Nonlinear finite element simulation of superelastic shape memory alloy parts

Abstract

This article presents a methodology to simulate the nonlinear thermomechanical behaviour of shape memory alloys (SMA) by the finite element method. After a brief presentation of the remarkable thermomechanical properties of SMA materials, a general and simplified constitutive law is formulated based on plastic flow theory, which takes into account the stress and temperature induced phase transformation in the alloy. The reason for this connection between plasticity and the superelastic behaviour of SMA lies in the phase transformation itself, the effect of which is somehow similar to a plastic flow. This approach, however, differs from plasticity in the sense that upon unloading the initial state of the material can be recovered through a hysteresis cycle. To simulate this hysteresis, two different von Mises plastic criteria for three-dimensional problems are used for the loading and unloading procedures, respectively, so that unloading can also be treated as a transition from elasticity to plasticity. It is first suggested to use a bilinear model as uniaxial material law. Then a more precise model based on dual kriging interpolation is also proposed and implemented. The nonlinear finite element equations of the approximate problem are briefly stated and the methodology is validated by comparison with experimental results. Finally, one example of industrial application is given concerning stress analysis of a SMA spring disc.