechanical deformation of ferrite caused by stiffness degradation. Ductile damage

criteria have been incorporated in the ferrite matrix as well. The RVE generated by using the EBSD data shown in Figure 2 was subjected to quasi-static tensile load with a strain rate of 10−<sup>3</sup> s<sup>−</sup><sup>1</sup> in the x-direction.

**Figure 7.** (**a**) 10 × 10 × 10 size RVE containing 1000 individual grain orientations, (**b**) comparison of experimental and simulation flow curves, showing a good match of results.

**Table 3.** Elastic parameters of second phase inclusions obtained from the literature [10,20,23,26,28,41,51, 52] and calibrated parameters of ferrite adopted from the literature [23,26,28,41,52] and adjusted by comparing with the flow curve from in situ tests. The ductile damage parameters were calibrated by comparing them with the in situ test results.

