Is the Stress Distribution Uniform in the Cross Section of SMA Bars Subjected to Uniaxial Loading? Is it Related to Rate Dependency?

In this paper, a coupled thermo-mechanical framework which takes into account the effect of phase transformation latent heat is presented for shape memory alloys. The governing equations are discretized for SMA bars and wires with circular cross sections by considering the non-uniform temperature distribution in the cross section. It is shown that a combination of three various effects (boundary condition, loading rate, and size) governs the intensity of temperature gradient in the cross section of SMA bars subjected to uniaxial loading. Also, it is shown that because of the strong coupling between the thermal and mechanical fields in SMAs, temperature difference in the cross section causes a non-uniform stress distribution in the cross section. The maximum non-uniformity in the stress and temperature distributions are calculated for a vast range of practical sizes, boundary conditions, and loading rates. The relation between the latent heat flux in the cross section and the rate dependency is studied. It is shown that the rate dependency in the response of SMAs cannot be studied independent of size and boundary condition effects. This phenomenon reveals that the definition of quasi-static loading is not absolute; it is affected by a number of parameters, e.g., the ambient condition and size of the structure.