A Crystal Plasticity Extended Finite Element Method for simulating grain boundaries in polycrystalline materials

During the last few decades, significant attention has been given to the incorporation of micromechanical effects in continuum descriptions of inelastic deformation. This has led to the development of sets of viscoplastic constitutive equations that describe the plastic deformation in terms of crystalline slip. Efforts are underway to embellish crystal plasticity formulations with micromechanical effects not directly accounted for, by introducing dislocation density and other parameters related to the discreteness of the microstructure. In this study, a crystal plasticity material model is implemented in the open source FE package OOFEM, to study grain structure effects such as slip system mismatch and strain discontinuity across the grain boundaries in a polycrystal. Grain boundaries are discontinuous in material properties, or strain, and may be discontinuous in displacement (strong discontinuity) when decohesion or relative sliding occurs. Using dissimilar orientations for the crystal plasticity material models on either side of the material interfaces, micro-structural effects such as slip incompatibility and accumulation, due to the lattice mismatch, may be captured. Further development of the formulation will enable new rules to be implemented linking strong discontinuities at the grain boundaries, such as decohesion and grain boundary sliding, to the underlying average dislocation and vacancy structures, for example. Also, grain growth, recrystallisation, etc., could be modelled by prescribing evolution equations for the level sets. In this paper, the technique described above is used to simulate MnS inclusions in a polycrystalline austenitic matrix. This is carried out using OOFEM which is one of the few FE packages with XFEM capability for weak discontinuities [1]. The effect of lattice mismatch and crystal orientation are studied and compared against results obtained using conventional crystal plasticity, e.g. Gaskell et al. [2] for validation purposes. The dominant parameters affecting decohesion between the inclusion and matrix, and at grain boundaries, will be presented. The future development of CPXFEM will be discussed and an initial grain boundary strong discontinuity problem proposed.