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Phase field approach for stress- and temperature-induced phase transformations that satisfies lattice instability conditions. Part I. General theory

TitlePhase field approach for stress- and temperature-induced phase transformations that satisfies lattice instability conditions. Part I. General theory
Publication TypeJournal Article
Year of Publication2018
AuthorsLevitas, VI
JournalInternational Journal of Plasticity
Volume106
Pagination164-185
Date Published07
Type of ArticleArticle
ISBN Number0749-6419
Accession NumberWOS:000434744000010
KeywordsDislocations, Engineering, finite-element simulations, formulation, ginzburg-landau theory, instability condition, interface stresses, Interpolation functions, large strains, lattice, Martensitic phase transformation, martensitic-transformation, Materials Science, mechanics, model, Phase-field approach, shape-memory alloys, transitions
Abstract

e lattice instability conditions obtained with MD: (a) one has to use the fifth degree polynomial interpolation functions of the order parameter for all material parameters; (b) each component of the transformation strain tensor should have a different interpolation functions; and (c) the interpolation functions for tensors of the elastic moduli of all ranks should have zero second derivatives for the parent and product phases, so that terms with elastic moduli, which are nonlinear in stresses, do not contribute to the lattice instability conditions. Specific interpolation and double-well functions have been derived for all parts of the Helmholtz free energy and for two models for the transformation deformation gradient. For these models, explicit expressions for the Ginzburg-Landau equations and lattice instability conditions are derived. Material parameters have been calibrated using results of MD simulations. In Part II of this paper, the developed model is further refined and studied, and applied for the finite element simulations of the nanostructure evolution in Si under triaxial loading.

DOI10.1016/j.ijplas.2018.03.007
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Short TitleInt. J. Plast.