Macroscopic modeling of functional fatigue in shape memory alloys

Abstract

We study a macroscopic homogenized model of shape memory alloys. Starting from the Souza-Auricchio model, we put forward some modifications fit to improve the capability of the model to predict and estimate the onset of functional fatigue in the material. More specifically, we consider the presence in the Helmholtz free-energy density of a macroscopic plastic term in order to represent the fact that microscopic plasticity involves macroscopic strains. We further introduce an evolution of the transformation domain, in order to represent the fact that the more plastic slips occur, the more limited is the phase space available for further microscopic phase transformations. We finally generalize the functional dependence of the rate of dissipation function in terms of the driving forces, in order to relax the previously introduced constraint that functional fatigue could arise if and only if microscopic phase transition occur. In this paper we discuss the constitutive consequence of the proposed modifications, we discuss the calibration of constitutive parameters by means of simple experiments, and evidence the qualitative agreement of the modeling predictions with the outcome of some reported experimental results.