Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part I: theoretical derivations

A generic form of Gibbs free energy for polycrystalline Shape Memory Alloys (SMAs) is first obtained in this work, by forming the increments of both e lastic potential energy and Gibbs chemical energy over a Representative Vol ume Element (RVE) with respect to an infinitesimal increment of martensite. A set of internal state variables, i.e., martensitic volume fraction, macr o-transformation strain, and back and drag stresses due to both martensitic phase transformation and its interaction with plastic strains, are introdu ced. The evolution of these internal state variables during phase transform ation is proposed based on the micromechanical analysis over the RVE. Four primary mechanisms governing the transformation induced hardening effect ar e discussed. It is concluded that the back and drag stresses related to pla stic deformation do not remain constant, but they vary during phase transfo rmation, even though the local plastic residual stresses are assumed to be constant. The initial material heterogeneity of SMAs, which is essential fo r the initiation of the phase transformation, is modeled by an initial resi dual stress field, which can be described by a probability distribution fun ction. In this Part I of a four-part paper, the theoretical derivations are presented. Specific cases of the thermomechanical response of SMAs predict ed by the model will be presented in Part II, together with experimental re sults for phase transformation at constant plastic strains. Experimental re sults and model predictions for cyclic loading of SMAs with evolving plasti c strains will be considered in Part III, while the modeling of minor hyste resis loops of SMAs will be presented in Part IV of this series of four pap ers on SMAs. (C) 1999 Elsevier Science Ltd. All rights reserved.