Quantitative modeling of the variation in stress–strain response of shape memory alloys in partial phase transformed state

This work proposes a thermodynamic-based constitutive model for shape memory alloy, which captures the gradual variation in stress–strain response from the shape memory effect to the pseudoelastic effect. The present model also provides a framework for modeling various other responses, such as strain temperature hysteresis and thermally induced strain recovery effect. The model classifies the different phases of the material, such as twinned martensite, detwinned martensite, and austenite, and the mix of these phases using only two internal variables, namely austenite volume fraction and inelastic martensite strain. The proposed model shows that introducing two independent yield conditions corresponding to each internal variable is sufficient to describe all the phase transformations. After presenting the theoretical framework of the model, the procedure for numerical implementation has been discussed. The simulation shows the gradual variation in the stress–strain curve at different temperatures in the phase transformation range and is observed to have an adequate quantitative agreement with the experimental data The model is further implemented for different shape memory alloys to show the possibility of the generalized framework for this class of materials. In addition, the capability of simulating other phenomena of SMA, such as strain response for thermal loading at constant stress and the complete response of strain recovery in shape memory behavior, is also presented.