Finite-element (FE) simulations were employed to study the LPBF process as well as the tensile and compression tests. Exemplarily, the stack of 5 cells of type 31 was chosen for this part of the investigation. To minimize the model size while maintaining all distinct features of the sample, the sample geometry was reduced to the stack of cells, the additional support columns, and 2 mm of the mount as illustrated in Fig. 6a.
The commercial software Simufact Additive was used to perform a thermo-mechanically coupled analysis of the LPBF process [8, 9]. As described in [9], the complexity of the LPBF process is reduced by the introduction of a voxel mesh in which several powder layers are represented by a single voxel layer. The LPBF process is modeled by a sequential activation and thermal loading of entire voxel layers. The total time Tt required to print a voxel layer representing N powder layers follows from the process scan rate and the volume of the voxel layer. With the effective laser time Te, laser power P, and laser efficiency μ, the voxel layer is exposed to the total energy \(E_{t}=\mu PT_{e}\). For each voxel layer the following phases are considered:
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1.
A new voxel layer representing N powder layers is activated. Melting of the powder is achieved within an initial heating phase representing the passing of the laser over a given point of material. This phase is characterized by its short time step termed the exposure time Tp and the exposure energy fraction used to define the portion of the total energy applied in this phase as fpEt.
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2.
The dissipation of energy into the surrounding material is represented by a second heating phase that is characterized by the time step (Te−Tp) in which the material is subjected to the remainder of the energy Et(1−fp).
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3.
The two heating stages are followed by a cooling phase of length (Tt−Te) after which the process simulation continues with step (1) for the next voxel layer.
The filigree geometry of the chosen specimen required a voxel size of 0.075 mm resulting in 219 voxel layers. Numerical process parameters were chosen as to represent the experimental settings for contour and area (Table 2). The energy exposure fraction fp and exposure time Tp were calibrated such that the peak temperatures reached within the bottom mount just exceeded the melting temperature of 660 °C. A summary of the applied simulation parameters is given in Table 4.
TABLE 4 Parameters for thermo-mechanically coupled LPBF simulation The numerical investigation of mechanical tests was performed in the commercial software Simufact Forming. To achieve the mechanical loading, the specimen was positioned between two rigid plates contacting the top and bottom of the specimen mount. For tension/compression, the top plate was moved +/− 0.5 mm in its normal direction. Reaction forces were recorded and engineering stresses were evaluated with the nominal cross section of the corresponding vertex cube of 6.25 mm2. As in the experimental setup, engineering strains were evaluated from the change of distance between the bottom and top surfaces of the specimen mount.
The voxel mesh used for the simulation of the LPBF process is not suitable for the simulation of the mechanical tests because the resulting mechanical response is significantly affected by the voxel structure and size. Accordingly, a mesh of tetrahedral elements was used for this part of the numerical investigation. Convergence with respect to element size was carefully probed for the compressive stress reached at final loading and was achieved with a nominal element size of 0.04 mm and a total of about 2.3 million elements. This mesh was selected for all mechanical test simulations. Where applicable, results were mapped from the LPBF voxel mesh.
Whenever applicable, mechanical and thermal properties for the AlSi10Mg material were transferred from the experimental part of this study. In order to stabilize the LPBF simulation, temperature-independent values were assumed for the Young’s modulus and Poisson ratio. For the mechanical testing, no temperature data was considered.
Fig. 6 specifies distinct parts of the considered geometry and displays the results of the LPBF simulation after cooling of the sample and release from the baseplate. The peak temperature, Fig. 6b, refers to the highest temperature reached during the entire build process, and it emphasizes the influence of the sample geometry on the temperature distribution. As discussed above, the numerical parameters were calibrated to yield a peak temperature just above the melting temperature within the bottom mount. However, the filigree structure of the unit cells constrains the path for heat conduction through the sample to the baseplate. This results in significantly higher peak temperatures in all diagonal sections of the unit cells above position 1 where the vertical path for heat transfer is not available. This effect is especially pronounced for the bottom of the top mount where heat must flow horizontally to the connection supports or to the unit cell corners before it can be conducted into the underlying structure. It is here that the highest temperature peaks are observed.
The effective plastic strain, Fig. 6c, emphasizes the influence of the thermal history of the process. Plastic deformations concentrate at all cell centers and at the cell corners connecting cells as well as the bottom part of the top mount and the upper half of cell 5. Residual stresses, displayed in Fig. 6d, accumulate during the LPBF process and show a distinct gradient from the bottom to the top of the sample. Typically, removal of the geometric constraint of the baseplate releases residual stresses and results in a deformation of the LPBF component. However, in case of the present sample the removal of the baseplate mainly affects residual stresses in the bottom mount. As the bottom mount acts as the major geometric constraint for the cells, most of the residual stresses within the cells are maintained even after release of the baseplate.
Fig. 7 displays the results of the numerical compression and tensile tests in comparison to the corresponding experimental data. The two numerical curves highlight the impact of the LPBF process on the mechanical response of the sample: Due to the plastic deformation in critical parts of the sample, yielding is prolongated and the effective strength is increased both for tensile and compressive loading.
In the elastic regime, the simulation shows an effective stiffness of about 8 MPa for both loading conditions. A similar effective stiffness is observed experimentally for compressive loading while tensile loading results in a higher effective stiffness which may be caused by the applied pre-stress. The simulations predict well the onset of yielding in both loading conditions although the pronounced hardening observed in the experimental compression test is not fully reproduced numerically.
Differences between numerical and experimental results can have multiple causes, such as the applied material data, modeling approaches or differences between ideal and printed sample geometries. Although the applied material data was evaluated for LPBF specimens produced from the same powder, different printing parameters for bulk samples and cellular structures may result in different microstructure and porosity. While the results of the simulated LPBF process give a reasonable approximation to the arising stresses, they are still subject to the simplifications of the applied voxel approach and do not include effects due to local hatching or contour paths which inevitably influence the local stress distribution in the final sample. Finally, the geometric difference between the ideal STL geometry considered in the simulations differs from the real samples because the remelting of powder layers increases the strut thickness and reduces the notch arising at position 3 and similar cell junctions.
Although no failure criterion was considered for the numerical mechanical tests, the simulations explain well the experimental results. In both loading conditions, local yielding begins first at all inter-cell connections like positions 2 and 3, followed by cell centers similar to position 1. The inter-cell connection between cells 1 and 2 is the most critical area in both loading conditions as it is the position with minimal cross-sectional area, only moderate effective plastic strain and highest residual stress concentration. If a compressive load is applied to the sample, position 2 is loaded in tension, while the notch at position 3 is closed by a local compressive load. Numerically, the material strain to failure of 4.8% is reached at position 2 at an effective strain of 3.0%. A larger cross section at this position and less pronounced sharpness of the cell corners explain the experimentally observed strain to failure in the order of 6%. If a tensile load is applied to the sample, position 3 is loaded in tension pulling open the notch between contacting cells and resulting in much smaller strains to failure in the order of 1%.