Effects of Pore Distribution on Mechanical Properties of Selective Laser Melted Inconel-718

In recent years, Selective Laser Melting (SLM) technology has made significant advancements, offering high precision and near-net shaping capabilities that are widely applicable in aerospace, mechanical, and electrical industries. Inconel-718, known for its exceptional high-temperature corrosion resistance, fatigue endurance, and wear resistance, has found extensive use in aerospace applications such as gas turbine disks, rocket engines, and spacecraft components. However, the presence of porous defects in SLM-manufactured metal parts is inevitable, and these pores significantly affect the mechanical properties of the materials. While contemporary studies have focused on the influence of individual or a limited number of pores, the impact of pore distribution has been largely overlooked. This oversight leads to reduced prediction accuracy and hampers the practical implementation of SLM technology. Therefore, this paper specifically investigates the impact of pore distribution on the performance of SLM-manufactured metal materials, using Inconel-718 as an example. The study establishes simulation experiment models to explore diverse pore distribution patterns, including spatial position distribution models and spatial quantity distribution models. The Finite Element Method (FEM) model utilizes the Johnson-Cook constitutive model, and the pores are equivalently modelled as two-dimensional plane ellipses. Uniaxial tension simulations are performed to analyze the mechanical behavior of the materials. The results demonstrate that the mechanical properties of SLM-fabricated Inconel-718 are significantly influenced by the spatial position distribution, spatial quantity distribution, and spatial orientation distribution of the pores. Under different spatial position distributions, materials with more pores parallel to the stretching direction exhibit poorer mechanical performance due to earlier and more significant stress concentration. Under different spatial quantity distributions, materials with a higher pore density and smaller pore spacing show worse mechanical performance due to earlier and more severe stress concentration. Under different spatial orientation distributions, materials with a larger angle between the pore’s major axis and the stretching direction exhibit worse mechanical performance due to enhanced stress and earlier and more severe stress concentration. Overall, this study highlights the importance of considering pore distribution in SLM-manufactured metal materials, providing insights into the impact of spatial position, quantity, and orientation distributions on the mechanical properties of Inconel-718.


Introduction
Selective Laser Melting (SLM) technology, utilizing high-energy laser as the energy source and based on the layer-by-layer precise powder deposition on powder bed and laser-based layer-by-layer melting accumulation, is able to form high-density and complex-shaped metallic components, featuring high precision and near-net forming.With broad prospects for application, SLM technology is increasingly applied in aerospace [1], mechanical [2], electrical [3] and other fields.Inconel-718 exhibits exceptional characteristics, including superior high-temperature corrosion resistance, fatigue resilience, wear resistance, excellent weldability and remarkable strength at elevated temperatures.The material is extensively employed in various applications, such as gas turbine disks, rocket propulsion systems, aerospace engineering, nuclear reactors, industrial pumps and high-precision tooling [4][5][6].Unfortunately, porous defects in metallic components manufactured by the SLM fabrication process cannot be eliminated [7], even with the use of process parameter optimization [7], powder optimization [8], vacuum fabrication [9] and post-treatments [10].The material properties of components produced through Selective Laser Melting (SLM) [11] are significantly influenced by the presence of multiple pores, which imposes restrictions on their utilization in various crucial fields.Hence, examining the impact of porosity generated in the SLM process has emerged as a significant research direction.Current research primarily focuses on the effects of porosity rate and pore size on mechanical properties such as fatigue life and tensile strength.The influence of pore distribution on material performance has received limited attention in the existing literature.However, several researchers have made significant progress in investigating the effects of SLM process parameters, microstructure, and porosity on mechanical properties.
Abele et al. [12] conducted a comprehensive analysis of the impacts of SLM process parameters, such as laser power, scan speed, and hatch distance, on porosity and mechanical properties.They developed statistically significant regression models for porosity and tensile strength, allowing for tailored performances within the design space.Chen et al. [13] employed various techniques, including Finite Element Modeling (FEM), microscopy, X-ray Computed Tomography (CT), and mechanical property testing, to investigate the microstructure, porosity, and mechanical properties of an AlSi10Mg alloy fabricated via SLM.Their results indicated anisotropic ductility, potentially attributed to the morphology and distribution of the pores.Zhao et al. [14] discovered the presence of gas pores in Al-Si alloy components fabricated using SLM.They found that fatigue failures often initiated from surface or subsurface gas pores, leading to the development of fatigue life prediction equations that considered the impact of pores.They observed that the fatigue life of SLM-produced samples decreased with increasing pore size at identical applied stress levels.While these studies have made significant contributions to understanding the effects of porosity and microstructure on mechanical properties, the influence of pore distribution on material performance has not been extensively explored.This highlights the need for further research in this area to gain a more comprehensive understanding of the relationship between pore distribution and material properties.Therefore, taking Inconel-718 as the example, this paper focuses on the influence of pore distribution on the properties of SLM-manufactured metallic materials.This study investigates diverse pore distribution through the establishment of simulation experiment models, including spatial position distribution models, spatial quantity distribution models and spatial orientation distribution.

Materials
The Inconel-718 specimens in the study were manufactured using an FF-M140 SLM machine sourced from Fastform, China.The fabrication process employed a chessboard scanning strategy, and no heat treatment was applied to the specimens.The SLM parameters provided by the manufacturer are presented in Table 1 [17], while Table 2 [17] provides the primary chemical element compositions of the Inconel-718 material.
During the investigation of Inconel-718, the volume fraction of pores in the samples was determined to be 0.22%.A significant quantity of 57591 pores per cubic millimeter was detected.The identified pore defects were classified into three distinct types: gas pores, keyhole pores, and lack-of-fusion (LOF) pores.These pore types were then approximated using single or multiple ellipsoidal models [17].
This information provides an overview of the manufacturing process, SLM parameters, chemical compositions, and pore characteristics of the Inconel-718 specimens studied.

Pore-considered Finite Element Modelling
In order to elucidate the impact of pore distribution on the mechanical properties of SLM-produced Inconel-718, a series 2D representative porous volume element model with different types of pore distributions were constructed and uniaxial tension simulations were performed.The pore-considered finite element model is shown in Figure 1.(taking 4×4 uniform distributed pores as the example).The dimensions of the representative volume element were fixed at 10mm×10mm.Ellipses with the major axis and minor axis were kept fixed at 0.168mm and 0.084mm were used to represent pores, based on the results of Ji et al. [17] and practical limitations such as equipment performance.
The Johnson-Cook constitutive model was used to describe the elastic-plastic behaviors of SLMproduced Inconel-718, and the constitutive parameters are presented detailly in Tables 3 [15] and 4 [16], respectively.214.58 0.305 Considering large-scale grid distortions in the simulation, a linearly reduced integration scheme with fine grid partitioning was adopted, and plane-strain elements were chosen to enhance the simulation efficiency.The specimens were meshed and assigned with plane strain element types CPE3 and CPE4R.Taking accuracy and cost into account, a non-uniform grid distribution was selected with larger overall dimensions and smaller dimensions around the pore regions.Static, general analysis step was used.The boundary conditions were: the left boundary of the specimen is symmetrical along x-direction and the top boundary is y-direction symmetry.As the material properties exhibited significant strain-rate dependencies, the right boundary was subjected to displacement stretching with a constant strain rate of 0.001s -1 .

PORE Distribution Effects on SLM-produced Inconel-718
To investigate the influence mechanism of pore distribution on SLM-produced Inconel-718, the researchers conducted three sets of uniaxial tension simulations.Firstly, they compared three different distribution patterns: uniform distribution, period distribution, and random distribution.By examining these patterns, the researchers aimed to understand the effects of position distribution patterns on the behavior of porous materials.Secondly, the simulation results of different pore quantities were compared.This analysis focused on researching the effects of quantity distribution patterns on the behavior of porous materials.By varying the number of pores and observing the corresponding simulation results, the researchers aimed to understand how pore quantity distribution influences material behavior.Finally, the researchers compared the simulation results of different pore attitudes.This investigation aimed to understand the effects of orientation distribution patterns on the behavior of porous materials.By varying the orientations of the pores and analyzing the simulation results, the researchers sought to identify how pore attitude distribution impacts material behavior.

The Effects of Position Distribution Patterns
By conducting these three sets of simulations and comparing the results, the researchers aimed to gain insights into the influence mechanism of pore distribution on the mechanical behavior of SLM-produced Inconel-718.
The number of pores was set to 36.For the uniform distribution, rectangular pore arrays with dimensions of 6×6 were selected.There were two types of the period distribution: 3×12 mean a distribution of 3 rows along the x-direction and 12 columns along the y-direction, and 12×3 means a distribution of 12 rows along the x-direction and 3 columns along the y-direction, denoted as.And the random distribution of the positions of 36 pores were randomly generated.The stress contour of different spatial location distributions of pores is compared in Figure2.
The results illustrate that stress concentration is distributed around the pore, with the maximum stress located on both sides of the pore perpendicular to the tensile direction, while the minimum stress occurs on both sides of the pore parallel to the tensile direction.This result may be attributed to the fact that the location of maximum stress corresponds to the smallest cross-sectional area perpendicular to the tensile direction, and stress is redistributed around the pore, leading to the appearance of minimum stress on both sides of the pore parallel to the tensile direction.Besides, as the distance between neighboring pores decreases, the distribution of pores becomes denser, and stress concentration becomes more severe.
The stress-strain curves for the different spatial position distribution forms are shown in Figure 3.As can be seen in this figure, the distribution of pores has little effect on the elastic modulus, but it does have a significant impact on the yield stress.The comparison of stress-strain curves from various spatial distributions reveals that the X-directional yield was highest for the 12×3 distribution, followed by the 6×6 distribution, while the remaining two distributions had the smallest yield stress values and showed little difference.This may be due to the fact that fewer pores are distributed parallel to the tensile direction, resulting in better mechanical properties of the material in this direction.Besides, In the tensile direction, the fracture performance of the 12×3 distribution is superior to that of the 6×6 distribution, while the fracture performance of the 6×6 distribution is superior to that of the 3×12 distribution and the random distribution, with no significant difference observed between the 3×12 distribution and the random distribution.This may be due to the fact that stress concentration occurs earlier and more pronounced in the 3×12 distribution and the random distribution parallel to the tensile direction, resulting in larger stress and easier fracture of the specimens.

The Effects of Quantity Distribution Patterns
In this comparative simulation study, four types of quantity distributions were selected, including rectangular pore arrays with dimensions of 4×4 distribution with 16 quantities, rectangular pore arrays with dimensions of 5×5 distribution with 25 quantities, rectangular pore arrays with dimensions of 6×6 distribution with 36 quantities, and rectangular pore arrays with dimensions of 7×7 distribution with 49 quantities.The stress contour comparison plot is shown in Figure4.
The maximum stress appears in the case of a 7×7 pore distribution, which may be due to the close spacing and large number of pores resulting in significant stress concentration and smaller crosssectional area perpendicular to the stretching direction.The minimum stress also appears in the 7×7 distribution, as the stress redistribution results in the presence of maximum and minimum stresses around the pores.
The stress-strain curves for the four different spatial quantities distribution forms are shown in the Figure 5.The comparison of stress-strain curves from various quantities distributions reveals that the yield stress of the 4×4 distribution is slightly higher than that of the 5×5 distribution, which is higher than that of the 6×6 distribution and the random distribution.The yield stress of the 7×7 distribution is the smallest and differs relatively pronounced from the other distributions.This may be attributed to the fact that the more pores there are and the denser the pore distribution, the more significant stress concentration is, resulting in poorer mechanical properties of the material.Besides, in the tensile direction, the fracture performance of the 4×4 distribution is slightly superior to that of the 5×5 distribution, while the fracture performance of the 5×5 distribution is slightly superior to that of the 6×6 distribution.The fracture performance of the 7×7 distribution is the worst, with relatively pronounced differences from the other distributions.This is likely attributed to the fact that stress concentration by 7×7 distribution

The Effects of Attitude Distribution Patterns
The study focused on a fixed porosity number of 36 and utilized rectangular pore arrays with dimensions of 6×6.Four different spatial orientation distribution models were created by varying the angles between the major axis of the elliptical pores and the stretching direction.The angles considered were 0°, 30°, 60°, and 90°. Figure 6 presents a stress contour comparison plot.The results demonstrate that the location of stress concentration is influenced by the distribution of pore orientations, providing further evidence of the impact of pores on material properties.Stress concentration occurs at the upper and lower boundary points of the pore ellipse, indicating stress transmission along the pore boundary.The stress reaches its highest value when the angle between the major axis of the pore and the direction of the applied tensile load is 90°.This is followed by a descending sequence of angles: 60°, 30°, and 0°.The increase in stress is attributed to the decrease in the cross-sectional area of the specimen perpendicular to the stretching direction as the angle increases.Figure 7 shows the stress-strain curves for the four different spatial quantity distribution forms.A comparative analysis of the stress-strain curves for different orientation distributions reveals that the yield stress is highest when the angle between the pore's major axis and the direction of the applied tensile load is 0°.It then decreases in the order of angles 30°, 60°, and 90°.This can be attributed to the larger cross-sectional area perpendicular to the stretching direction as the angle increases, resulting in higher stress and more pronounced stress concentration, ultimately leading to a deterioration in the material's mechanical properties.Furthermore, in the tensile direction, the material exhibits the lowest fracture performance when the angle between the major axis of the pore and the stretching direction is 90°.Conversely, at 0°, the material demonstrates superior fracture performance.This can be attributed to the larger stress and earlier and more intense stress concentration around the pores as the angle increases, making the specimens more susceptible to fracture in the stretching direction.0-degree angle between the major axis and the stretching direction 30-degree angle between the major axis and the stretching direction

Conclusion
In order to investigate the effect of pore distribution on the mechanical properties of Inconel-718 manufactured by SLM process, porous models were established and mechanical simulations were carried out.The influence of spatial position distribution, spatial quantity distribution and spatial attitude distribution on the mechanical and damage properties of Inconel-718 manufactured by SLM process were studied.
For the spatial position distribution, under different distribution forms, the higher number of pore distribution and smaller spacing in the stretching direction led to a lower yield stress and worse fracture performance.The reason could be that with more pores distributed in parallel to the direction and smaller spacing between them, stress concentration occurs earlier and is more intense, resulting in inferior mechanical performance of the material.
In terms of spatial quantity distribution, different forms of distribution result in varying effects on the material's behavior.A higher number of pore distributions, concentrated pores, and smaller spacing between them are associated with lower yield stress and inferior fracture performance.This can be attributed to the fact that an increased number of pores and smaller spacing lead to earlier and more intense stress concentration, ultimately compromising the mechanical properties of the material.
Regarding spatial orientation distribution, different distribution forms also impact the material's behavior.When the angle between the major axis of the pore and the direction of the applied tensile load is larger, the yield stress decreases, and the fracture performance worsens.This can be explained by the fact that as the orientation of the pore's changes, the dimensions of the pores perpendicular to the stretching direction increase.This results in larger stress and earlier, more intense stress concentration, leading to a decline in the mechanical properties of the material.
The simulation results presented in this study offer valuable insights for optimizing SLM process parameters.Specifically, optimizing the process to achieve a sparse pore distribution, larger pore spacing, fewer pores in the tensile direction, and a spatial orientation with a smaller angle between the major axis of the pore and the direction of the applied tensile load can contribute to improved mechanical properties of the material.
Figure1.Boundary conditions in the simulation

1st
International Conference on Applied Physics and Mathematics Journal of Physics: Conference Series 2729 (2024) 012008 IOP Publishing doi:10.1088/1742-6596/2729/1/01200811 60-degree angle between the major axis and the stretching direction 90-degree angle between the major axis and the stretching direction

Figure 6 .
Figure 6.Stress contour of slm-fabricated Inconel-718 under different spatial orientation distributions of pores