Phase field approach with anisotropic interface energy and interface stresses: Large strain formulation

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dc.contributor.author Levitas, Valery
dc.contributor.author Warren, James
dc.contributor.author Levitas, Valery
dc.contributor.department Aerospace Engineering
dc.contributor.department Ames Laboratory
dc.contributor.department Mechanical Engineering
dc.contributor.department Materials Science and Engineering
dc.date 2018-02-19T00:27:00.000
dc.date.accessioned 2020-06-29T22:46:19Z
dc.date.available 2020-06-29T22:46:19Z
dc.date.copyright Fri Jan 01 00:00:00 UTC 2016
dc.date.issued 2016-06-01
dc.description.abstract <p>A thermodynamically consistent, large-strain, multi-phase field approach (with consequent interface stresses) is generalized for the case with anisotropic interface (gradient) energy (e.g. an energy density that depends both on the magnitude and direction of the gradients in the phase fields). Such a generalization, if done in the “usual” manner, yields a theory that can be shown to be manifestly unphysical. These theories consider the gradient energy as anisotropic in the <em>deformed</em> configuration, and, due to this supposition, several fundamental contradictions arise. First, the Cauchy stress tensor is non-symmetric and, consequently, violates the moment of momentum principle, in essence the Herring (thermodynamic) torque is imparting an unphysical angular momentum to the system. In addition, this non-symmetric stress implies a violation of the principle of material objectivity. These problems in the formulation can be resolved by insisting that the gradient energy is an isotropic function of the gradient of the order parameters in the <em>deformed</em> configuration, but depends on the direction of the gradient of the order parameters (is anisotropic) in the <em>undeformed</em> configuration. We find that for a propagating nonequilibrium interface, the structural part of the interfacial Cauchy stress is symmetric and reduces to a biaxial tension with the magnitude equal to the temperature- and orientation-dependent interface energy. Ginzburg–Landau equations for the evolution of the order parameters and temperature evolution equation, as well as the boundary conditions for the order parameters are derived. Small strain simplifications are presented. Remarkably, this anisotropy yields a <em>first order</em> correction in the Ginzburg–Landau equation for small strains, which has been neglected in prior works. The next strain-related term is third order. For concreteness, specific orientation dependencies of the gradient energy coefficients are examined, using published molecular dynamics studies of cubic crystals. In order to consider a fully specified system, a typical sixth order polynomial phase field model is considered. Analytical solutions for the propagating interface and critical nucleus are found, accounting for the influence of the anisotropic gradient energy and elucidating the distribution of components of interface stresses. The orientation-dependence of the nonequilibrium interface energy is first suitably defined and explicitly determined analytically, and the associated width is also found. The developed formalism is applicable to melting/solidification and crystal-amorphous transformation and can be generalized for martensitic and diffusive phase transformations, twinning, fracture, and grain growth, for which interface energy depends on interface orientation of crystals from either side.</p>
dc.description.comments <p>This article is published as Levitas, Valery I., and James A. Warren. "Phase field approach with anisotropic interface energy and interface stresses: Large strain formulation." Journal of the Mechanics and Physics of Solids 91 (2016): 94-125. doi:<a href="https://doi.org/10.1016/j.jmps.2016.02.029" id="x-x-ddDoi">10.1016/j.jmps.2016.02.029</a>. Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/aere_pubs/89/
dc.identifier.articleid 1091
dc.identifier.contextkey 10962903
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath aere_pubs/89
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/2092
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/aere_pubs/89/2016_Levitas_PhaseFieldApproachAnisotropic.pdf|||Sat Jan 15 02:18:49 UTC 2022
dc.source.uri 10.1016/j.jmps.2016.02.029
dc.subject.disciplines Aerospace Engineering
dc.subject.disciplines Condensed Matter Physics
dc.subject.disciplines Structures and Materials
dc.subject.keywords Phase field approach
dc.subject.keywords Phase transformation
dc.subject.keywords Large strains
dc.subject.keywords Anisotropic interface energy and interface stresses
dc.title Phase field approach with anisotropic interface energy and interface stresses: Large strain formulation
dc.type article
dc.type.genre article
dspace.entity.type Publication
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