An analytical model for phase transitions of an SMA wire under uniaxial tension

Abstract eng:
This paper considers isothermal stress-induced phase transitions of shape memory alloys (SMAs) based on a two-variant constitutive model. Specifically, inhomogeneous deformations of a slender circular cylinder under uniform axial stress are investigated analytically. By utilizing two small parameters, the complex three-dimensional (3-D) mechanical system is reduced to a 1-D coupled system of two strains for each of three phase regions. Then, for given load parameter, inhomogeneous deformations with two and three regions are constructed, and many analytical period-k solutions are found for the first time. For displacement-controlled process, the transition from homogeneous states to localized inhomogeneous ones is identified, capturing the possible instabilities at nucleation. The analytical results reveal that phase transition starts from a small band rather than a point. This work can also shed light on the difficulties of direct numerical simulations.

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