Path Dependence of Shape Memory Alloys during Cyclic Loading

Abstract

It has long been recognized that Ni-Ti shape memory alloys (SMAs) behave pseudo-elastically above the austenite finish temperature (Af) with a nearly perfectly plastic character during the initial cycles of transformation. Under conditions of cyclic loading with a maximum strain ∈max, the critical stress to initiate stress-induced martensitic (SIM) transformation decreases, the strain-hardening rate increases, residual strain accumulates and the hysteresis energy progressively decreases over many cycles of loading. Hence the hysteresis energy available for dissipation gradually decreases during cycling. Recent work (Miyazaki et al., 1981, 1986; Contardo and Guenin, 1990; Filip and Mazanec, 1994) has shown that dislocations are generated in the alloy during the phase transformation to accommodate formation of SIM, giving rise to the change of hysteresis behavior of the SMA. Upon loading the SMA to a strain level higher than ∈ max, the alloy behaves almost identical to the "virgin material". Likewise, it has been shown (Huo and Muller, 1993) that the stress at which either the forward or reverse transformation occurs, even in the absence of significant matrix dislocation effects, depends upon the strain level (transformation level) prior to the last unloading event. This behavior is attributed to the distribution and configuration of austenite-martensite interfaces which evolve during the transformation and requires additional internal state variable(s) beyond the mass fraction of martensite for description. These path dependent mechanisms are expected to invalidate current internal state variable models which assume that the free energy depends only on strain, temperature and martensite mass fraction. In this paper, some modelling features are discussed to address the effects of dislocation arrays generated in the parent phase as well as the distribution of transformation product/interfaces. Several uniaxial experiments are reported on Ni-Ti to highlight the path dependence of the cyclic deformation behavior and progressive decrease of dissipated energy. Implications for multiaxial loading behavior are also discussed.