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 austenitemartensite and martensite-martensite phase transformations (PTs) and nanostructure evolution. A similar approach can be developed for reconstructive, electric, and magnetic PTs. 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 martensitemartensite phase transformations (PTs) and nanostructure evolution. A similar approach can be developed for reconstructive, electric, and magnetic PTs.

Thermodynamic Ginzburg-Landau potential for temperature-and stress-induced phase transformations (PTs) between n phases is developed. It describes each of the PTs with a single order parameter without an explicit constraint equation, which allows one to use an analytical solution to calibrate each interface energy, width, and mobility; reproduces the desired PT criteria via instability conditions; introduces interface stresses, and allows for a controlling presence of the third phase at the interface between the two other phases. A finite-element approach is developed and utilized to solve the problem of nanostructure formation for multivariant martensitic PTs. Results are in a quantitative agreement with the experiment. The developed approach is applicable to various PTs between multiple solid and liquid phases and grain evolution and can be extended for diffusive, electric, and magnetic PTs.

The main conditions for the thermodynamic potential for multiphase Ginzburg-Landau theory are formulated for temperature-induced phase transformations (PTs). Theory, which satisfies all these conditions for n−phase material, is developed. The key point is a new penalizing term in the local energy that allows controlling absence or presence and the extent of the presence of the third phase within the interface between two other phases. A finiteelement method is applied for studying PT between β and δ phases of HMX energetic crystal via intermediate melting more than 100 0 C below melting temperature. Depending on material parameters (ratio of the width and energy of the solid-solid (SS) to solid-melt interface and the magnitude of the penalizing term), there are either two (meta)stable stationary interfacial nanostructures, corresponding to slightly and strongly disordered interfaces (in the limits, pure SS interface or complete melt within SS interface), or these nanostructures coincide. A parametric study of these nanostructures is presented. The developed requirements and approach are applicable to various PTs between multiple solid and liquid phases and can be elaborated for PTs induced by mechanical and electromagnetic fields, diffusive PTs, and the evolution of multi-grain and multi-twin microstructures.

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