Multivariant micromechanical model for SMAs. Part 1. Crystallographic issues for single crystal model

A general 3-D multivariant model for shape memory alloy constitutive behavior is further developed in this paper. The model is based on the habit planes and transformation directions for variants of martensite and uses a thermodynamic and micromechanics approach to develop the governing equations for thermomechanical response. The model accounts for the self-accomodating group structure exhibited during martensitic plate formation and utilizes this concept in its calculation of the interaction energy between variants. In this paper, we expand the multivariant model to consider the impact of inclusion shape on model predictions. A direction selection scheme is proposed for penny shaped inclusions and is based on the fact that several habit plane variants tend to cluster about one of the {011} or {001} poles. We also explore in detail the crystallographic basis of material response and the impact of specific crystallographic changes on the macroscopic single crystal constitutive response. Differences between type I and type II twinning are examined and it is shown that choice of the proper twinning type is essential to capture experimental data. The grouping structure is examined and several different options published for a NiTi alloy are implemented and results compared. Several concepts, i.e. artificial merging, exclusive and non-exclusive grouping, are raised to assist exploration of NiTi grouping possibilities. The anisotropy of the single crystal material response is illustrated and implications on higher level modeling are discussed. It is noted that properly representing the details of the crystallographic microstructure is crucial to obtaining accurate macroscopic stress-strain predictions.