Phase‐field modeling of stress‐ and temperature‐induced hysteresis behavior of shape memory alloys incorporating rate‐independent dissipation

Abstract

AbstractShape memory alloys (SMAs) are a unique class of multifunctional materials, which exhibit distinctive thermomechanical properties. They are primarily characterized by their ability to recover their original shape under stress and temperature‐controlled loading scenarios. This exceptional property is attributed to the phase transformation that occurs within these alloys, wherein SMAs undergo reversible transition between austenite and multi‐variant martensite phases. The phase transformation in SMAs during a complete load cycle results in a hysteresis, which represent the dissipated energy in the transformation cycle. More specifically, SMAs exhibit a rate‐independent response to a sufficiently slow loading, so that their cyclic response is characterized by a hysteresis loop that maintains a finite width even when the external loading rate approaches zero. Understanding and accurately predicting the rate‐independent hysteresis behavior of SMAs is therefore crucial for their efficient utilization in various engineering applications. In this regard, the phase‐field method has emerged as an appropriate modeling framework resolving the evolution of complex interface topologies as observed in phase‐transforming solids. However, the majority of already existing models typically rely on rate‐dependent formulations and thus remain incapable of reproducing thermoelastic hysteresis behavior at quasi‐static loading scenarios. To overcome this issue, a thermomechanically coupled—and variationally consistent—Allen–Cahn based phase‐field approach incorporating both rate‐dependent and ‐independent driving force formulations is introduced in this work. In order to demonstrate potential applications of the proposed model, two‐dimensional finite‐element simulations were performed to resolve the microstructure formation of twinned martensite in ZrO2. In addition, rate‐dependent and ‐independent stress‐ and temperature‐induced hysteresis curves are predicted qualitatively within the given approach, thus proving its adaptability. Furthermore, the influence of model specific parameters on resulting austenitic and martensitic start and finish temperatures is discussed for cyclic undercooling simulations. The proposed model is thus shown to serve as a valuable tool for the design and optimization of SMA‐based devices.