An analytical model for the phase transformation front propagation in superelastic SMA under impact tensile loading

Shape-memory alloys (SMAs) exhibit superelastic behavior due to reversible phase transformations. Under dynamic (impact) loading, phase transformation is experimentally observed to occur along a band whose front propagates throughout the specimen. However, unlike the static case, the nucleation and propagation of these bands require further understanding. Recently, a Finite Element Method (FEM) simulation based on Thamburaja and Nikabdullah's constitutive model successfully reproduced the experimental observations. In this study, the model is revisited in the specific case of a one-dimensional dynamic tension test, which allows for the derivation of an analytical closed-form one-dimensional stress-strain relation. When compared to FEM simulations of a single element, this analytical solution shows excellent agreement. From this closed form stress-strain relation, the propagation speed of the phase transformation shock front can be analytically computed. It also highlights that the shock front speed is primarily controlled by the strain reached after the complete transformation from the Austenite to the Martensite phase.