Periodic Homogenization in Crystal Plasticity: A Comparative Study Between 3D and 2D

In this paper, macroscopic behavior obtained from crystal plasticity finite element simulations of irregularly shaped 3D and 2D volume elements (VEs) are compared. These morphologically periodic VEs are generated using the open-source software library Voro++. Periodic boundary conditions are utilized to homogenize the material response employing a prescribed macroscopic deformation gradient tensor. To accelerate the assignment of periodic boundary conditions, a conformal mesh is employed by which periodic couples of faces on the hull of the volume element have identical mesh patterns. In the simulations, plane strain conditions are assumed, which means that the average thickness strain in 3D VEs is set to zero. However, grains are allowed to strain in the thickness direction. In the case of 2D VEs, plane strain elements are used. The principal goal of this comparison is to evaluate the accuracy of 2D VEs simulations. In the current study, two kinds of 2D VEs are generated: 1) Slicing 3D VEs normal to the thickness direction, 2) Separately generating 2D VEs. The first method corresponds to sectioning 3D microstructures using EBSD. This approach is generally used as an assumed more accurate alternative to 2D VEs. Based on the results, there is a large gap between the flow curves of 2D and 3D VEs. Additionally, 2D sectioning of 3D VEs does not necessarily end up in higher precision in material behavior predictions.