Interfacial stresses within boundary between martensitic variants: Analytical and numerical finite strain solutions for three phase field models

The origin of a large elastic stress within an interface between martensitic variants (twins) within a finite strain phase field approach has been determined. Notably, for a sharp interface this stress is absent. Three different constitutive relations for the transformation stretch tensor versus order parameters have been considered: a linear combination of the Bain tensors (kinematic model-I, KM-I), an exponential-logarithmic combination (KM-II) of the Bain tensors, and a stretch tensor corresponding to simple shear (KM-III). An analytical finite-strain solution has been found for an infinite sample for tetragonal martensite under plane stress condition. In particular, explicit expression for the stresses have been obtained. The maximum interfacial stress for KM-II is more than twice that which corresponds to KM-I. Stresses are absent for KM-III, but it is unclear how to generalize this model for multivariant martensitic transformation. An approximate analytical solution for a finite sample has been found as well. It shows good correspondence with numerical results obtained using the finite element method. The obtain results are important for developing phase field approaches for multivariant martensitic transformations coupled to mechanics, especially at the nanoscale.

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