Impact induced phase transformation in shape memory alloys

Abstract

A dynamic analysis is given of the impact induced phase transformation in a shape-memory alloy rod, with a special focus on the propagation of stress waves and phase transformation fronts in the rod. The material behavior of the shape-memory alloy is modelled by a thermomechanical constitutive theory developed by Lagoudas et al. (1996: A unified thermodynamic constitutive model for SMA and finite element analysis of active metal matrix composites. Mechanics of Composite Materials and Structures 3, 153–179), which is based on the formulation of Gibbs free energy that depends on, among other variables, the martensitic volume fraction and the transformation strain, along with evolution equations derived from a dissipation potential theory. Field equations and jump conditions of the fully coupled thermal-mechanical problem are derived to account for balances of linear momentum and energy. The equations are solved using the method of characteristic curves. The solutions are found to be associated with shocks, across which various field quantities suffer jump discontinuities. A typical solution involves two wave fronts which are initiated at the impact surface and propagate into the rod. One, travelling at the acoustic speed, separates the tranquil and disturbed regions. The other, travelling at a lower speed, separates the regions of the martensitic and austenitic phases. It is found that the stress and temperature jumps across the phase boundary can be significant. A numerical example is presented.