Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin films

Wang, Yu U.; Jin, Yongmei M.; Khachaturyan, A. G.

doi:10.1016/s1359-6454(03)00238-6

Cited by 209 publications

(232 citation statements)

References 23 publications

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“…Phase field or Ginzburg-Landau approach is broadly used for the simulation of various first-order phase transformations (PTs), including martensitic PTs (Artemev and Khachuaturyan (2001); Chen (2002) ;Finel et al (2010); Jin et al (2001a); Levitas et al (2004); Levitas and Lee (2007); Lookman et al (2008); Vedantam and Abeyaratne (2005), see also recent review Mamivand et al (2013)), reconstructive PTs (Denoual et al (2010); Salje (1991); Toledano and Dmitriev (1996)), twinning (Clayton and Knap (2011a,b); Hildebrand and Miehe (2012); ), dislocations (Hu et al (2004); Jin and Khachaturyan (2001); Koslowski et al (2002); ; Rodney et al (2003); Wang et al (2003); Wang and Li (2010)), PTs in liquids (Lowengrub and Truskinovsky (1998)), and melting ; Slutsker et al (2006); ). The main concept is related to the order parame-ters η i that describe material instabilities during PTs in a continuous way.…”

Section: Introductionmentioning

confidence: 99%

Phase field approach to martensitic phase transformations with large strains and interface stresses

Levitas

2014

Journal of the Mechanics and Physics of Solids

117

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Thermodynamically consistent phase field theory for multivariant martensitic transformations, which includes large strains and interface stresses, is developed. Theory is formulated in a way that some geometrically nonlinear terms do not disappear in the geometrically linear limit, which in particular allowed us to introduce the expression for the interface stresses consistent with the sharp interface approach. Namely, for the propagating nonequilibrium interface, a structural part of the interface Cauchy stresses reduces to a biaxial tension with the magnitude equal to the temperature-dependent interface energy. Additional elastic and viscous contributions to the interface stresses do not require separate constitutive equations and are determined by solution of the coupled system of phase field and mechanics equations. Ginzburg-Landau equations are derived for the evolution of the order parameters and temperature evolution equation. Boundary conditions for the order parameters include variation of the surface energy during phase transformation. Because elastic energy is defined per unit volume of unloaded (intermediate) configuration, additional contributions to the Ginzburg-Landau equations and the expression for entropy appear, which are important even for small strains. A complete system of equations for fifth-and sixth-degree polynomials in terms of the order parameters is presented in the reference and actual configurations. An analytical solution for the propagating interface and critical martensitic nucleus which includes distribution of components of interface stresses has been found for the sixth-degree polynomial. This required resolving a fundamental problem in the interface and surface science: how to define the Gibbsian dividing surface, i.e., the sharp interface equivalent to the finite-width interface. An unexpected, simple solution was found utilizing the principle of static equivalence. In fact, even two equations for determination of the dividing surface follow from the equivalence of the resultant force and zero-moment condition. For the obtained analytical solution for the propagating interface, both conditions determine the same dividing surface, i.e., the theory is noncontradictory. A similar formalism can be developed for the phase field approach to diffusive phase transformations described by the Cahn-Hilliard equation, twinning, dislocations, fracture, and their interaction.Keywords dividing surface, large strains, phase field approach, phase transformation, surface stresses and energy Disciplines Aerospace EngineeringComments NOTICE: This is the author's version of a work that was accepted for publication in Journal of the Mechanics and Physics of Solids. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal ...

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Section: Introductionmentioning

confidence: 99%

Phase field approach to martensitic phase transformations with large strains and interface stresses

Levitas

2014

Journal of the Mechanics and Physics of Solids

117

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“…An unexpected scale effect in the athermal resistance to the A-M interface motion due to nucleated incoherency dislocations is revealed. The phase-field approach (PFA) to dislocation evolution was developed just during the past decade and is widely used for the understanding of plasticity at the nanoscale (see the pioneering papers [1][2][3][4][5][6][7] and reviews 8,9 ). It allows one simulation of a coupled evolution of multiple interacting dislocations and a stress field without explicit tracking dislocation lines.…”

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confidence: 99%

“…(5) coincides with known expressions. [2][3][4][5] However, for M = 0, after nucleation, dislocation propagates within a band of one finite element high, which is unphysical. An additional term with M 1 penalizes gradients along the normal n α , which leads to dislocation propagation within the entire band of the height H .…”

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confidence: 99%

Advanced phase-field approach to dislocation evolution

Levitas

Javanbakht

2012

Phys. Rev. B

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“…The interactions of dislocations and martensites with free surfaces, voids and cracks have been demonstrated to work robustly in the framework of these models e.g. in [81][82][83]. An extension of this model to phase field simulations of crack tip domain switching in ferrorelectrics is presented in [84,85].…”

Section: Phase Field Modeling Of Fracture In Crystalline Materialsmentioning

confidence: 99%

Phase field modeling of crack propagation

Spatschek¹,

Brener²

2011

Philosophical Magazine

150

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Fracture is a fundamental mechanism of materials failure. Propagating cracks can exhibit a rich dynamical behavior controlled by a subtle interplay between microscopic failure processes in the crack tip region and macroscopic elasticity. We review recent approaches to understand crack dynamics using the phase field method. This method, developed originally for phase transformations, has the well-known advantage of avoiding explicit front tracking by making material interfaces spatially diffuse. In a fracture context, this method is able to capture both the short-scale physics of failure and macroscopic linear elasticity within a self-consistent set of equations that can be simulated on experimentally relevant length and time scales. We discuss the relevance of different models, which stem from continuum field descriptions of brittle materials and crystals, to address questions concerning crack path selection and branching instabilities, as well as models that are based on mesoscale concepts for crack tip scale selection. Open questions which may be addressed using phase field models of fracture are summarized.

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Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin films

Cited by 209 publications

References 23 publications

Phase field approach to martensitic phase transformations with large strains and interface stresses

Phase field approach to martensitic phase transformations with large strains and interface stresses

Advanced phase-field approach to dislocation evolution

Phase field modeling of crack propagation

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