Plastic deformation induced microstructure evolution through gradient enhanced crystal plasticity based on a non-convex Helmholtz energy

A gradient crystal plasticity model in the framework of continuum thermodynamics and rate variational formulation is presented for the description of plastic deformation patterning in a system with non-convex energetic hardening. The paper focuses on the extension of the 1D deformation patterning analysis of Yalcinkaya et al. (2011) to 2D for monotonic loading histories. Solution algorithm is based on the simultaneous solution of displacement and plastic slip fields, which have been considered as primary variables. The incorporation of non-convexity in the plastic slip potential in the Landau–Devonshire form makes the framework dual to phase field modeling approaches with a strong coupling between the deformation and the plastic slip fields. In the phase field modeling approaches the coupling is rather weak, i.e. fields do not have to be coupled as in the current approach based on the decomposition of the total strain. The numerical examples illustrate the intrinsic formation of (laminate type) microstructures and their evolution under mechanical loading together with the macroscopic hardening–softening–stress plateau response. The effect of different number of slip systems, loading rates and boundary conditions are investigated in detail.

► Rate dependent strain gradient crystal plasticity model.
► Non-convex energetic hardening contribution responsible for microstructure formation.
► Numerical examples exhibit laminate type of microstructures.
► Illustration of macroscopic hardening/softening/stress plateau behavior in 2D.
► Simulation of both equilibrium and non-equilibrium states of microstructures.