Phase Field Method to the Interaction of Phase Transformations and Dislocations at Nanoscale

In this paper, a new phase field method for the interaction between martensitic phase transformations and dislocations is presented which is a nontrivial combination of the most advanced phase field methods to phase transformations and dislocation evolution. Some of the important points in the model are the multiplicative decomposition of deformation gradient into elastic, transformational and plastic parts, defining a proper energy to satisfy thermodynamic equilibrium and instability conditions, including phase-dependent properties of dislocations. The system of equations consists of coupled elasticity and phase field equations of phase transformations and dislocations. Finite element method is used to solve the system of equations and applied to study the growth and arrest of martensitic plate and the evolution of dislocations and phase in a nanograined material. It is found that dislocations play a key role in eliminating the driving force of the plate growth and their arrest which creates athermal friction. Also, the dual effect of plasticity on phase transformations is revealed; due to dislocations pile-up and its stress concentration, the phase transformation driving force increases and consequently, martensitic nucleation occurs. On the other hand, the dislocation nucleation results in decreasing the phase transformation driving force and consequently, the phase transformation is suppressed.