A MACROSCOPIC PHENOMENOLOGICAL CONSTITUTIVE MODEL FOR THE UNIAXIAL TRANSFORMATION RATCHETING OF SUPER-ELASTIC NiTi SHAPE MEMORY ALLOY

Super-elastic NiTi shape memory alloy (SMA) has been extensively used in many fields such as civil engineering, aerospace and bio-medical fields due to its good mechanical properties, including unique super-elasticity and shape memory effect. In practical applications, the SMA-based devices are unavoidable subjected to cyclic loadings at different stress levels. However, it is necessary to establish a cyclic constitutive model to describe the transformation ratcheting behavior, i.e., the peak strain and valley strain accumulate cyclically during forward transformation and reverse transformation. Based on the existing experimental results of the transformation ratchetting of the super-elastic NiTi shape memory alloy obtained under the stress-controlled cyclic tension-unloading tests with different peak stresses, the one-dimensional macroscopic phenomenological constitutive model of super-elastic NiTi shape memory alloy proposed by Graesser, where super-elastic behavior is reflected by the nonlinear evolution equation of back stress, was extended to describe the uniaxial transformation ratchetting within the framework of generalized visco-plasticity. In the extended model, the differences of characteristic variables and their evolutions between the forward transformation and reverse transformation were considered, the evolution equations of the start stress of forward transformation, the start stress of reverse transformation, maximum transformation strain and residual strain were introduced by the internal variable of relative accumulated inelastic strain. In the meantime, the correlation coefficients in these evolution equations were determined by the ratio of the peak stress and the finish stress of forward transformation. The comparison of the experiments and simulations shows that the extended model can reasonably describe the dependence of uniaxial transformation ratchetting of super-elastic NiTi shape memory alloy on the peak stress, and the simulated results are in good agreement with the experimental ones.