A numerical study of the effect of discretization methods on the crystal plasticity finite element method

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Abstract

The present report describes a big data numerical study of crystal plasticity finite element (CPFE) modelling using static and grain-based meshing to investigate the dependence of the results on the discretization approach. Static mesh refers to the integration point-based representation of the microstructure in which the integration points (IPs) within a finite element may belong to different grains, while in the grain-based meshing the minimum discretization unit is an element that may only belong to one grain. The crystal plasticity constitutive law was coded using UMAT subroutine within commercial finite element software Abaqus. Multiple sets of RVEs were investigated under strain-controlled loading and periodic boundary conditions. The stress and strain contour maps obtained from RVEs with static mesh and grain-based mesh were compared. The simulation results reveal that both discretization methods provide reliable predictions of the stress-strain curves and the stress/strain localization points in polycrystalline alloys. Static mesh tends to smooth the stress/strain profile at the grain boundary, whilst stress/strain discontinuities are present in the grain-based mesh results. The above findings remain valid when the number of grains within an RVE increases from 34 to 1250. To quantify the difference between static and grain-based meshing, a relative measure of deviation is defined. The deviations of global stress were found to be relatively small, within 0.5%, while local deviations were significant up to 50%. Static mesh has the advantage of reducing both the preprocessing procedures and computational time compared to grain-based mesh. It is concluded that static mesh is preferred when investigating the material's macroscopic behaviour, whilst grain-based mesh is recommended for the study of the local response using CPFEM.