A Proposed Three-Dimensional Constitutive Model for Shape Memory Alloys

The shape memory alloy (SMA) stress-strain response associated with martensitic twinning hysteresis and austenite-martensite/martensite-austenite superelasticity is modeled using constitutive equations. Compared to the modeling work done on viscoelastic and viscoplastic be havior, this has been an area of limited study. The equations which are presented here express the growth of inelastic strain in a rate-type formulation similar to viscoplastic laws. This constitutive model is obtained by extending a one-dimensional evolutionary model of SMA behavior to three dimensions. The resulting model is then reduced to meet the loading conditions of three special cases: uniaxial loading, shear loading, and non-proportional biaxial loading (combined axial- torsional loading). The model which is being considered, although nonlinear, is relatively simple in that only two evolutionary equations are required to model inelastic strain and a generalized back stress at a material point. Thus the model being presented uses only one internal variable, which is analogous to viscoplastic backstress. The consequences of variations of parameters in the equations of the model are also discussed.