Multiphase phase field theory for temperature- and stress-induced phase transformations

Levitas, Valery I.; Roy, Arunabha M.

doi:10.1103/physrevb.91.174109

Cited by 111 publications

(44 citation statements)

References 34 publications

(57 reference statements)

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“…1(a)-(d) for symmetric and asymmetric ternary systems, in case of A 3 = 0 and A 3 = 0, respectively. We note, that similar terms are used by some authors [30,31] to control the presence of the third component at binary interfaces, however, our approach is quite different than theirs, as it will be shown.…”

Section: Multi-component Cahn-hilliard Liquidmentioning

confidence: 97%

Phase-field theory of multicomponent incompressible Cahn-Hilliard liquids

2016

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In this paper a generalization of the Cahn-Hilliard theory of binary liquids is presented for multi-component incompressible liquid mixtures. First, a thermodynamically consistent convectiondiffusion type dynamics is derived on the basis of the Lagrange multiplier formalism. Next, a generalization of the binary Cahn-Hilliard free energy functional is presented for arbitrary number of components, offering the utilization of independent pairwise equilibrium interfacial properties. We show that the equilibrium two-component interfaces minimize the functional, and demonstrate, that the energy penalization for multi-component states increases strictly monotonously as a function of the number of components being present. We validate the model via equilibrium contact angle calculations in ternary and quaternary (4-component) systems. Simulations addressing liquid flow assisted spinodal decomposition in these systems are also presented.

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Section: Multi-component Cahn-hilliard Liquidmentioning

confidence: 97%

Phase-field theory of multicomponent incompressible Cahn-Hilliard liquids

2016

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“…It also has to be generalized for fully large strain formulation [35] and multivariant martensitic transformations and multiphase materials [73].…”

Section: Discussionmentioning

confidence: 99%

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

Levitas

Warren

2015

Phys. Rev. B

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The main focus of this paper is to introduce, in a thermodynamically consistent manner, an anisotropic interface energy into a phase field theory for phase transformations. Here we use a small strain formulation for simplicity, but we retain some geometric nonlinearities, which are necessary for introducing correct interface stresses. Previous theories have assumed the free energy density (i.e., gradient energy) is an anisotropic function of the gradient of the order parameters in the current (deformed) state, which yields a nonsymmetric Cauchy stress tensor. This violates two fundamental principles: the angular momentum equation and the principle of material objectivity.Here, it is justified that for a noncontradictory theory the gradient energy must be an isotropic function of the gradient of the order parameters in the current state, which also depends anisotropically on the direction of the gradient of the order parameters in the reference state. A complete system of thermodynamically consistent equations is presented. We find that the main contribution to the Ginzburg-Landau equation resulting from small strains arises from the anisotropy of the interface energy, which was neglected before. The explicit expression for the free energy is justified.An analytical solution for the nonequilibrium interface and critical nucleus has been found and a parametric study is performed for orientation dependence of the interface energy and width as well as the distribution of interface stresses.2

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“…¼ 0 for any #, corresponds to the reference phase 0. In the current paper, it is a melt M; however, it can be any phase for a general three-phase system, in particular, austenite for multivariant martensitic transformations (Levitas and Preston, 2002b;Levitas et al, 2003Levitas and Roy, 2015). Points (!…”

Section: Polar Order Parametersmentioning

confidence: 98%

A phase-field approach to solid–solid phase transformations via intermediate interfacial phases under stress tensor

Momeni

Levitas

2015

International Journal of Solids and Structures

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a b s t r a c tA thermodynamically consistent phase-field (PF) theory for phase transformations (PTs) between three different phases is developed with emphases on the effect of a stress tensor and interface interactions. The phase equilibrium and stability conditions for homogeneous phases are derived and a thermodynamic potential which satisfies all these conditions is introduced using polar order parameters. Propagation of a solid-solid (SS) interface containing nanometer-sized intermediate disordered interfacial phases (IP) and particularly an interfacial intermediate melt (IM) is studied for an HMX energetic material using the developed PF model. The scale effects (the ratio of widths of SS to solid-melt (SM) interfaces, k d ), the effect of the energy ratio of SS to SM interfaces (k E ), and the temperature on the formation and stability of IM are investigated. An interaction between two SM interfaces via an IM, which plays a key role in defining a well-posed problem and mesh-independent solution, is captured using a special gradient energy term. The influence of the elastic energy on the formation and retainment of IM and its structure, hundreds of degrees below the melting temperature, is investigated. Elastic energy promotes barrierless IM in terms of an increasing degree of disordering, interface velocity, and width of IM, but it surprisingly increases nucleation temperature for the IM. The key effect, however, is the drastic reduction (by more than an order of magnitude) of the energy of the critical nucleus of the IM within the SS interface, which is caused by the elastic energy. The developed PF model is applicable for the general case of PT between three phases and can be applied (adjusted) to other physical phenomena, such as premelting/disordering at grain boundaries, martensitic PTs, surface-induced premelting and PTs, and developing the interfacial phase diagrams.

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Multiphase phase field theory for temperature- and stress-induced phase transformations

Cited by 111 publications

References 34 publications

Phase-field theory of multicomponent incompressible Cahn-Hilliard liquids

Phase-field theory of multicomponent incompressible Cahn-Hilliard liquids

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

A phase-field approach to solid–solid phase transformations via intermediate interfacial phases under stress tensor

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