TEMPERATURE-INDUCED PHASE-TRANSFORMATION IN A SHAPE-MEMORY ALLOY - PHASE-DIAGRAM BASED KINETICS APPROACH

In this article we develop a general framework to model the one dimens ional thermomechanical behavior of shape memory alloys (SMAs) based on phase diagram kinetics and a phenomenological constitutive law with m artensite fraction as an internal variable. As part of this framework, we construct a consistent mathematical description for martensite fra ction evolution to be used in conjunction with an experimentally defin ed phase diagram; the kinetics formalism is illustrated with examples of isostress and isothermal cycling. As an application, we consider th e thermo-induced martensite transformation of a 1D prestressed SMA pol ycrystalline body which proceeds by migration of the austenite-martens ite two-phase zone from the cooled boundary, converting the SMA body f rom an austenite (A) to a detwinned martensite (M) state. The mathemat ical model for the two-phase zone migration is based on the nonstation ary equation of energy balance and the quasistationary approximation f or the linear momentum equation and utilizes a quasistatic kinetic law , a macroscale constitutive law and an incompressibility constraint. T o close the formulated system of equations, the internal energy of an A/M mixture in the two-phase zone is heuristically derived. The mixed initial-boundary value problem is then solved numerically and compared to analytical results for a simplified model. The results stress the significance of the stress dependency in the kinetic law and the trans formation heat to the progress of transformation. (C) 1997 Elsevier Sc ience Ltd.