Publications
On the formulation of a crystal plasticity model
This report presents the formulation of a crystal elasto-viscoplastic model and the corresponding integration scheme. The model is suitable to represent the isothermal, anisotropic, large deformation of polycrystalline metals. The formulation is an extension of a rigid viscoplastic model to account for elasticity effects, and incorporates a number of changes with respect to a previous formulation [Marin & Dawson, 1998]. This extension is formally derived using the well-known multiplicative decomposition of the deformation gradient into an elastic and plastic components, where the elastic part is additionally decomposed into the elastic stretch V{sup e} and the proper orthogonal R{sup e} tensors. The constitutive equations are written in the intermediate, stress-free configuration obtained by unloading the deformed crystal through the elastic stretch V{sup e-}. The model is framed in a thermodynamic setting, and developed initially for large elastic strains. The crystal equations are then specialized to the case of small elastic strains, an assumption typically valid for metals. The developed integration scheme is implicit and proceeds by separating the spherical and deviatoric crystal responses. An ''approximate'' algorithmic material moduli is also derived for applications in implicit numerical codes. The model equations and their integration procedure have been implemented in both a material point simulator and a commercial finite element code. Both implementations are validated by solving a number of examples involving aggregates of either face centered cubic (FCC) or hexagonal close-packed (HCP) crystals subjected to different loading paths.