Phase-transformation wave propagating in a temperature-gradient shape-memory TiNi alloy rod under shock loading

In this work, the propagation of a phase transformation front in a temperature-gradient rod induced by an impact loading is studied. Based on the characteristic-line theory, it is found that for loading, with the decay of the phase boundary, the phase-transition shock wave is gradually transformed into a phase-transition wave and an elastic wave. As a consequence, a functional gradient medium (phase II, mixed phase and phase I) forms in such temperature-gradient rod. Dimensional analysis shows that the widths of phase II and the mixed-phase regions are directly proportional to the amplitude of the loading stress but inversely proportional to the temperature gradient. Numerical calculations, based on a first-order Lax–Friedrichs finite-difference scheme, are presented. The calculated results are in good agreement with the characteristic-line theory and dimensional analysis results.