Finite-element modeling of phase transformation in shape memory alloywires with variable material properties

Abstract

In this paper, we address the issue of modeling the temperaturedistribution in a shape memory alloy (SMA) wire with variable thermal andelectrical properties. This is done in the context of a one-dimensional (1D)boundary value problem where an initially martensitic SMA wire is electricallyheated under zero-stress conditions. The model accounts for an evolution inthe thermal conductivity, electrical resistivity and heat capacity during thephase transformation. The evolution in the 1D temperature field is found byimplementing a Galerkin-based finite-element method. This is used incombination with a recursive iteration scheme to accurately determine thechange in the material properties during a time step. The numerical approachis validated by comparing it with a known analytical solution with variablethermal properties. A parametric study on the SMA phase transformationindicates that, based on the considered values for the material properties,the heat capacity is the least important factor that needs to be accountedfor, whereas the electrical resistivity is the most important. It is alsodemonstrated that the time required to complete a martensite to austenitetransformation for a SMA wire subjected to an adiabatic boundary condition islower if the model accounts for property variations. In fact, when the cyclicresponse of a SMA wire actuator subjected to an adiabatic boundary conditionis the issue at hand, a model that does not account for property variationswill predict a lower frequency of actuation than a model that does account forthe property variations, as dealt with in this paper.