A Phase Field/Finite Element Approach to Model Coupled Phase Transformation and Plasticity in Shape Memory Alloys

A microstructural finite element (FE) model for shape memory alloys (SMA) is developed in which the austenite phase can plastically deform and/or transform to crystallographic martensite correspondence variants (CVs). The thermal and stress-induced phase transformation and reorientation of martensite is modeled using the phase field (PF) method. The plastic deformation is modeled using continuum-based crystal plasticity that is indexed to the crystallographic slip systems in austenite. Compared to PF formalisms based on Fourier transform techniques, the proposed FE-FP approach can handle arbitrary boundary conditions and it incorporates large deformation and rotation associated with transformation and plasticity.

Two key simulation results are presented: compression of micron-scale pillar samples and thermal cycling of single crystals. These are used to explore the nature of plasticity during forward and backward transformation. In particular, the simulations capture the high stress field in the vicinity of twinned martensite plates and the effect on fine-scale plasticity at austenite-martensite interfaces. The simulations also predict patterns of transformation and plasticity where incompatibilities between competing martensite plates may arise. Overall, the simulations offer insight to the origins of functional instability in shape memory alloys, where plastic strain can accumulate during repeated thermal cycling under load. In principle, these simulations can be seamlessly integrated with coarse-grained FE approaches to study the response at larger (polycrystalline) scales.

This work is supported by the National Science Foundation, Division of Materials Research, DMR-1207494.