An Expanded Martensite Variant Selection Theory Accounting for Transformation Rotations and Applied Stress Fields: Predictions of Variant Clusters in Titanium

Abstract

An expanded strain energy-based criterion for predicting preferred martensite variants and multivariant clusters is developed and verified. Building upon previous inclusion-based formulations that considered only the strain energy of lattice stretches, here the authors also incorporate the strain energy of lattice rotations that result from martensitic transformations. Using this more complete single-variant strain energy formulation as a foundation, a micromechanical construct is developed to calculate energy reductions from transforming to clusters of multiple martensite variants from a single austenite crystal. Using elastic constants calculated at the β-transus temperature for pure titanium via molecular dynamics simulations, this new energy criterion is verified to exactly predict the same eight preferred self-accommodation variant cluster triplets identified in previous experiments. Finally, a modification to the strain energy formulation is made to consider externally applied fields. Using this modification, effects of applied loads during transformation are considered in calculating predictions of stress-accommodating multivariant triplets.