Probabilistic modeling of microstructure evolution using finite element representation of statistical correlation functions

A probabilistic finite element scheme is presented for simulating evolution of polycrystalline microstructures during deformation. The microstructure is described using conditional orientation correlation function (COCF), defined as the probability density of occurrence of a crystal orientation g′ at a distance r from a given orientation g. The COCF is represented using three interconnected layers of finite element meshes in the g′, r and g spaces. As the microstructure evolves, the reoriented neighborhood and strain fields close to an orientation (g) are captured by updating probability fields in these finite element meshes. For this purpose, a novel total Lagrangian approach has been developed that allows evolution of probability densities while satisfying normalization constraints, probability interdependencies and symmetries. The improvement in prediction of texture and strains achieved by the COCF approach over ODF-based methods is quantified through deformation analysis of a planar polycrystalline microstructure.