Multiple twinning and variant-variant transformations in martensite: Phase-field approach

A phase-field theory of transformations between martensitic variants and multiple twinning within martensitic variants is developed for large strains and lattice rotations. It resolves numerous existing problems. The model, which involves just one order parameter for the description of each variant-variant transformation and multiple twinnings within each martensitic variant, allows one to prescribe the twin interface energy and width, and to introduce interface stresses consistent with the sharp interface limit. A finite-element approach is developed and applied to the solution of a number of examples of twinning and combined austenite-martensite and martensite-martensite phase transformations (PTs) and nanostructure evolution. A similar approach can be developed for reconstructive, electric, and magnetic PTs.