An Analytical Study on the Instability Phenomena During the Phase Transitions in a Thin Strip under Uniaxial Tension

TL;DR

This paper analytically investigates the instability phenomena during phase transitions in SMA strips under uniaxial tension, revealing the roles of geometric parameters and the nature of localization-induced buckling.

Contribution

It introduces a combined series and asymptotic expansion methodology to derive leading-order equations, providing new analytical insights into phase transition instabilities in SMA strips.

Findings

Inclination of phase front is due to localization-induced buckling.

Stress-induced transformations in SMA are analogous to Luders band development in steel.

Geometrical parameters significantly influence instability behavior.

Abstract

In the experiments on stress-induced phase transitions in SMA strips, several interesting instability phenomena have been observed, including a necking-type instability, a shear-type instability and an orientation instability. By using the smallness of the maximum strain, the thickness and width of the strip, we use a methodology, which combines series expansions and asymptotic expansions, to derive the asymptotic normal form equations, which can yield the leading-order behavior of the original three-dimensional field equations. Our analytical results reveal that the inclination of the phase front is a phenomenon of localization-induced buckling (or phase-transition-induced buckling as the localization is caused by the phase transition). Due to the similarities between the development of the Luders band in a mild steel and the stress-induced transformations in a SMA, the present results give a strong analytical evidence that the former is also caused by macroscopic effects instead of microscopic effects. Our analytical results also reveal more explicitly the important roles played by the geometrical parameters.