Thermodynamically consistent phase field theory of phase transformations with anisotropic interface energies and stresses

Levitas, Valery I.; Warren, James A.

doi:10.1103/physrevb.92.144106

Cited by 13 publications

(7 citation statements)

References 84 publications

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“…This resolves the problem with description of anisotropy of the gradient and interface energies. This idea is realized within non-strict small strain formulation in Levitas and Warren (2015).…”

Section: Anisotropic Interface Energymentioning

confidence: 99%

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

Levitas

Warren

2016

Journal of the Mechanics and Physics of Solids

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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 deformed 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 deformed configuration, but depends on the direction of the gradient of the order parameters (is anisotropic) in the undeformed 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

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Section: Anisotropic Interface Energymentioning

confidence: 99%

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

Levitas

Warren

2016

Journal of the Mechanics and Physics of Solids

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“…At this point, we also want to emphasize that our model is thermodynamically consistent; if elastic stresses are incorporated, while incorporating interfacial energy anisotropy, the evolution equation needs modifications as shown by Levitas and Warren. 36 As described by Nye in his classic text, 37 using intrinsic symmetries (such as, for sufficiently smooth f,…”

Section: ■ Formulationmentioning

confidence: 99%

Phase Field Modelling of Morphologies Driven by Tetragonal Interfacial Energy Anisotropy

Roy

Gururajan

2021

Crystal Growth & Design

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A wide range of morphologies, such as dipyramids, rods, plates, and their truncated variants with more than one type of facet, are experimentally observed in tetragonal systems. In many cases, the origin of these morphologies is the strong anisotropy in the interfacial free energy. Phase field models that are restricted to the second-rank tensor term for the gradient energy coefficient can give rise to neither square cross sections nor such faceted and truncated morphologies. In this paper, using phase field simulations based on the implementation of a family of extended Cahn–Hilliard (ECH) models, we show that we can obtain all these experimentally observed morphologies. In addition to describing the formulation briefly, we (i) list the sufficient and necessary nonzero and independent parameters needed to describe the anisotropic interfacial free energy and (ii) enumerate the constraints on these parameters based on the demand that the interfacial free energy is positive definite. We analyze the precipitate morphologies and show that they indeed are equilibrium morphologies consistent with the Wulff construction. Our study is useful in understanding the origin of multiple facets that are formed as a result of interfacial free energy anisotropy; it can also serve as a guide for choosing parameters for obtaining specific morphologies consistent with tetragonal anisotropy.

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“…The papers on the thermodynamics of stressed solids are huge in number: see for example [142][143][144][145][146][147][148][149][150][151][152][153]. However, as seen in some of these recent attempts [154][155][156] the quest for the formulation of thermodynamically consistent phase field models that obey relevant principles and laws of mechanics is far from complete.…”

Section: Some Basics Of Thermodynamics and Mechanicsmentioning

confidence: 99%

Elastic stress effects on microstructural instabilities

Gururajan,

Lahiri

2016

Preprint

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Microstructure (which, for the purposes of this article, defined as the sizes, shapes and distributions of interfaces in a material) is the key bridge between processing and properties. Hence, a study of the formation and evolution of microstructures is of great interest: see, for example, [1] and references therein. Naturally, during the formation and evolution of microstructures, new interfaces may form and old ones might disappear; in addition, interfaces might merge or split.Instabilities is one of the key phenomena that leads to interesting microstructural features; for example, compositional instabilities in binary alloys aged inside the spinodal region of a miscibility gap lead to spinodal microstructures and dendritic microstructures result from the breaking up of planar solidliquid interfaces during solidification. Martin, Doherty and Cantor, in their * We dedicate this paper to the memory of John W Cahn. His immense contributions to the field of elastic stress induced microstructural instabilities are seen not only in his papers, but also in a large number of acknowledgements that we noticed during the preparation of this manuscript -such as the acknowledgement of Tien and Copley in their classic paper on rafting.

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Thermodynamically consistent phase field theory of phase transformations with anisotropic interface energies and stresses

Cited by 13 publications

References 84 publications

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

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

Phase Field Modelling of Morphologies Driven by Tetragonal Interfacial Energy Anisotropy

Elastic stress effects on microstructural instabilities

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