Phase field approach for stress- and temperature-induced phase transformations that satisfies lattice instability conditions. Part I. general theory Levitas, Valery Levitas, Valery
dc.contributor.department Aerospace Engineering
dc.contributor.department Ames Laboratory
dc.contributor.department Mechanical Engineering
dc.contributor.department Materials Science and Engineering 2018-04-05T22:00:57.000 2020-06-29T22:45:21Z 2020-06-29T22:45:21Z Mon Jan 01 00:00:00 UTC 2018 2019-03-20 2018-01-01
dc.description.abstract <p>Recently, results of molecular dynamics (MD) simulations were obtained for the crystal lattice instability conditions for the phase transformations (PTs) between semiconducting Si I and metallic Si II under action of all six components of the stress tensor (Levitas et al. (2017a, b)). These conditions are linear in terms of stresses normal to the cubic faces of Si I and are independent of the shear stresses. In the current paper, we (a) formulated the requirements for the thermodynamic potential and transformation deformation gradient tensors and (b) developed a phase field approach (PFA) for the stress-induced martensitic PTs for large strains while allowing for interfacial stresses, which are consistent with the obtained instability conditions. The general system of equations for coupled PFA and nonlinear elasticity is presented. Crystal lattice instability criteria are derived within a PFA, and it is proven that they are independent of the prescribed stress measure. In order to reproduce the 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.</p>
dc.description.comments <p>This is a manuscript of the article Levitas, Valery I. "Phase field approach for stress-and temperature-induced phase transformations that satisfies lattice instability conditions. Part I. general theory." <em>International Journal of Plasticity</em> (2018). DOI: <a href="" target="_blank">10.1016/j.ijplas.2018.03.007</a>. Posted with permission.</p>
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dc.identifier archive/
dc.identifier.articleid 1119
dc.identifier.contextkey 11910719
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath aere_pubs/118
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 18:58:45 UTC 2022
dc.source.uri 10.1016/j.ijplas.2018.03.007
dc.subject.disciplines Aerospace Engineering
dc.subject.disciplines Structures and Materials
dc.subject.keywords Phase-field approach
dc.subject.keywords Martensitic phase transformation
dc.subject.keywords Lattice instability condition
dc.subject.keywords Interpolation functions
dc.subject.keywords Large strains
dc.title Phase field approach for stress- and temperature-induced phase transformations that satisfies lattice instability conditions. Part I. general theory
dc.type article
dc.type.genre article
dspace.entity.type Publication
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