High power selective laser melting of crack sensitive nickel-base alloy CM247LC, including dimensional analysis and modelling


 Compared to reference parameters in the low power and scan velocity range, which lead to dense and crack-free CM247LC LPBF samples due to in-situ crack healing, high power, high scan velocities and increased laser beam diameters are investigated, to decrease the production time further. By keeping the maximum laser intensity from the reference and the laser power to scan velocity ratio constant, the intensity approach provides an initial estimation for the laser spot size regarding the measured Archimedean density and crack density in the high power and high scan velocity range. The investigated cracks are identified as re-melting cracks. Solidification or hot cracks are not observed, since the crack healing effect for those kinds of cracks still occurs. Furthermore, a melt pool depth range is discovered, where not only solidification cracks can be avoided, but also re-melting cracks, which are resulting from higher laser power inputs. This theory can be proven by further laser spot size optimization, where the melt pool depth comes closer to the mentioned range. The Archimedean density and crack density results, in case of the 600 W power parameter with 2400 mm/s scan velocity and a beam diameter of 164 µm, are close to the one obtained from the reference with 200 W, a scan velocity of 800 mm/s and a laser spot of 90 µm. With the intensity approach and laser beam diameter optimization, the production time can be reduced by 300%. Based on dimensional analysis, a model, which combines the samples density with the crack density through the melt pool depth, is presented. Six main and two additional process and laser parameters are taken into relation. The result from the model and the measured values from experiments are in good agreement. Additionally, the influence of the doubled layer thickness and an increased hatch distance by 50% with varying scan velocities on the Archimedean density and crack density is analysed.

Compared to reference parameters in the low power and scan velocity range, which lead to 16 dense and crack-free CM247LC LPBF samples due to in-situ crack healing, high power, high 17 scan velocities and increased laser beam diameters are investigated, to decrease the production 18 time further. By keeping the maximum laser intensity from the reference and the laser power to 19 scan velocity ratio constant, the intensity approach provides an initial estimation for the laser 20 spot size regarding the measured Archimedean density and crack density in the high power and 21 high scan velocity range. The investigated cracks are identified as re-melting cracks. 22 Solidification or hot cracks are not observed, since the crack healing effect for those kinds of 23 cracks still occurs. Furthermore, a melt pool depth range is discovered, where not only 24 solidification cracks can be avoided, but also re-melting cracks, which are resulting from higher 25 laser power inputs. This theory can be proven by further laser spot size optimization, where the 26 melt pool depth comes closer to the mentioned range. The Archimedean density and crack 27 density results, in case of the 600 W power parameter with 2400 mm/s scan velocity and a beam 28 diameter of 164 µm, are close to the one obtained from the reference with 200 W, a scan velocity 29 of 800 mm/s and a laser spot of 90 µm. With the intensity approach and laser beam diameter 30 optimization, the production time can be reduced by 300%. Based on dimensional analysis, a 31 model, which combines the samples density with the crack density through the melt pool depth, 32 is presented. Six main and two additional process and laser parameters are taken into relation. 33 The result from the model and the measured values from experiments are in good agreement. 34 Additionally, the influence of the doubled layer thickness and an increased hatch distance by 35 50% with varying scan velocities on the Archimedean density and crack density is analysed. 36 37 1. Introduction 1 Selective laser melting (SLM) is a synonym for a layer-wise solidification of a deposited 2 powder layer with a laser source. Since standard SLM-processes have an increased production 3 time, two main strategies are found for increasing the productivity, according to  Sistiaga et al. [1]. In the first case, several "standard" lasers are working in parallel, whereas in 5 the second case high power lasers are used for SLM-processing. The last mentioned approach 6 is called High Power SLM (HP SLM). 7 Most studies about HP SLM are based on steel powders. With a laser power of 380 W 8 compared to 100 W, the laser scan speed can be enhanced by approximately 3.8 times, which 9 increases the build rate about 72% in case of SS316L (1.4404 steel), as reported by Sun et al. 10 [2]. A direct relationship between the laser power input and the build rate is identified. The 11 influence of high laser powers up to 800 W in conjunction with strongly increased beam 12 diameters up to 262 µm, in case of SS316L, is investigated in the research of Metelkova et al. 13 [3]. The combination of laser defocusing and high power inputs increases the productivity up 14 to 840%. In the study of Montero-Sistiaga et al. [1], HP SLM of SS316L with a 1 kW top hat 15 power distribution laser and a beam radius of 700 µm is analysed. Independent of the applied 16 scan strategy, meaning different rotation angle between the layers, cracks occurred parallel to 17 the build direction in all SS316L samples during HP SLM with a top hat. By varying the laser 18 power from 80 to 480 W and the scan velocity from 493 to 2958 mm/s, a minimum energy 19 density of about 9.34 J/mm 3 is identified to guarantee relative densities over 99.5% in case of 20 SS316L, as reported by Bang et al. [4]. At a fixed power of 400 W, the microstructural 21 properties, the mechanical properties and the chemical composition changes with varying 22 energy density from 9.58 to 47.95 J/mm 3  spatter reduction and part density, the use of the larger beam provides significant improvements 23 due vaporization reduction. The build rate could only be improved moderately (up to 8 mm 3 /s). 24 In addition, several problems are investigated in case of HP SLM of nickel-base alloy 25 Inconel 718 with laser powers from 350 W to 1550 W, as explained in detail in the study of Yin 26 et al. [20]. With an increase in laser energy input, the fluctuation of the melt pool is more 27 intensive. A droplet column, which is an advanced form of droplet spatters, occurs more likely 28 with high laser power. Furthermore, large spatter tend to be generated also with a high-power 29 laser. The melt pool instability, the collision of spatters and the powder agglomeration are the 30 dominant mechanisms for large spatters. 31 In the current study, HP SLM of nickel-base alloy CM247LC is investigated. The major 32 difficulty during SLM-processing of precipitation-hardened nickel-base alloys, especially 33 CM247LC, is their high susceptibility to hot cracking, as reported by Carter et al. [21]. Based 34 on reference parameters with 200 W, which results in dense and crack free CM247LC samples, 35 high power and high scan velocity parameters are re-scaled and optimized to decrease 36 production time further with similar results regarding Archimedean density and crack density, 1 as obtained from the reference samples. The reference process and laser parameters for dense 2 and crack-free CM247LC are described in detail in the research of [22] and summarized in the 3 study of [23]. To increase the productivity further, all samples are manufactured with a bi-4 directional scan strategy. Furthermore, a relation between the relative density and crack density 5 over the melt pool depth is found, based on Buckingham`s Π -theorem for dimensional analysis 6 and modelling. Additionally, the influence of double the layer thickness on the Archimedean 7 density and crack density is analysed, based on the mentioned re-scale approach. To further 8 increase the productivity, an increased hatch distance of 50% is investigated, in conjunction 9 with the doubled layer thickness.

Sample analysis 24
The relative Archimedean density and crack density of the XY plane of the cubic samples 25 with the dimensions of 10 x 10 x 10 mm 3 are equally measured as in the study of Gerstgrasser 26 et al. [22]. For each high power parameter with the corresponding scan velocity, three cubic 27 samples are manufactured. Additionally, fifty melt pool cross-sections of the last layer in the 28 build up plane (XZ plane) are quantified and analysed for each high power parameter, including 29 the reference at 200 W with a bi-directional scan strategy. All images are taken with a Keyence 30 VHX-5000 and quantified with ImageJ. 31 1

Process parameters and intensity Approach 2
Based on dense and crack-free reference samples in conjunction with the corresponding 3 process parameters at 200 W with a beam diameter of 90 µm, as explained in the research of 4 [22] and summarized in the study of [23], the bi-directional scan strategy is applied, not only 5 to reduce the process time further, but also for the comparison with the high power parameter 6 samples, manufactured with 500 and 600 W. By using the same peak intensity and the same 7 track energy density, as known from the crack-free reference samples, higher laser powers and 8 scan velocities should be achieved with nearly equal results as under the circumstances of the 9 reference, by simply changing the laser beam diameter in the build plane. Since crack healing 10 is dependent on the melt pool geometry, especially in case of the melt pool depth, similar melt 11 pool dimensions have to be achieved, as obtained from the reference. The intensity distribution 12 for a Gaussian beam is defined as follows, according to Poprawe et al. where P D is the power dependent laser beam diameter in the focus plane, based on the value of 8 laser power P . Based on the track energy density from the reference, which is also kept 9 constant, the corresponding high laser scan velocity is calculated as follows: 10 where P v is the power dependent laser scan velocity in mm/s, t E is the track energy density in 12 J/mm and has a value of 0.25 J/mm, as obtained from the reference samples. In case of SLM-13 processed CM247LC, equation (5) can be written as follows: 14 where the proportionality factor has the unit mm/J. 15 16

Dimensional analysis and modelling 1
The Rosenthal equation is well-known and a widely used analytical model, not only to 2 describe the weld pool geometry in case of welding, but also the melt pool dimensions in AM, 3 especially for SLM, as reported by Mosallanejad where the melting point of the alloy is described by f T , the temperature far from the melt pool 9 is presented by 0 Equation (9) demonstrates, that the melt pool dimensions are proportional to the square root of 1 the laser power to scan velocity ratio, as discussed by Mosallanejad et al. [28]. Since the laser 2 power to scan velocity ratio is kept constant for re-scaling in this research, as mentioned in 3 section 2.4, the same melt pool depths are proposed, independent of the power or scan speed 4 values. Furthermore, the intensity or power density, which is a function of the laser beam 5 diameter and is needed to explain the experimental observations in a proper way, has to be 6 considered. Additionally, not only a relation between the melt pool depth to density is required, 7 but also to the crack density.
which is a unit free physical law and represents any mathematical equation in Physics and 17 Engineering with k dimensional variables of l fundamental units, according to Jazar [  In case of doubling the layer thickness and increased hatch distance of 50%, only one 8 cubic sample for each parameter is produced, to reduce effort and to test the intensity approach 9 with reasonable outlay also for the last two mentioned process parameters with decreasing scan 10 velocity. The Archimedean density and crack density are equally measured as explained in 11 section 2.2. 12 13 3. Results and discussion 14

Re-scaled high power and scan velocity parameters 15
Based on equation (4) and (6), the laser beam diameter and scan velocity can be directly 16 obtained from the selected higher power values. In this study, the power values of 500 W and 17 600 W, which are 2.5 and 3 times higher compared to the reference, are investigated with the 18 intensity approach. The re-scaled parameters are summarized in Table 2. Since the track energy 19 t E is kept constant, also the scan velocity increases 2.5 and 3 times, in case of 500 and 600 W, 20 respectively. 21  Archimedean density and crack density values are obtained as with the uni-directional 16 reference, which lead to dense and crack-free samples, as explained in section 2.3. In Fig. 4   Further investigations reveal that the cracks in the SLM-processed CM247LC samples, 1 manufactured with the 500 W and 600 W parameter, can be identified and classified as re-2 melting cracks due to their specific morphology, similar as investigated in the research of 3 Gerstgrasser et al. [23]. The re-melting cracks from the examined XY plane are shown in Fig.  4 5, in case of the 500 W and 600 W parameter, respectively. Considering not only the higher average Archimedean density of the 600 W parameter in 11 comparison to the 500 W parameter, but also the fact that the production time is decreased by 12 300%, compared to the reference, the 600 W parameter is favoured and further investigated. 13 The qualitative difference of the melt pool geometry for the 200 W reference and 600 W 14 parameter, which are obtained from digital microscopy, are illustrated in Fig. 6  Since the melt pool depth from the 600 W parameter with a beam diameter of 156 µm and a 19 scan velocity of 2400 mm/s has a value of 86 (expected value), the beam diameter or the scan 20 velocity has to be increased further, to reach the mentioned crack-free melt pool depth range. 1 In this study, the increased beam diameter is further investigated.

Laser spot size optimization 8
To proof the theory with the widened beam diameter and the required melt pool depth in case 9 of the 600 W parameter, also two smaller spot diameters, compared to the 156 µm beam size, 10 are investigated. The analysed beam diameters are 132 µm, 148 µm and 164 µm. The quantified 11 melt pool geometries for each beam diameter with 600 W and a scan speed of 2400 mm/s are 12 presented in Fig. 8. The corresponding error bar presents the standard deviation of the fifty 13 measured melt pools. With an increased laser beam diameter, the melt pool depths are coming 14 closer to the above-mentioned crack free range, between solidification and re-melting cracks. 15 The  The quantified values of the average Archimedean and crack density from the different laser 5 spot diameters, 132, 148 and 164 µm, are shown in Fig. 9. Remarkably, the Archimedean 6 density increases with increased laser spot diameter, whereas the crack density decreases. In 7 case of 600 W, a scan velocity of 2400 mm/s and a beam diameter of 164 µm, the Archimedean 8 and crack density results are coming closer to the values obtained with the 200 W reference, a 9 scan speed of 800 and a beam diameter of 90 µm. The samples manufactured with 600 W, 2400 10 mm/s and spot size of 164 µm have only a few, small observed re-melting cracks, as presented 11 in Fig. 10 a), based on the sample with the highest measured crack density value in case of the 12 164 µm laser beam diameter. In case of a 132 µm beam diameter instead of 164 µm, the amount 13 of cracks are drastically higher, as shown in Fig. 10 b) qualitatively. To consider not only the 14 worst-case with a laser power of 600 W, scan speed of 2400 mm/s and a spot size of 164 µm, 15 half of the analysed XY plane from the sample with the smallest measured crack density is 16 presented in Fig. 11

Crack density model 5
To explain the experimental observations in section 3.2 with different beam diameters, 6 in case of 600 W and a scan speed of 2400 mm/s, the intensity I , the scan speed scan v and the 7 hatch distance h are defined as fundamental variables. The intensity I is not only a function 8 of the laser power, but also a function of the laser beam diameter and quality. The 9 Buckingham`s Π -theorem is applied for two dependent systems, to reduce the complexity and 10 to create reasonable relations with the three remaining variables -sample density s ρ , melt pool 11 depth d and crack density crack ρ -including the measured results from the experiments in 12 section 3.2. The density s ρ will be coupled with the crack density crack ρ over the melt pool 13 depth d , which is a key factor for both parameters. The remaining variables are permuted for 14 each of the two systems (1. System: density -melt pool depth; 2. System: melt pool depth -15 crack density). The parameters, their units and dimensions are summarized in Table 3. 16 17

ML − ⋅
Crack density crack ρ mm/mm 2 = 1/mm In case of the first system, the fundamental variables are I , scan v and h , which are 3 permuted with the melt pool depth d and the sample density s ρ . In this system, the number of 4 dimensionsl has a value of 3 and the amount of variables k is equal to 5, which leads to 2 kl −= 5 , meaning two dimensionless Π -terms: 6 Considering the fundamental dimensions for each parameter, the Π -terms can be expressed as: 7  (16) Using the same procedure for the remaining variables crack density crack ρ and melt pool depth 1 d in case of the second system, the following two dimensionless Π -terms are determined and 2 asterisked, to mark the second system: 3 (17) As mentioned in equation (11), a relation between the two Π -terms for each system has to be 4 found. Therefore, the process and laser parameter in conjunction with the experimentally 5 measured Archimedean density, melt pool depth and crack density are used from section 3.2, 6 to find the corresponding function between each of the Π -terms with curve fitting. Further 7 information about the least square fit approach for curve fitting can be found in the research of 8 Gerstgrasser et al. [39]. In case of the first system, a linear relation between the dimensionless 9 1 Π and 2 Π -term is observed, as presented in Fig. 12. The associated linear relation of the Π -10 terms for the first system can be expressed mathematically as follows: Since the Archimedean density is usually the first measured parameter and can be classified as 7 a non-destructive material test, the sample density is defined as an input-parameter, to calculate 8 the melt pool depth. Furthermore, the crack density strongly depends on the melt pool depth, as 9 mentioned in section 3.1. 10 In case of the second system, a power function can be observed between the two 11 dimensionless 1 * Π and * 2 Π -term, as shown in Fig. 13 (21) where the relation between the crack density crack ρ and the melt pool depth d is described with 7 equation (21). 8 Fifty measured melt pool depths from the experiments are compared to the predicted 9 ones, based on equation (19). As shown in Fig. 14 Compared to the classic phenomenological modelling with linear regression in case of two 1 parameters, the Buckingham`s Π -theorem provides a good alternative to set several process, 2 laser, material and geometrical parameters in relation. In this study, six main and two additional 3 parameters, including the laser power and beam diameter, which are part of the intensity, are 4 taken into relation. Furthermore, Buckingham`s Π -theorem is an user-friendly approach to 5 create reasonable models, based on important influence parameters from the process. The low 6 expenditure of time for finding a solution is an additional advantage of this approach. This 7 shows the high potential of dimensional analysis and modelling with the Buckingham`s Π -8 theorem in case of HP SLM regarding sample density and crack density. 9 10 11

Influence of increased layer thickness and hatch distance 12
Using the intensity approach, as explained and discussed in section 2.3 and 3.1, for 13 further investigations regarding increased layer thickness with gradually decreased scan 14 velocity values, interesting results can be obtained in case of Archimedean density and crack 15 density, as presented in Fig. 16. In case of a scan speed of 2100 mm/s and a doubled layer 16 thickness, the crack density is close to the one obtained in section 3.2 with a beam spot of 132 17 µm. Independent of the scan velocity, the Archimedean density is quite low. With a decreased 18 scan velocity, the Archimedean density increases, but simultaneously the amount of cracks. The 19 reason could be found in deeper melt pools, which are required to produce more base or bulk 20 material, in case of a doubled layer thickness. At the same time, more re-melting cracks are 21 generated due to an increased melt pool depth, as investigated in section 3.1. In case of an 22 additionally increased hatch distance of 50%, the Archimedean density drops even more, as 23 shown in Fig. 17 with varying scan speeds. Further investigations are needed, to find an 24 optimum with increased layer thickness and hatch distance.  Using the same maximum laser intensity of 62876 W/mm 2 and line energy of 0.25 J/mm, 2 as received from dense and crack-free SLM-processed C247LC samples with 200 W power, 3 similar results are obtained regarding Archimedean density and crack density with an increased 4 beam diameter in case of 600 W power and a scan velocity of 2400 mm/s. The productivity can 5 be increased relatively by 300%. A melt pool depth range from 66 μm to 81 μm is discovered, 6 where not only solidification cracks can be avoided, but also re-melting cracks, which result 7 from higher laser power inputs. Based on dimensional analysis, a model is described and 8 presented, which combines the samples density with the crack density through the melt pool 9 depth. The model includes six main and two additional process and laser parameters. Results 10 from the model and the experimental measured values are in good agreement. Furthermore, the 11 influence of a doubled layer thickness and additionally increased hatch distance by 50% with 12 different laser scan speeds on the Archimedean density and crack density is investigated. In 13 case of a doubled layer thickness, not only the Archimedean density increases with a decreased 14 scan velocity, but also the crack density. Since deeper melt pools are required to produce more 15 base or bulk material for that case, also more re-melting cracks are generated, at the same time. 16 Combining a doubled layer thickness with an increased hatch distance by 50%, the 17 Archimedean density drops even more. Further investigations are needed, to find an optimum 18 regarding highly increased layer thickness, Archimedean density and crack density.