Localized and Diffuse Thermoinduced Phase Transformation in 1-D Shape Memory Alloys

Abstract

In this paper we further explore the thermoinduced shape memory alloy transformation using a model developed in a previous publication. The problem investigated in detail is that of a semi-infinite SMA rod under uniaxial tension, subjected to boundary cooling or heating. The boundary conditions lead to propagation of a martensite/austenite transformation along the rod starting at the cooled/heated boundary. The mathematical model for the problem is formulated via the energy equation coupled with a one-dimensional constitutive law and phase diagram based kinetics and solved numerically. In this paper, the previous solution technique for boundary cooling is extended to the case of boundary heating, nonuniform initial states are considered, and particular attention is focused on the transition two-phase zone of the transformation. It is shown that even though the problem is formulated using a phase diagram with finite width transformation regions, a localized interface type solution may be obtained. The results have important implications for applications and modeling of SMA behavior.