Modeling of the cyclic thermomechanical response of SMA wires at different strain rates

Abstract

A one-dimensional coupled thermomechanical model is presented for shape memory alloys (SMAs) under non quasi-static loading by defining a Helmholtz free-energy function consisting of strain energy, thermal energy, and the energy of phase transformation. The first law of thermodynamics is used to address the thermomechanical coupling due to the influence of strain rate on the SMA temperature. The convective heat transfer coefficient of an SMA wire is calculated by using temperature-dependent empirical relations, and it is shown that no single empirical formula for the heat transfer coefficient can be applied to obtain experimentally consistent results under different loading conditions. The martensite fraction is decomposed into stress-induced and temperature-induced fractions so that the model is capable of predicting both the shape memory effect and the pseudoelasticity. Cyclic loading, the effect of wire diameter and the variation of dissipated energy with strain rate are studied, and the general features of the responses are found to be in agreement with the experimental observations.

A review on shape memory alloys with applications to morphing aircraft

“…This is a form of machine learning that utilizes the interaction with multiple situations many times in order to discover the optimal path that must be taken to reach the pre-determined goal. Kadkhodaei et al (2007a) presented a one-dimensional coupled thermo-mechanical model of SMAs under non-quasistatic loading by defining a Helmholtz free energy function consisting of strain energy, thermal energy, and the energy of phase transformation. Kadkhodaei et al (2007bKadkhodaei et al ( , 2008 presented a three-dimensional microplane constitutive model which included the statically constrained formulation with volumetric-deviatoric split for the shape memory alloys.…”

A non-local implicit gradient-enhanced model for thermomechanical behavior of shape memory alloys

“…Most of the existing SMA constitutive models (Arghavani et al, 2010; Bo and Lagoudas, 1999; Brinson, 1993; Kadkhodaei et al, 2007a, 2007b, 2008) have not considered unstable behaviors and have mainly focused on the overall response of these alloys. Shaw and Kyriakides (1997a) suggested a constitutive model in which a three-line up–down–up stress–strain response was used to capture the unstable behavior of SMAs.…”

“…Phase transformations in SMAs are accompanied by release/absorption of latent heat which causes variations in the temperature and, subsequently, the stress–strain response of the alloy. These variations have shown to increase by raising the loading–unloading speed (Kadkhodaei et al, 2007a; McCormick et al, 1993; Ahmadian et al, 2015). Shaw and Kyriakides (1995) conducted experiments on SMAs in air and water.…”

Investigation on local and global behaviors of pseudoelastic shape memory alloy wires in simple tensile test considering stress concentration of grippers

“…At first, a finite element (FE) model is created in ABAQUS/Standard in order to obtain the distributions of cross-sectional area and stress along the wire length during fastening the grippers. These distributions are fed as pre-stress to a numerical solution based on a thermomechanical model derived in a continuum framework (Kadkhodaei et al, 2007) to determine distributions of stress, strain, martensite volume fraction, and temperature in the course of applying tension at any desired strain rate. Using this method, the gripper effects are directly considered in studying the simple tensile test of SMA wires leading to the nucleation and propagation of transformation fronts to be detectable.…”