Response of 2D and 3D crystal plasticity models subjected to plane strain condition

The plane strain assumption is generally applied in crystal plasticity finite element (CPFE) simulations in a 2D space to characterize the macroscopic material response considering microstructural features. However, the reliability and accuracy of 2D approximations need to be addressed. In this paper, crystal plasticity finite element simulations of 2D and 3D RVEs are performed with local and averaged plane strain assumptions in Abaqus/Standard. Plane strain postulation is implemented via plane strain elements in 2D and zero average thickness strain in 3D. Irregularly shaped RVEs are generated using the open-source software library Voro++. A conforming mesh is rendered to assign periodic boundary conditions on geometrically periodic RVEs. Periodic boundary condition (PBC) is applied using a prescribed macroscopic deformation gradient tensor. A rate-independent finite strain crystal plasticity model is employed as the user-defined material behavior in finite element simulations. A discrepancy is observed between macroscopic flow curves of 2D and 3D RVEs. The comparison was made for three cases of latent hardening in the crystal plasticity model. In all cases, 3D flow curves exceed 2D results. The results indicate that the deviation is caused by out-of-plane slip activation in 3D simulations, which proves to be an additional hardening source.