A finite strain thermomechanically-coupled constitutive model for phase transformation and (transformation-induced) plastic deformation in NiTi single crystals

A 3D finite-strain constitutive model for the deformation response of NiTi at the single crystal level is proposed. The model accounts for reversible phase transformation from austenite to martensite habit plane variants, plastic deformation in the austenite phase, and rate effects induced from latent heat. It is developed within the formalism of irreversible thermodynamics with internal state variables based on the Eulerian logarithmic strain and its corrotational objective rate. The inelastic deformation is defined as an average over a representative volume element as classical in the micromechanics-based modeling approach. Transformation-induced plastic deformation is viewed as a mechanism for accommodation of the local deformation incompatibility at the austenite?martensite interface. It is accounted for by introducing an interaction term in the free energy, which is described through the Eshelby tensor by regarding the habit plane variants as ellipsoidal inclusions embedded in the austenite matrix, in order to accurately reflect the internal stress states that contribute to dislocation slipping. The numerical implementation of the model in an efficient scheme and its calibration are described in detail. The proposed model is validated by comparing simulations with available experimental data in single NiTi crystals. Numerical simulations of polycrystals are performed to obtain an insight into the interaction between phase transformation and plastic deformation induced by intergrannular constraints. The efficiency of the numerical implementation of the model is verified by simulations of indentation tests.