PSI - Issue 35

Varvara Romanova et al. / Procedia Structural Integrity 35 (2022) 196–202 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

199

4

u 

, ij j  = ,

(9)

i

where  is the current density calculated from the mass conservation law

V V u

, 0 i j (10) and V is the relative volume. The constitutive model of grains was introduced into ABAQUS/Explicit solver through a VUMAT subroutine. Two calculations were performed to simulate uniaxial tension along parallel and perpendicular to the build direction. Two parallel-to-load adjacent sides of the microstructural model were free surfaces, while other two were symmetry planes. Two perpendicular-to-load opposite sides k S were assigned with kinematic boundary conditions set in the surface nodal points as | k i S t u v = , (11) where t v is the peak value of tension velocity. 3. Results and discussion For analyzing the non-homogeneous behavior of an AlSi10Mg alloy fabricated by SLM, the grain-scale model is subjected to uniaxial tension parallel or perpendicular to the build direction. Figure 2 shows the von Mises stress distributions for the models loaded parallel (Fig. 2a) and perpendicular (Fig. 2b) to the build direction. In Fig. 2 green color corresponds to the average equivalent stress value, while blue color corresponds to the lower stress values compared to the average stress level. Section I in Fig. 2b, e matches with the hatch overlap area, and Section II in Fig. 2c, f is compliant with the melt pool center. In order to gain a better understanding of the grain-scale stress inhomogeneity, let us complement the stress field analyses with the statistical estimations. Figure 3 demonstrates frequency count curves for the von Mises stress distributions in the models under study. In both cases two peaks are observed in the frequency count curves which supports the idea about the presence of two distinct stress levels taking place in the melt pool centers and in the hatch overlap zones, respectively. However, the peak rate for each case is different. For the model loaded parallel to the building direction the major part of the material experiences lower stress values (Fig. 3, green solid line) compared to the mean value (Fig. 3, green dashed line), while the opposite behavior is a characteristic of the model loaded perpendicular to the build direction where the major part of the material experiences higher stresses (Fig. 3, red solid line) in comparison to the mean level (Fig. 3, red dashed line). In line with the stress analysis, the equivalent plastic strain distributions and surface roughness patterns in the two cases of loading are strongly non-uniform. However, opposed to the stress distributions, the plastic strains deviate from the mean level in a wider range when loading is applied perpendicular to the build direction (cf. Fig. 4a and b). Dark elongated regions of higher strains faintly visible on the top faces of the both models match with melt pool centers; the distance between the regions being longer for the model loaded perpendicular to the build direction (Fig. 4b). Important data can be derived from the analysis of the surface roughness patterns originating from the structural anisotropy, see Ferro at al. (2020). A distinct roughness pattern caused by out-of-plane displacements of the neighboring grains relative to each other develops in the models under uniaxial tension. Out-of-plane surface displacements as a main process governing the surface roughening are measurable values which makes it possible to compare simulation results with the experimental data provided by digital image correlation or scanning microscopy. Figure 4c and d presents the deformation-induced roughness patterns at 5% tensile strain in the SLM models subjected to tension parallel (Fig. 4c) and perpendicular (Fig. 4d) to the build direction. The distinct grooves aligning with scanning tracks are seen on the top free surface in the model loaded perpendicular to the build direction (Fig. 4d). For the case of loading parallel to the build direction, the roughness patterns at the lateral sides follow the shapes of the melt pools or inclined grain boundaries (Fig. 4c). − =