Multivariant modeling and characterization of SMAs based on hierarchical characteristics of martensite crystallography

Multivariant modeling to describe shape memory alloy (SMA) constitutive behavior is developed at several levels, ultimately resulting in a general 3-D Two-tier Multivariant model with correspondence variants (CVs) as minimum units. We start from a previous Multivariant model, based on habit plane variants (HPVs), which uses a thermodynamic and micromechanics approach and accounts for the self-accommodating group structure in its interaction energy calculation within a group. The previous model is first extended and explored with special attention to the crystallographic basis of SMA phase transformation and the impact of specific crystallographic changes on the constitutive response for different types of alloys under complex load states. Based on the invariant plane nature of most martensitic transformation, the explicit interaction energy calculation in the previous model is removed, which lowers transformation stresses and calculation times. This step leads to the Simplified Multivariant model that achieves excellent agreement with experimental data and allows anisotropy at single crystal level. However both models are unable to consider the inherent hierarchical features of SMA martensite, i.e., a HPV is either composed of two twinned CVs or a faulted CV. Therefore, in order to more accurately model SMA response including 2nd stage conversion process, a Two-tier model is pursued which consider the interaction of variants in a more natural way.; The proposed Two-Tier Multivariant model considers the CV as the minimum subunit and recalculates the transformation strain of a HPV based on the current proportion of its component CVs. For a given thermomechanical loading, driving force is calculated at two levels: at the CV level as the resolved shear stress on the twin plane (determining whether detwinning of the HPV to a single CV will occur) and at the HPV level using the transformation strain of the HPVs (determining preferred HPV(s) in the system by a maximum transformation work criterion). The Two-tier model is demonstrated for several basic cases and can capture both the positive features of the simplified Multivariant model as well as handle more complicated second stage detwinning processes.; The modeling was stimulated and supported by extensive experimental studies by the author as well as publications from others. Several types of experiments performed by the author and typical experimental results are shown in the appendix.