Direct numerical determination of stabilized dissipated energy of shape memory alloys under cyclic tensile loadings

When shape memory alloys are subjected to cyclic loadings, the stabilized dissipated energy is an effective parameter in studying their performance, for instance, the fatigue life. However, thermomechanical coupling in the behavior of shape memory alloys under cyclic loadings causes the amount of stabilized dissipated energy to be obtainable once the responses of all transient cycles are determined. In this article, direct formulae are proposed to numerically evaluate stabilized dissipated energy of a shape memory alloy under cyclic tensile loadings as a function of maximum and minimum applied stresses as well as the loading frequency. A one-dimensional fully coupled thermomechanical constitutive model with a cycle-dependent phase diagram is utilized to be able to directly predict the uniaxial stress-strain response of a shape memory alloy in a specified cycle with no need of solving the previous cycles. The results are experimentally assessed for NiTi and CuAlBe specimens. Since the backward transformation in CuAlBe is realized to more gradually occur than that in NiTi, an enhanced phase diagram is proposed in which different slopes are considered for the start and finish of backward transformation strip. The numerical predictions of the present approach are shown to be in a good agreement with the experimental findings for cyclic tensile loadings.