Dynamics of steps along a martensitic phase boundary II: Numerical simulations

Abstract

We investigate the dynamics of steps along a phase boundary in a cubic lattice undergoing antiplane shear deformation. The phase transition is modeled by assuming piecewise linear stress–strain law with respect to one component of the shear strain, while the material response to the other component is linear. In the first part of the paper we have constructed semi-analytical solutions featuring sequential propagation of steps. In this work we conduct a series of numerical simulations to investigate stability of these solutions and study other phenomena associated with step nucleation. We show that sequential propagation of sufficiently small number of steps can be stable, provided that the velocity of the steps is below a certain critical value that depends on the material parameters and the step configuration. Above this value we observe a cascade nucleation of multiple steps which then join sequentially moving groups. Depending on material anisotropy, the critical velocity can be either subsonic or supersonic, resulting in subsonic step nucleation in the first case and steady supersonic sequential motion in the second. The numerical simulations are facilitated with an exact non-reflecting boundary condition and a fast algorithm for its implementation, which are developed to eliminate the possible artificial wave reflection from the computational domain boundary.