Microscale phase field modeling of the martensitic transformation during cyclic loading of NiTi single crystal

Abstract

A microscale phase field model developed in Levitas et al. (2004) and Idesman et al. (2005) is slightly advanced for different and anisotropic elastic moduli of phases and is employed for the study of the stress-induced cubic-monoclinic phase transition in NiTi single crystal involving all 12 martensitic variants. The model is scale-independent, without the gradient term, and it is applicable for any scale greater than 100 nm. This model includes strain softening and the corresponding transformation strain localization, and it reproduces a discrete martensitic microstructure. The model only tracks finite-width interfaces between austenite and the mixture of martensitic variants, and does not consider the interfaces between martensitic variants. The model is implemented as a UMAT subroutine in a commercial finite element (FE) package, ABAQUS. Multiple problems for a uniaxial cyclic loading are solved to study the effect of mesh, strain rate, crystal orientation, different numbers of pre-existing nuclei, and the magnitude of the athermal threshold on the stress-strain responses as well as the microstructure evolution. The obtained results exhibit that the microstructure and global stress-strain responses are practically independent of mesh discretization and the applied strain rate for relatively small strain rates. While the presence of the initial nuclei in the sample decreases the nucleation stress, it slightly increases the total energy dissipation. The observed microstructure, the sudden drop in the stress-strain curve after initiation of the martensitic transformation, and the absence of a similar jump for the reverse phase transformation are in qualitative agreement with known experiments. Changing the crystallographic orientation of the sample varies the entire behavior, namely, the variants which are involved in the phase transformation, the morphology of the associated microstructure, the stress-strain curve, and the total dissipation. Athermal threshold, in addition to the expected increase in the magnitude of hysteresis, leads to some strain hardening for the direct phase transformation.