One-dimensional sharp phase front-based continuum models of phase transformations in shape memroy alloys

摘要

The issue of phase transformations in shape memroy alloys is revisited in the one-dimensional context. we focus on problems where there is a sharp interface between the two phases of austenite and martensite. Apart from the usual conservations equations(mass, lienar momentum and energy), it is proposed that an extra equation (followign from the balance of chemical potential at the interface) be used to render the system of equations complete, when a first-order transition(as in a shape memory alloy) is considered. Seen within this context, the following two approaches can be derived as special cases: (i) Leo et. al.~1 approach where the phase boundary temperature is taken to be linearly related to the stress, (ii) Abeyaratne and Knowles~2 approach where a kinetic relation(expression for the phase boundary velocity) is assumed. Certain other implications of hte new approach are discussed in light of these special cases.