On martensitic phase nucleation with surface effects

Abstract

C ontinuum treatments of martensitic phase transitions are capable of accounting for a variety of surface effects caused by the interaction of coexisting phases of a material. Such phenomena are thought to play a critical role in determining the size, shape and stability of nucleated embryos as well as to affect the conditions under which nucleation occurs. These issues are examined within a purely mechanical context with the interaction modeled by traction and energy fields defined on the interface between phases. A class of isotropic, hyperelastic materials is introduced that is capable of modeling the dilatational component of martensitic phase transformations. Such materials are considered in a noninertial, axisymmetric setting that provides a means of exploring a variety of surface effects. Here nucleation events are modeled as deterministic, temporal shocks that are global in spatial extent, and a criterion for nucleation is suggested that is based on the energy available to create an embryo composed of a new phase. The model presented does more than capture the desired surface effects. It shows how they are related to specific assumptions regarding the constitution of interfaces. Three different types of interface are presented that serve to illustrate this.