Heat Input Control Strategies in DED

Abstract

In the context of directed energy deposition (DED), the production of complex components necessitates precise control of all processing parameters while mitigating undesirable factors like heat accumulation. This research seeks to explore and validate with various materials the impact of a geometry-based analytical model for minimizing heat input on the characteristics and structure of the resultant DED components. Furthermore, it aims to compare this approach with other established methods employed to avoid heat accumulation during production. The geometry of the fabricated specimens was assessed using a linear laser scanner, cross-sections were analyzed through optical microscopy, and the effect on mechanical properties was determined via microhardness measurements. The specimens manufactured using the developed analytical model exhibited superior geometric precision with lower energy consumption without compromising mechanical properties.

1. Introduction

Additive manufacturing (AM) is a class of manufacturing processes that involves creating objects layer by layer from 3D model data [1]. AM offers reduced time from the sketch to the final part, cost-effectiveness for small-batch production and freedom in geometric variety over conventional technologies [2]. Building the objects by adding material layer upon layer leads to reduced waste and more efficient use of expensive materials, e.g., superalloys [3]. Metal AM (MAM) can be divided into two main principles: PBF (powder bed fusion) and DED (directed energy deposition). LDED (laser directed energy deposition) is one of the representatives of the second group. LDED is a MAM technology that involves the layer-by-layer deposition of metal powder using a focused energy source (e.g., laser) to melt and fuse the powder particles onto a substrate or previously deposited layers. This process allows for repairs, applying wear- and corrosion-resistant coatings and creating complex metal parts. Parts made by LDED are already used in certain fields of technology and are on par in terms of mechanical properties with parts made by conventional methods.

For the LDED process, factors affecting the quality of the fabricated part can be mainly divided into three categories: laser, material and feed. Laser control factors mainly involve laser power, scanning speed, focal distance, laser spot size, number of laser passes and hatch distance. The selection of a particular value of a laser parameter is not always a straightforward action. It depends on the type of powder, powder particle size and shape distribution and thermo-physical characteristics of the material used in the process—raw material parameters. Feeding control factors involve powder flow rate, stability and repeatability of flow rate and traverse speed of the substrate. The selection of individual levels of each control factor is determined by the melting rate, melt pool size and rate of solidification. It is known that the control of the above-mentioned parameters within the process is limited (Figure 1). For example, (1) spot size is most often fixed in industrial machines and cannot be adjusted during the process; (2) powder flow control in most industrial devices is time delayed; (3) and tool path parameters are predetermined. These process control limits can cause difficulties in obtaining a stable melt pool and, therefore, the required part quality.

It is known that geometric accuracy is also influenced to a large extent by the heat accumulation phenomenon caused by the repetitive application of energy in consecutive material layers. Wu B. et al. [5] concluded that the process of excessive heat accumulation during manufacturing leads to a change in the shape of the melt pool. This results in a loss of dimensional accuracy and a structural change due to the change in thermal history for different areas of the part. The problem of heat accumulation and ways to prevent it are highlighted in some of the studies described below.

One of the most straightforward and implementable techniques of heat accumulation reduction is the application of the inter-layer dwell time. The method represents a waiting period after each layer or several layers, allowing the part to cool down between layers, which changes the thermal history. The main disadvantage of the above-mentioned technique is a significant increase in the manufacturing time and cost of the process.

Hagenlocher et al. [6] investigated the effect of heat accumulation on the local grain structure in the LDED of aluminum. They identified the influence of the process velocities on heat accumulation and microstructure. Their work demonstrated that the layer frequency has the major influence on heat accumulation. As a result, the investigation proved that heat accumulation significantly affects the local grain structure of the LDED fabricated parts. The obtained results are important for understanding the heat accumulation process and propose a strategy to reduce it. The determined optimization strategy reveals that an equiaxed dendritic grain structure over a large range of the built part can be achieved by manufacturing parts at high process velocities and low layer frequencies. Nevertheless, this strategy may have limited applicability for complex shaped parts of varying cross-sections and may reduce process productivity due to the layer frequency adjustment.

Ranjan et al. [7] worked on a model termed “hotspot detector”, and identified zones of heat concentration in a given geometry through dedicated thermal analysis. The authors developed a mathematical formulation to integrate this detector with density-based topology optimization using an adjoint sensitivity calculation method. However, the approach’s limitation lies in its inability to address local overheating other than by the altering support structure geometry, which increases material expenditure and post-processing effort and limits the feasibility for certain parts, especially in LDED.

Yu et al. [8] conducted finite-element model (FEM)-based research on the temperature control strategy for thin-walled parts fabricated by LDED. In their study, the layer-wise laser power reduction strategy and different waiting times between the layers were investigated. The combination of both was found to be an effective method to reduce heat accumulation, is straightforward and easily implementable, though significantly increasing the build time and process cost. The FEM approach requires a significant amount of time and computational power.

Rameez et al. [9] introduced a temperature management approach based on adjusting of the weld-bead cross-section by controlling of the welding power to reduce the heat accumulation in the WAAM process. The authors concluded that adjusting the input power in the process helps to reduce the accumulation of heat and allows for shorter inter-layer pause times. In the article, single bead FE simulations were carried out for different process parameters and different initial temperatures of the previous layer (substrate) to establish the database with essential information of weld-bead cross-section and corresponding power. Then, a surrogate model was created using an artificial neural network (ANN) trained on simulation data to output optimal welding power for different bead sizes and surface temperatures. Successful experimental validation of their approach was carried out by fabrication of rectangular specimens. Nevertheless, the creation of a complete database requires computationally expensive FE simulations and the behavior of the mentioned approach for complex geometries and non-uniform weld beads is not known.

Eisenbarth et al. [10,11] developed a geometry-based analytical model that reduces an excessive heat input by adapting the laser power, therefore reducing heat accumulation in the obtained part without prolonging the built with dwell times. The algorithm creates a digital twin of the part from a given NC code, analyses the massiveness of the part by calculating a local geometric factor, and alters the laser power proportional to this factor: The heat flux in a thin wall is limited compared to a massive block due to its smaller cross-section and requires, therefore, less laser power to generate a comparable melt pool. The algorithm correlates experimentally determined laser power to the local geometric factor. Since no physical simulation is performed, it is fast, easy to use, and enables a clearly defined and repeatable process. However, the work only verified the feasibility of the model for one material (stainless steel 1.4404), limited geometrical variability and did not investigate the effect of the presented algorithm on mechanical properties, microstructure, and geometry.

As can be seen from the overview above, heat accumulation reduction is a very important and essential topic for investigation. The solution proposed by Eisenbarth et al. [10,11] is the only one that does as investigated so far not introduce further detrimental effects, is cost-effective and energy efficient, but despite its potential lacks comprehensive exploration and validation. Thus, the aim and novelty of the present study are to validate and investigate the influence of the geometry-based analytical model for heat input reduction on the properties and structure of the obtained LDED parts and compare it with other heat accumulation reduction strategies used in production. Additionally, this study addresses previously unexplored aspect of applicability across various materials.

2. Materials and Methods

This section describes the materials used and the methods followed in this study. Detailed descriptions of the equipment, experimental setups, and analytical techniques are included to ensure the results can be reproduced.

2.1. Geometry-Based Analytical Model

In the present study, an in-house developed Computer-Aided Manufacturing (CAM) software, referred to as RCAM, was employed, built upon the analytical model established by Eisenbarth [10,12]. Initially, a set of discrete points, equidistant from one another, is generated according to the tool path, effectively defining the dimensions of the component at different time intervals during the fabrication process. These points are typically spaced at a distance equal to half the size of the melt pool. Each point represents one cuboid and an entry within a three-dimensional matrix, initially assigned a default value of 0. The lateral size of the cuboid is fixed and equal to half of the melt pool size when the height of the cuboid is equal to or smaller than the layer height. As the tool path is simulated, a virtual melt pool modifies the corresponding matrix entries to a value of 1, signifying the deposition of material in the evolving part. Subsequently, the algorithm assesses the local geometry of the component. To gauge the solidity or massiveness of the part, the algorithm defines a control volume encompassing the melt pool. This volume adopts a circular shape in the horizontal plane with a lateral radius r_cv,xy, ensuring its independence from any particular direction, and paraboloid in the vertical dimension with a depth r_cv,z. For each designated point in the dataset, the algorithm calculates the fraction “k” by counting the proportion of activated elements with a value of 1 within this control volume. This fraction, denoted as k, serves as a metric to quantify the solidity of the adjacent workpiece and is referred to as the “geometric factor”. Figure 2 shows the control volumes and k at different positions of a test geometry. As the melt pool develops on the substrate, the control volume (green) is completely filled by material there, thus k = 1. This is also true for the center of the part, as it is larger than the control volume. As soon as the melt pool reaches the wall, k decreases. At the top edge of the thin wall, k reaches an exemplary minimum of 0.17. This geometry is chosen for its larger variability than everything so far tested of the defined geometrical factor k. The required size of the control volume is determined experimentally by analyzing the influencing distance of geometric elements. The experiment to determine this control volume looks like making thin-walled specimens with variation in the before mentioned parameters and determining the specimens with the least shape deviation. For instance, when building a high, thin wall on a massive substrate, r_cv,z equals the height in which the substrate does not influence the boundary conditions of the processing zone anymore.

To calculate the laser power P_L values, the global geometry of the part is taken into consideration by comparing the cross-sectional area of the part in the slicing plane A_p with the minimum A_p,min and maximum A_p,max values. A_p,min is a cross-section area of the part, below which the application of the dwell time is required. A_p,max is an area, above which the reduction in the laser power is not required. Since the LDED requires certain power values to form a melt pool, therefore, a minimum laser power is introduced that enables a continuous, proper DMD process on the smallest geometric element, which is a semi-infinite wall with a thickness equal to the melt pool width. Furthermore, the initial temperature of the wall needs to be considered. Thus, P_L0H and P_L0C values are introduced for the minimum laser power for hot conditions (the maximum temperature at which the LDED process works properly) and for cold conditions (when the part temperature is roughly at room temperature), respectively. P_L1 is a power for large substrates and workpieces at initial temperature. Above mentioned values, as well as the control volume, depend on the specific LDED process and material properties (e.g., thermal conductivity) and are experimentally defined (Table 1). According to Eisenbarth et al. [10,12] the superposition of the linear interpolation of P_L as a function of A_p and k results in the following equation:

$$P_L\left(A_p,k\right)=\frac{A_p-A_{p,min}}{A_{p,max}-A_{p,min}}\left(\psi -\zeta \right)+\zeta$$

(1)

With the substitution variables

$$\zeta =k{P}_{L1}+\left(1-k\right)P_{L0H}, \forall k\in \left[0,1\right]$$

(2)

$$\psi =k{P}_{L1}+\left(1-k\right)P_{L0C}, \forall k\in \left[0,1\right]$$

(3)

For each point on the path, the adapted laser power is assigned to the NC code. It is considered in this model that once a steady-state process is reached, it can be supposed that thermal radiation, convection, and material flows in the processing zone remain relatively constant and can be disregarded by the model. Consequently, the model can focus only on geometric aspects, which simplifies calculations and eliminates the need for material and process properties that are often unavailable.

Table 1. Model basic parameters.

rcv,xy	rcv,z	Ap,max	Ap,min	PL0H	PL0C	PL1
15 mm	25 mm	600 mm2	50 mm2	550 W	650 W	1000 W

Table 1. Model basic parameters.

rcv,xy	rcv,z	Ap,max	Ap,min	PL0H	PL0C	PL1
15 mm	25 mm	600 mm2	50 mm2	550 W	650 W	1000 W

2.2. Specimens Fabrication

A 5-axis combined milling and LDED machine GF HPM 450 U (Georg Fischer AG, Schaffhausen, Switzerland) was used for additive buildup of specimens. Additive manufacturing of the LDED structures was performed with the integrated laser processing system Ambit S5 from HMT (Hybrid Manufacturing Technologies, Midlands, UK) that includes an IPG YLR-1000-MM-WC (IPG Photonics Corporation, Oxford, MA, USA) fiber laser. The working distance of the processing head was set at 8.0 mm, which resulted in an approximate melt pool width of 2.2 mm. Argon is used as shielding gas, nozzle protection, and powder carrier gas at flow rates of 8 L/min, 6 L/min, and 4 L/min, respectively.

The geometry of the specimens is shown in Figure 3a. This specimen shape was chosen due to the need to investigate methods to prevent heat accumulation in its different sections (thin-walled and massive). The massive section of the specimen has a square cross-section to clearly demonstrate the effect of the heat accumulation being studied on the specimen (in particular, a square cross-section will show defects in the corners). The dimensions of the specimen model are marked on the image. The width of the thin-walled section consists of two tracks formed by moving the nozzle forward and backward and turning at the endpoint. The scanning raster orientation in the thick part was changed by 45° for each layer (Figure 3b). The scanning speed was 200 mm/min for the contour and 333 mm/min for the raster, as defined in the previous study by Soffel et al., where the mechanical properties of the parts fabricated by LDED were tested [13].

The specimens were fabricated using the four different power settings shown in Figure 4, three of which include adaptive energy input strategies: application of dwell time between layers, stepwise power reduction, and heat control based on the geometric factor, the method described in Section 2.1. The dwell time for the corresponding specimen after each layer was 20 s. For the specimen with stepwise reduction, the power was decreased from 1000 W by 50 W every layer till 650 W at the 8th layer and kept constant for the next layers. The specimen with constant power was fabricated at 1000 W for every layer. The specimen manufactured with the geometry-based reduction strategy was fabricated with power in the range of 500–1000 W, and the power differs for each point according to the geometric factor. A map of the geometric factor for the reduction in the laser power projected on the specimen geometry is shown in Figure 5. The laser power was controlled according to the geometric factor, where maximum laser power corresponds to the factor “1” and blue color on the map and minimum power with the factor “0” and red color. The last method was implemented by the RCAM software. The laser power graph for the specimen shown in Figure 5a is indicated in Figure 4a. Figure 5b illustrates that the distribution of factor k becomes constant after reaching r_cv,z height, i.e., 25 mm in this case. Therefore, it is also means that the substrate does not influence the boundary conditions of the processing zone anymore.

2.3. Materials

Nickel-based superalloy Inconel 718 and martensitic stainless steel EN X3CrNiMo13-4 (1.4313) were selected for the experiments. The purpose of using these two alloys was to compare the effect of the investigated strategies on materials with different structures (BCC and FCC), hardening mechanisms, and thermal conductivity. Together with the work of Eisenbarth [10], who explored 1.4404, three different materials have been explored. Thermal conductivity at room temperature is 9.94 W/m⋅K for Inconel 718 [14] and 16 W/(m⋅K) for 1.4313 steel [15]. The material composition of the used powders is detailed in

Table 2. Material composition.

Inconel 718
Element	Fe	Ni	Cr	Nb + Ta	Mo	Ti	Al	C	N	O
wt.%	18.1	53.4	18.9	5.1	3.05	0.88	0.44	0.05	0.02	0.01
Steel 1.4313
Element	Fe	Ni	Cr	Mn	Mo	Si	N	C	S	O
wt.%	80.54	4.01	13.07	0.53	0.49	0.31	0.03	0.02	0.003	0.028

. Particle size distribution graphs for both materials are shown in Figure 6.

2.4. Experimental Characterization

The cross-sections were ground flat with SiC papers from 240 to 4000 and polished with 1 μm and 0.1 μm diamond suspension. The cross-sections were analyzed on a digital microscope Keyence VHX-1000 (Keyence, Osaka, Japan). Kalling II was used as an etchant to reveal the microstructure. The melt pool geometry analysis was conducted on the obtained images. In the polished condition, the porosity was determined from four cross-sections by image analysis with the software ImageJ (version 1.51p, ImageJ, Bethesda, MD, USA). The cross-sections for porosity analysis are passing through the middle YZ plane of each specimen. Vickers hardness measurements with a load of 98 N (HV10) and dwell time of 20 s were performed on specimens with a Qness Q10 M testing device (ATM Qness GmbH, Salzburg, Austria). The hardness values were measured at 21 points for each cross-section in the YZ plane. The distance between the measurement points was chosen in accordance with ASTM E92-82 standard, and the points have, respectively, similar positions on each specimen. Profile measurements were provided by a Micro-Epsilon scanCONTROL laser scanner (Micro-Epsilon Messtechnik, Germany). Profile measurements were conducted along the midplane of the specimen.

3. Results

The specimens obtained with the different heat input control techniques are presented in Figure 7.

Some of the obtained specimens show significant shape deviation in the thin-walled section. The height profiles of the specimens, measured by laser scanning, are shown in Figure 8.

A noticeable difference in the profiles of the obtained specimens can be observed in Figure 8. The red line shows the dimensions of the initial CAD model.

The reference specimen with a constant power value has a significant drop in height in the thin-walled part. The specimen produced with the dwell time approach has the same profile as the specimen with a constant power value. The specimen with stepwise power reduction has a different profile and behaves differently for the two investigated materials. For Inconel 718 (Figure 8a), the stepwise reduction proved to be effective in the thin-walled part of the specimen, where the height is only slightly higher than for the CAD model. However, there is an underbuilt in the massive section of the specimen. For 1.4313 steel (Figure 8c), the stepwise reduction showed an underbuilt in both massive and thin-walled sections. However, it is overbuilt on the tip of the thin-walled section of the specimen.

The specimen with the applied heat input control strategy based on the geometric factor shows the closest geometry to that specified in the CAD model. Another geometric factor specimen achieved the nominal height also if the part height was increased to 30 mm (Figure 8b). In both the massive and thin-walled sections, it is slightly overbuilt in height, which can be neglected in subsequent post-processing. The specimen produced using the geometric factor heat input control strategy showed the closest to the specified dimensions (had enough stock material on top for the subsequent processing by milling), so further investigation aims to study the structure and properties of this particular specimen. A constant power specimen was chosen as the reference for comparison.

The results of the cross-sectional analysis of the Inconel 718 specimens using optical microscopy are presented in Figure 9 and Figure 10. Figure 9 on the left shows first a slight increase in the width of the segment and then a narrowing of the segment along the nominal width. This appears to be due to negligible insufficient heat reduction for the first few layers, but the subsequent process is stable and yields the desired thin-walled width. In Figure 9 on the right, the opposite pattern is observed. The first layer is of nominal width and the subsequent layers have significantly increased widths. It appears that for the first layer the heat dissipation through the substrate is sufficient, but then the heat flow through the small cross-section of the thin-walled segment is insufficient for heat dissipation and leads to the spreading of the melt pool and an increase in the segment width. The higher heat accumulation for the constant power specimen resulted in height reduction in the thin-walled section (see the results of the laser profile measurement, Figure 8). The microstructure observed in Figure 10 shows the grains elongated more in the vertical direction (marked with a dotted line). This shows the predominant direction of heat dissipation—towards the substrate. The shape of the layers in the thin-walled section is shown in Figure 10. For the specimen fabricated with constant power, a significant inclination of the layer is observed throughout the length of the thin-walled segment, with the effect intensifying towards the end of the segment. Cross-sectional data corroborate the results of laser scanning and lead to the conclusion that this effect is more pronounced for layers situated higher in the structure. Conversely, for the specimen fabricated with the geometric factor algorithm, the layer is nearly horizontal along its entire length, except at the very tip. Moreover, analyzing the results of melt pool width and layer height measurements shows more consistent values from the massive to the thin-walled part for the specimen fabricated with geometric factor. Thus, the higher stability of the melt pool for the specimen made by the geometric factor algorithm, which leads to higher geometrical accuracy, is confirmed for the different kinds of materials. Results are summarized in

Table 3. Melt pool dimensions.

Specimen	Segment	Melt Pool Width, µm	Layer Height, µm
Constant	Massive	2807 ± 72	828 ± 15
	Thin walled	3051 ± 103	622 ± 35
Geometry Based	Massive	2199 ± 62	810 ± 10
	Thin walled	2240 ± 71	804 ± 34

.

The average porosity values for the Inconel 718 specimens are 0.05% and 0.06% for the constant power and geometric factor specimens, respectively. The 1.4313 steel specimens have porosity values of 0.06% and 0.07% for the constant power and geometric factor specimens, respectively. The porosity values for the thin-walled and massive segments for both materials and a porosity image are shown in Figure 11. Observed pores for both materials have a spherical shape, no lack of fusion defects are detected on the cross-sections of the studied specimens, and the porosity can be classified as a gas entrapped.

The hardness results for IN718 are shown in Figure 12. The data points on the graph (Figure 12b,c) represent the average value from the corresponding column of imprints, and the error bars are the standard deviation. The average hardness values of Inconel 718 for the constant power and geometric factor specimens are 237 ± 18 HV and 232 ± 15 HV, respectively. The difference of 5 HV can be considered insignificant with regard to the standard deviation. However, a slight drop in hardness is observed within specimens from the massive to the thin-walled segment. The difference between the average hardness value of the massive segment and the average hardness value of the thin-walled segment, shown in Figure 12c is 18 HV (8%) and similar for the constant power and geometric factor control specimen. The drop in hardness towards the end of the thin-walled structure shows that heat dissipation from the substrate is the most prominent cooling effect and gives higher hardness near the substrate than further away from the substrate, and especially low values are observed in the corner area. The difference in hardness between the thin-walled and massive segment, shown in Figure 12c, is the result of better cooling at larger contact area with the substrate. Apparently, cyclic heating of the layers during multiple depositions in the massive section leads to the phenomenon of in situ heat treatment and affects the part properties accordingly. As noted, this is the aging process for IN718, which results in the γ′ and γ″ phases precipitation, and an increase in hardness. It is discussed more in detail in the Section 4.

The hardness results for steel 1.4313 are shown in Figure 13. Hardness data indicate a different tendency. The average hardness values for the constant power and geometric factor specimens are 413 ± 7 HV and 420 ± 5 HV, respectively. For this material, however, a slight drop in hardness can be seen in the massive part. This drop is 8 HV for the constant power and geometric factor control specimens.

The explanation of this difference between the massive and thin-walled segments is, presumably, annealing, which increases the ductile phase content, leading to reduced hardness values. The thin wall part is subjected to less heating due to its size and scanning without an infill raster. Therefore, the effect of cyclic heat treatment is less pronounced. It will be explained more in detail in Section 4.

4. Discussion

A noticeable difference in the profiles of the obtained specimens can be explained by the following reasons. The reference specimen with a constant power value has a significant drop in height in the thin-walled part and increased massive part height due to the overheating. This is confirmed by the larger melt pool size, which caused the powder efficiency to increase and more material to be deposited in the massive section. In turn, in the thin section, the overheating caused the melt pool to spread to the sides, which increased its thickness and resulted in a significant reduction in height.

The same profile is observed for the specimen produced with the chosen dwell time. It seems that the applied dwell time does not reduce the shape deviation for the difference to be visible. This shows the inefficiency of the dwell time strategy in terms of geometry. This effect is probably due to the chosen geometry. For a given ratio of massive to thin-walled part, the larger effect results from the accumulation of geometrical defects due to the relatively high heat per layer, which is confirmed by Figure 9, where for a specimen with constant power, the width first increases for a few layers and then remains constant. It is possible that increasing the dwell time will increase the effect of reducing heat build-up, but this will result in a significant drop in performance.

The specimen with stepwise power reduction has a different profile. The stepwise power reduction resulted in a reduction in overheating in the thin-walled section, and a sufficient height was obtained. However, for the massive section, this reduction was excessive, which led to a decreased powder catching efficiency and resulted in insufficient power to reach the target height. This method can be considered ineffective for parts with large sectional size differences.

The specimen with the applied heat input control strategy based on the geometric factor shows the closest geometry to that specified in the CAD model. The applied strategy also showed efficiency for the part of a double height (namely 30 mm), which indicates the applicability of this strategy for parts with a high height-to-width ratio. This confirms the correctness of the chosen dimensions of the control volume in this analytical model and confirms that, for a given part geometry and chosen materials, at a certain height there is an equilibrium between heat input and heat dissipation, so that the influence of the substrate can be neglected. Analysis of cross-sections shows a more constant melt pool geometry within the specimen (thin-walled and massive sections) compared to the reference specimen, which, together with the laser scanning results, indicates the effectiveness of the chosen method. In addition, the porosity values for the investigated specimens did not exhibit a statistically significant difference. The porosity values between the thin-walled and the massive sections do not differ significantly for the observed specimens within one material.

Based on the hardness results, it can be concluded that the observed difference between constant power and geometric factor specimens is within the range of standard deviation. Since the difference between the segments is similar for both investigated specimens, and the average values are reasonably close, the effect of the applied heat accumulation reduction strategy on the mechanical properties can be recognized as limited. Nevertheless, the data obtained show a more consistent distribution of hardness across the cross-section of the geometric factor specimen. In addition, a difference in hardness for the thin-walled and massive segments is noticed for this geometry. According to the results [13], for Inconel 718 processed with AM, the dominant contributor to the material’s hardness is grain boundary strengthening, which is increased for smaller grain sizes due to faster cooling. In addition, Inconel 718 is a precipitation hardened alloy, which also contributes to the hardness gradient shown. Aging for this alloy occurs at 600–750 °C [16]. Due to the fact that each subsequent layer reheats the previous one during deposition and reaches, supposedly, the aging range, the γ’ and γ” phases are precipitated. It also leads to an increase in the hardness gradient shown. This process is more pronounced for the massive segment since there each layer consists of multiple beads and heating to a greater extent than two tracks, as in the thin-walled one.

For 1.4313 steel, the explanation of this difference between the massive and thin-walled segments through the grain size and Hall–Patch equation may be difficult for martensitic structures, in accordance with the conclusion of Lehto et al. [17]. Another theory from Colaco and Vilar [18], proposes that reduced heat input boosts austenite formation in soft-martensitic steel. Niederau [19] states that the austenitic range for steel with 12–15% chromium and 4–5% nickel reaches approximately 600 °C. Reheating layers of the part leads to temperatures in the annealing range, which could produce fine austenite not visible under light microscopy, enhancing ductility significantly. And since the massive segment heats to a greater extent, the amount of the ductile phase is higher, and the resulting hardness is lower. Thus, the use of reduced heat input results in lower temperatures in the workpiece and less annealing process, which is observed in higher hardness values for the specimen with geometric factor.

Expanding on the findings presented in Figure 10, it becomes evident that the cooling behavior within the thin-walled sections is predominantly influenced by the substrate material, rather than through the walls themselves. This observation is crucial for understanding the thermal management within the specimen, as it indicates a minimal role of ambient air and convective cooling in affecting the temperature reduction in the thin-walled sections. The role of the substrate in dissipating heat further aligns with the observed geometrical stability and accuracy of the layers for specimens fabricated with the geometric factor algorithm.

Validation was successfully conducted for various materials, namely Inconel 718 and steel 1.4313. Despite differences in thermal conductivity among the chosen materials, the heat accumulation reduction algorithm, based on a geometric factor, was effectively applied to both materials. Both sets of specimens exhibited no adverse differences in mechanical properties compared to the reference specimen. A noticeable enhancement in geometric accuracy was observed for both sets. A conclusion can be drawn regarding the applicability of this approach to different materials. Considering prior research [10], the approach demonstrated its effectiveness across three alloy types.

5. Conclusions

The geometry-based analytical model was successfully tested and showed efficiency in the heat input control and heat accumulation reduction for various materials. The influence of the model on the properties, melt pool dimensions and geometry of the obtained DMD parts was investigated. Heat accumulation reduction strategies used in production were compared. The results of this work can be generalized as follows:

• Three different techniques for power adaptation were tested and compared. Shape accuracy measurements showed that only the specimen built using the geometric factor method achieved the target height in both massive and thin-walled sections. Thus, the developed model can be applied to more complicated geometries.
• The improvement in geometric accuracy is associated with the power adaptation, thereby enhancing the stability of the melt pool, particularly in the thin-walled section, which indicates the main mechanism for the increase in geometric accuracy by this model.
• The power adaptation with geometric factor has an equalizing effect on mechanical properties making them more independent from the level above the substrate, the aspect ratio and the wall thickness, which can improve the quality of manufactured parts.

Further research can be focused on the influence of the applied algorithm on dynamic mechanical properties, the temperature fields, a deeper investigation of the obtained microstructures, and the finer adaptation of the control volume to the material properties.