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A Peridynamics Framework for Laser Powder Bed Fusion
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Laser Powder Bed Fusion (LPBD) enables rapid manufacturing of highly customized and complex geometries but is currently limited by difficulties in predicting the final material properties. LPBD is characterized by rapid phase changes, large thermal gradients, discontinuities as well as varying length and time scales. These challenges can only be addressed computationally by utilizing a bottom-up multiscale framework consisting of different numerical methods, each operating on their respective scales. Our aim is to provide a consistent connection between micro-scale simulations and macro- scale methods. Considering length scales from 1 μm to 100 μm, the most prominent structural feature is the single crystal grain. LPBD process parameters such as e.g. heat source energy density, scan speed and cooling rates influence crystal grain shape and lattice orientation, which in turn affect the bulk material parameters such as hardness and ductility at the macro scale. For computational modeling of the solid phase, we rely on Peridynamics (PD) due to its close relation to Molecular Dynamics (MD) as both are non-local methods. Upscaling MD to PD was already considered in [1] where both models yield corresponding dispersion relations. For the modeling of the liquid phase SPH was chosen. Through a coupled SPH-PD simulation we can combine the strengths of both methods in their respective domain. We present a PD material law where single crystal grains grow from a super-cooled liquid phase based on spontaneous nucleation. Post-solidification processes such as solid-state transformation which is necessary for modelling heat treatment (e.g. annealing) are considered. We demonstrate that our PD based model can predict grain structures arising from LPBF processes very well and present a coarse scaling methodology build upon the Crystal Plasticity Peridynamics (CPPD) considered in [2] that will lead to predictability of macroscopic material response.