Plasticity and Transformation in Polycrystalline Shape Memory Alloys

Inelastic deformations due to a combination of plastic slip and martensitic phase transformations are observed in numerous materials, including steels and shape-memory alloys, but resolving the fine microstructures generated by slip and phase-transformation becomes prohibitively expensive for macroscopic polycrystalline models.  Consequently, the interplay between these two mechanisms and their combined effects on the macroscopic response of polycrystalline materials remains poorly understood.  Since both mechanisms originate as lattice-scale deformations constrained along slip- and habit-planes of single crystals, we develop a model that treats the two as competing constraint sets on lattice-scale deformations.  Beginning with a non-convex energy potential at the micro-scale, we relax this potential using well-established homogenization techniques to coarse-grain over the fine microstructure, producing an analytical model for the effective response of an inelastic single crystal.  We then extend this model numerically to polycrystals.  Computational results are discussed, especially the effects of the relative transformation- and flow-stress.