Nanoscale Phase Field Modeling and Simulations of Martensitic Phase Transformations and Twinning at Finite Strains

A thermodynamically consistent phase field approach to martensitic phase transformations for a system with austenite and two martensitic variants has been developed. The model considers two order parameters, describing austenite \( \leftrightarrow \) martensite and variant \( \leftrightarrow \) variant transformations, respectively. The coexistence of three phases at a single material point are consistently penalized. Twinning in the nanoscale sample was studied for two different kinematic models (KMs) for the transformation stretch tensor \( {\mathbf{U}}_{t} \). In KM-I, \( {\mathbf{U}}_{t} \) is taken as a linear combination of the Bain strains, and in KM-II, \( {\mathbf{U}}_{t} \) is an exponential of the logarithm of the Bain stretch tensors. For these two KMs and for an additional model based on simple shear, analytical solutions for elastic stresses within a variant-variant boundary in an infinite twinned sample are presented. The results can be easily generalized for an arbitrary number of variants. They are crucial for further development of phase field approaches to multivariant martensitic transformations coupled to mechanics.