Modeling the coupling between martensitic phase transformation and plasticity in shape memory alloys

The thermo-mechanical response of NiTi shape memory alloys (SMAs) is predominantly dictated by two inelastic deformation processes---martensitic phase transformation and plastic deformation. This thesis presents a new microstructural finite element (MFE) model that couples these processes and anisotropic elasticity. The coupling occurs via the stress redistribution induced by each mechanism. The approach includes three key improvements to the literature. First, transformation and plasticity are modeled at a crystallographic level and can occur simultaneously. Second, a rigorous large-strain finite element formulation is used, thereby capturing texture development (crystal rotation). Third, the formulation adopts recent first principle calculations of monoclinic martensite stiffness. The model is calibrated to experimental data for polycrystalline NiTi (49.9 at% Ni). Inputs include anisotropic elastic properties, texture, and DSC data as well as a subset of pseudoelastic and load-biased thermal cycling data. This calibration process provides updated material values---namely, larger self-hardening between similar martensite plates. It is then assessed against additional pseudoelastic and load-biased thermal cycling experimental data and neutron diffraction measurements of martensite texture evolution. Several experimental trends are captured---in particular, the transformation strain during thermal cycling monotonically increases with increasing bias stress, reaching a peak and then decreasing due to intervention of plasticity---a trend which existing MFE models are unable to capture. Plasticity is also shown to enhance stress-induced martensite formation during loading and generate retained martensite upon unloading. The simulations even enable a quantitative connection between deformation processing and two-way shape memory effect. Some experimental trends are not captured---in particular, the ratcheting of macrostrain with repeated thermal cycling. This may reflect a model limitation that transformation-plasticity coupling is captured on a coarse (grain) scale but not fine (martensitic plate) scale. Lastly, Crystallographic Theory of Martensite (CTM) and micromechanics-based modeling is applied to analyze recent TEM observations. In particular, the observation of sub-micron dislocation loops is explained in terms of the large stress generated by the phase transformation at the variant (sub-micron) scale. Second, the observation of atypical compound twin related martensite variants in TEM foils is explained in terms of the loss of constraint produced by free-surfaces.