Process window prediction in stainless steel selective laser melting using various energy densities: laser power, scan speed, and defocusing distance

The process window of selective laser melting (SLM), a set of optimum process parameters, is crucial for producing defect-free components with excellent mechanical properties. This study aims to predict the optimum process window for SLM of stainless steel by varying the defocusing distance (f) which changes the laser beam diameter (d) and using laser power (P) and scan speed (V) as process parameters. The process window was predicted using empirical formulae related to the energy density equations, instead of the conventional approach based on simple experimental results. To predict the process window, we analyzed the melt pool geometry of components with different features, such as depth (D), width (W), layer thickness (t), and hatch distance (h). Using the energy density equation, we correlated the effect of these process variables on the melt pool geometry and derived empirical equations. The upper limit of the process window (D/W) was strongly correlated with local applied energy and expressed as P ≤ 34Vd2. The lower limits, D/t and W/h, showed good correlation with linear energy density and laser energy density, respectively, and expressed as P > 2.16Vd and P < 0.13V. Finally, we used these empirical equations to predict the process window, which was experimentally verified.


1. Introduction
Selective Laser Melting (SLM) is an additive manufacturing process that utilizes a high-energy-density laser heat source and consumable metal powder bed to create intricate three-dimensional components. It has gained popularity in industries such as aerospace, power plants, medical care, and automotive due to its high degree of design freedom and superior dimensional precision [1,2]. Compared to traditional manufacturing processes, additive manufacturing has the advantage of improving performance, reducing weight, and shortening the manufacturing period. However, in order to apply additive manufacturing to various industries, it is crucial to derive optimal process conditions that satisfy strict quality and high reliability requirements [3]. The process window is a method for determining the ideal process conditions in manufacturing processes [4]. Developing a process window that combines multiple process variables is essential for creating parts with minimal defects and excellent mechanical properties in selective laser melting [4]. The procedure of deriving the process window involves numerous experiments due to the wide range of parameters and process conditions. Furthermore, additional experiments using the same method are necessary to refine the process window [5]. Therefore, many studies have focused on predicting the process window to overcome the challenge of repeated experiments required to derive the process window [6].
The key process parameters for predicting the process window in selective laser melting (SLM) are laser power and scan speed [7], with the defocusing distance being an important additional parameter that can alter the beam diameter [8][9][10]. Figure 1 illustrates the schematic diagram of the defocusing distance, which is denoted as 'f' in table 1. The laser beam diameter is smallest at the focal plane, and changing the defocusing distance in the focal plane can alter the beam diameter and intensity. When the build plate does not move, the beam is narrow and tall. When the build plate moves in the positive direction, the beam appears convergent below the plate, while it appears divergent when the build plate moves in the negative direction. The defocusing distance affects the meltpool geometry and relative density as it alters the laser beam intensity [11,12]. Therefore, it is a critical factor in predicting the process window in SLM [13,14].
The existing process window prediction studies can be classified into three types: simulation-based prediction [15][16][17][18], density and porosity prediction models based on process conditions [5,[19][20][21][22][23][24][25], and melt pool geometry analysis-based prediction according to process conditions [7,26]. However, few studies have investigated the process window prediction using defocusing distance, and it is currently not possible to predict the process window for conditions that involve defocusing distance using existing methods.
This paper aimed to predict the optimum process window using defocusing distance in SLM. Therefore, the research goal was to derive empirical formulae based on the correlation with the energy density equations, rather than using simple experimental results as in conventional methods. The derived empirical formulae was then used for process window prediction, which was further verified through experiments. To predict the process window, the melt pool geometry was analyzed based on three process variables: defocusing distance, laser power, and scan speed. The effect of these variables was evaluated using the energy density equations. An empirical equation was derived based on the correlation between the energy density equations and the melt pool geometry analysis results. Finally, the empirical equation was used for process window prediction and experimentally verified.

Experimental
The samples were built using stainless steel 316L powder in Concept Laser M1 (Ge Additive) machine. Table 1 shows the range of process conditions set in this study. A 5 × 15 × 10 mm 3 sample was made by layer-by-layer addition using laser melting of the powder, and the laser pattern was continuous laser scanning, with an initial angle of 90º and a rotating angle of 0º.
The macro-and micro-structure of the solidified melt pool in the cross section of the component were analyzed using optical microscopy (OM), scanning electron microscopy (SEM) and electron backscatter  diffraction (EBSD). The electro-polishing was performed using Lectropol-5 with a solution of 5 % perchloric acid and 95% methyl alcohol [27]. The polished samples were then etched at a voltage of 4 V in a solution of 50 ml HNO 3 and 50 ml distilled water for 40 s in order to observe the melt pool geometry, microstructure and grain growth in the OM and SEM. The melt pool geometries, i.e., the width (W) and depth (D), were measured as shown in figure 2, and the top layer melt pool of building sample was observed as shown in a study by Qi al [10]. OM analysis was also used to inspect the presence of defects namely porosity and lack of fusion. FE-SEM(JSM-IT800) at the Converging Materials core facility of Dong-Eui University was used to analyze the grain orientations between grains and phases based on the defocusing distance. To analyze the grain orientation, the EBSD analysis was performed on the center of the building sample with size of 430 mm × 500 mm formed by the building.

Geometry and microstructure of melt pool
Melt pool geometry is considered as one of the fundamental aspects of SLM component quality as it decides the solidification mode and hence the defect formation. The ratio of depth and width (D/W) is used to identify the type of melting mode in SLM melt pool. Generally, three types of melting modes are defined based on the D/W value: (a) keyhole mode (KM) when D/W > 0.8; (b) transition mode (TM) when D/W value is less than 0.8 but more than 0.5; (c) conduction mode (CM) when D/W < 0.5. Among these, conduction mode is the only acceptable melting mode as the two others exhibit excessive defects such as gas porosity, balling and spatter. Therefore, the conditions using which SLM samples exhibit CM considered as one of the deciding factors for optimum conditions. Mapping of melting mode in power-scan speed plane and the optical images of melt pool geometry of printed samples with various defocusing distances are shown in figure 3. As KM and TM are unacceptable conditions, both are considered together in the mapping and denoted as KTM. For precise comparison, the melting modes in same power and scan speed conditions but varying defocusing distance are listed in table 2. As defocusing distance increased, the melting mode changed from keyhole mode to conduction mode owing to the decrease in depth and increase in width of melt pool. It is known that a decrease in depth to width ratio results in change of laser melting mode. More precisely, keyhole mode was observed with f = 0 mm; transition mode with f = −3 mm; and conduction mode with f = −6 mm. When the defocusing distance increases, the laser beam intensity becomes spread out over a wider area while becoming less intense as illustrated schematically in figure 1(b). Consequently, the melt pool depth decreases and the width increases. However, the melt pool width was smaller when the defocusing distance was −6 mm than when it was −3 mm since a larger beam diameter increases the amount of laser reflection, resulting in greater energy loss [8,28]. It is important to note that the reflection of laser light is not only wavelength-dependent but also influenced by the material's physical properties, such as surface roughness, absorption coefficient, and refractive index. When the beam diameter is larger, it illuminates a larger surface area, leading to increased reflection and scattering of the light, resulting in energy loss. These findings highlight the importance of carefully considering the impact of beam diameter and other material properties when optimizing the SLM process to achieve desired outcomes [8,28]. Gaussian nature of the beam can also contribute to the energy loss at the edges, as the intensity of the beam decreases gradually towards the edges. This can result in incomplete ablation or melting of the material at the edges, which can affect the quality and accuracy of the laser processing.
Microstructure is another important characteristic of the solidified weld pool, along with melt pool geometry, and is shown in figure 4. The grain orientation of the printed samples with various process parameters, as shown in table 2 and obtained from EBSD analysis, are displayed in figure 4 as inverse pole figure (IPF). Columnar structured grains grown in the building direction were observed in samples with all conditions. Different grain orientations are observed for each layer in the sample made with f = 0 mm, as it does not grow in alignment with the grain orientation [29].
Grain orientation formed a strong texture in 〈100〉 directions under f = −3 mm conditions in figure 4(e), and with epitaxial growth parallel to the building direction, elongated grains were observed. This aligns the heat flow due to the increase in the melt pool width and the decrease in the melt pool depth so that the previously solidified layer and the molten melt pool are aligned, resulting in epitaxial growth [11,30]. Figure 4(h) was observed to have unbalanced grain orientation compared to figures 4(b) and (e) because, due to the lower melt pool depth compared to the f = −3 mm condition, heat flow was not aligned, resulting in various patterns of heat flow and unbalanced grain orientation. Figure 4 shows the results of the grain boundary misorientation angle according to the defocusing distance. High angle grain boundaries (HAGBs) are observed along the border of the grain orientation, while low angle grain boundaries (LAGBs) are observed inside the grain for all conditions. The defocusing distance affects the solidification behavior, causing the grain boundary misorientation angle to vary. The specimen with a defocusing distance of 0 mm showed HAGBs along different grain orientations for each layer, with an average grain size of 55.9 μm and a higher fraction of HAGBs compared to other conditions. The specimen with a defocusing distance of −3 mm showed epitaxial growth parallel to the building direction, with HAGBs along the elongated grains and a strong texture in the direction of 〈100〉, resulting in the lowest fraction of HAGBs (0.189) and an average grain size of 179.7 μm, which is larger than that of the other conditions. Figure 4(c) shows nonuniform epitaxial growth due to misaligned heat flow. The specimen in figure 4(i) had a smaller fraction of HAGBs and an average grain size between those of figures 4(f) and (c).

Defects and tensile properties
Defects such as porosity are visible in the optical images of defocusing distances 0 and −3 mm, whereas the samples with f = −6 mm did not exhibit any defects in the cross-sectional images. To verify the presence of defects on a larger scale and to study their effect on mechanical properties, tensile tests and subsequent SEM fractography were conducted. The fractography images in figures 5(d)-(i) confirmed the optical results  regarding the presence of porosity in the samples with f = 0 and −3 mm. The tensile test results of the samples with conditions in table 2 and tensile orientations of 90º and 45º with respect to the building direction are shown in figure 6. In both orientations, the f = −6 mm sample showed better ductility and slightly higher strength. It is evident from the curves that porosity significantly affected the tensile properties, especially ductility.
3.3. Prediction of optimum process window from energy density equations 3.3.1. Energy density equations in selective laser melting As shown in table 3, melt pool geometry was analyzed using equations of the energy density with laser energy density, linear energy density, and local applied energy. Laser energy density is a one-dimensional equation with laser power divided by scan speed, and linear energy density is a two-dimensional equation with laser power divided by the multiplication of scan speed and beam diameter. Local applied energy is a three-dimensional equation with laser power divided by the multiplication of the width of scan speed and beam diameter.
Beam diameter calculation according to defocusing distance was carried out through Rayleigh length. The relationship between beam diameter (d) and defocusing distance is presented in equation (1) [9,39].  where, d 0 is beam diameter in the focal plane, f d is Defocusing distance, and f R can be derived from Rayleigh length as in equation (2).  where, λ is the wavelength of the Gaussian beam, the istrument used in this study is equipped with a ytterbium fiber laser, the length is 1070 nm, and the d 0 is 50 μm, so the f R is calculated as 1.835 mm.

Criteria for optimum condition: Upper and lower limits of process window
Deriving the process window is essential for developing an optimal combination of process parameters. The process window consists of the upper and lower limits of the optimum conditions based on laser power and scan speed, while excluding the balling effect. The upper limit is determined by the melting mode, which occurs at high energy density and is categorized into three modes based on D/W (Depth by Width) values of the melt pool (table 4): keyhole mode for D/W > 0.8, transition mode for 0.5 < D/W 0.8, and conduction mode for D/W 0.5 [10,25]. The optimum condition is based on the conduction mode as it produces high-quality products without defects. In contrast, the keyhole mode has a higher probability of generating spatters and pores due to recoil pressure inside the melt pool. The lower limit is set based on the lack of fusion, which occurs at low energy density. Geometrically, the lack of fusion occurs when W/h (Width by Hatch distance) is less than 1 and/or D/t (Depth by Layer thickness) is less than 1.1 [40][41][42]. Lack of fusion may occur on the side of the melt pool when W/h < 1 and at the bottom of the melt pool when D/t < 1.

Correlating energy density with melt pool geometry and lack of fusion
The upper limit prediction of the process window was derived from the correlation between the melt pool geometry and the energy density equation for each process condition. The upper limit is set when D/W < 0.5, and the process conditions are shown in table 1. Figures 8(a)-(f) show the correlation results between D/W and energy density equations to predict D/W based on experimental results. D/W shows a strong correlation with local applied energy, and thus the trend line for the correlation between D/W and local applied energy could be derived as equation (3).   The next step involved predicting the lower limit using the same approach as for the upper limit, but with defocusing distance applied. The lower limit is reached when D/t > 1.1 and W/t > 1, and the process conditions are shown in table 1. Figures 8(g)-(i) shows the correlation between D/t, W/h, and energy density equations. D/ t has a good correlation with linear energy density, and the trend line for the correlation between D/W and linear energy density was derived as equation (4). W/h has a good correlation with laser energy density, and the trend line for the correlation between W/h and laser energy density was derived as equation (5).

Process window prediction
The optimal process window is predicted using empirical equations for upper and lower limits, which are derived for specific melt pool geometry and defect-free conditions. Firstly, it was observed that the criterion for the lower limit, W/h, has a good correlation with laser energy density. Since the hatch distance is a fixed variable, only the melt pool width was considered, resulting in a one-dimensional laser energy density equation that can be interpreted as laser movement. Therefore, laser movement is considered advantageous for analyzing melt pool width. Secondly, it was observed that W/h, which is the criterion for the lower limit, has a good correlation with linear energy density. Since the hatch distance is a fixed variable, the linear energy density equation is twodimensional and takes into account the beam diameter and scan speed. This is advantageous for analyzing the trend towards depth because it considers the interaction of the beam diameter and scan speed with powder and solid areas in a two-dimensional manner. In other words, when the beam diameter is large and the speed is high, the interaction between the powder and solid area decreases, resulting in decreased dilution and depth. Thirdly, it was found that the upper limit criterion, D/W, has a strong correlation with local applied energy. This parameter considers the area of the beam and the scan speed in three dimensions, representing the threedimensional energy input into the melt pool geometry. Therefore, local applied energy is considered advantageous for changing the melting mode of the melt pool geometry and has a strong correlation with the trend towards D/W, which is the standard for the melting mode [10,25].
The empirical equation for the upper limit of the process window is derived as equation (6)

( ) 
The empirical equation for the lower limit is derived by substituting equation (4) into D/t < 1.1, the first criterion of the lower limit, to derive equation (7) below, (8) is derived by substituting formula (5) for the second criterion W/h < 1. Figure 9 displays the process window, which was predicted based on the defocusing distance derived from the empirical equation. Keyhole mode was mostly observed in the cases of f = 0 mm and f = −2 mm, and the optimum condition section was not observed. However, the optimum condition section was observed starting from f = =−3 mm. As the defocusing distance increased, the optimum condition section increased at high laser power and low scan speed, while it decreased at low laser power and high scan speed. Figure 10 presents a comparison between the process window obtained from the actual experimental results and the predicted process window. As with the predicted process window, an increase in the defocusing distance resulted in an increase in the size of the optimum condition section at high laser power and low scan speed. While the predicted process window and experimental results did not match in all areas, they were similar in many areas.

Validation of predicted process window
The predicted conditions were validated through a building test as shown in table 5, wherein a defocusing distance of −4 mm was used, which was not tested before. The test included building one keyhole mode, two optimum, and one lack of fusion conditions (shown in figure 11). The results of the verification showed that the keyhole mode condition transformed to a transition mode with a D/W of 0.62. The lack of fusion condition was confirmed as such, as the D/t value was 0.9, which is less than the threshold of 1.1. The two optimal conditions met both the upper and lower limit conditions and exhibited higher relative density with fewer or no defects compared to other conditions. This study successfully developed empirical equations based on energy densities to predict the process window for SLM of stainless steel, and experimentally validated the predicted process window under various conditions. The outcomes of this study can help optimize the process window for producing defect-free components with excellent mechanical properties. However, the applicability of the empirical relations obtained from this study may vary when different lasers or materials are used. These relations are developed based on experimental data obtained from a specific laser and material system (stainless steel), and therefore, their validity may be limited to that system only. When using a different laser or material, the empirical relations should be validated through additional experiments or simulations before applying them to the new system. It is also important to note that the laser and material properties, such as beam profile, pulse duration, energy density, and material absorption coefficient, can significantly affect the ablation and melting behavior, and therefore, the empirical relations may need to be modified or adjusted accordingly.

Conclusion
The aim of this study was to predict the process window for selective laser melting of stainless steel using empirical equations based on energy density, rather than relying solely on experimental data, and to experimentally validate the predicted process window under conditions outside those used to establish the empirical relationships. The following conclusions were drawn: The upper limit of the process window was identified as the expression D/W, which determines the transition from conduction mode to transition and/or keyhole mode. The lower limit of the process window was defined by geometric factors such as D/t and W/h, which indicate a lack of fusion defect in the component. Changing the defocusing distance from 0 mm to −6 mm resulted in a decrease in melt pool depth and an increase in width, which corresponded to a shift from keyhole to conduction mode and a decrease in D/W value.
The upper limit of the process window, D/W, had the strongest correlation with local applied energy (P/Vd 2 ), and an empirical expression for the upper limit in the P-V plane was derived as P34Vd 2 . The first and second criteria of the lower limit, D/t and W/h, showed the best correlation with linear energy density (P/Vd)   and laser energy density (P/V), respectively. Therefore, expressions for the lower limit were obtained as P > 2.16Vd and P < 0.13V in the P-V plane. Verification tests were also performed under conditions (defocusing distance of −4 mm) that were not used to establish the empirical relationships, including one keyhole mode condition, two optimal conditions, and one lack of condition, which showed good agreement with the prediction results.
In summary, the findings of this study provide useful insights into the effect of process parameters on the melt pool geometry and the transition between melting modes, and can help optimize the process window for producing defect-free components with excellent mechanical properties.