A temperature dependent constitutive model for functional fatigue in shape memory alloys

Abstract

Functional fatigue is a vital aspect when considering the design of components made with shape memory alloys, since it can affect their short- and long-term behavior. With this in mind, a constitutive model considering the functional fatigue in shape memory alloys is developed. The functional fatigue is based on the residual strain, residual stress, residual martensite and a defect volume fraction, which are assumed to all evolve in a similar manner. The evolution is prescribed based on a saturation differential equation which is exponentially dependent on temperature. The residual martensite and defect volume fraction are defined to influence the development of hardening through a hardening energy term and the reduction in dissipation with an appropriate limit function. The model is validated by simulating several experiments of cyclic isothermal and isobaric tests. A fit and prediction is also offered for a set of complex thermomechanical loading paths. The results demonstrate the strong applicability of the model to capture the degradation of the transformation response associated with cyclic loads, even when different temperatures and loads are applied. Moreover, the results point out areas of improvement, such as the use of a logarithmic evolution for the saturation of the internal variables.