A three-dimensional constitutive model for shape memory alloy

Abstract

Shape memory alloy (SMA) has a wide variety of practical applications due to its uniquesuper-elasticity and shape memory effect. It is of practical interest to establish aconstitutive model which predicts its phase transformation and mechanical behaviors. Inthis paper, a new three-dimensional phase transformation equation, which predicts thephase transformation behaviors of SMA, is developed based on the results of adifferential scanning calorimetry (DSC) test. It overcomes both limitations: thatZhou’s phase transformation equations fail to describe the phase transformationfrom twinned martensite to detwinned martensite of SMA and Brinson’s phasetransformation equation fails to express the influences of phase transformation peaktemperatures on the phase transformation behaviors of SMA. A new three-dimensionalconstitutive equation, which predicts the mechanical behaviors associated with thesuper-elasticity and shape memory effect of SMA, is developed on the basis ofthermodynamics and solid mechanics. Results of numerical simulations show that thenew constitutive model, which includes the new phase transformation equationand constitutive equation, can predict the phase transformation and mechanicalbehaviors associated with the super-elasticity and shape memory effect of SMAprecisely and comprehensively. It is proved that Brinson’s constitutive modelof SMA can be considered as one special case of the new constitutive model.