Phase-Field Reaction-Pathway Kinetics of Martensitic Transformations in a Model<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Fe</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mi>Ni</mml:mi></mml:math>Alloy

Denoual, Christophe; Caucci, Anna Maria; Soulard, Laurent; Pellegrini, Yves-Patrick

doi:10.1103/physrevlett.105.035703

Cited by 32 publications

(27 citation statements)

References 26 publications

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“…[12].] On the other hand, our strategy of consistently using strain instead of stress as the control variable is finally rewarded by the tame numerical behavior of the expansions (15) and (16). We would, therefore, advocate the statement that our Helmholtz approach is likely to be the only one that, in practice, leads to a manageable formulation of the theory.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…However, in the context of structural phase transitions, these assumptions may not always be justified. Important ambient-pressure examples in which the relevant strains are so large that it is mandatory to introduce a proper finitestrain measure such as the Lagrangian strain tensor and eventually even deal with elastic anharmonicity are, e.g., martensitic phase transformations [13], twinning at strongly first-order phase transformations [14], and reconstructive phase transformations [15]. In the context of highpressure phase transitions, the question of how to construct a corresponding Landau theory coupled to finite strain has been addressed for the first time in Ref.…”

Section: Landau Theory Coupled To Nonlinear Elasticitymentioning

confidence: 99%

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Fully Consistent Finite-Strain Landau Theory for High-Pressure Phase Transitions

et al. 2014

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Landau theory (LT) is an indispensable cornerstone in the thermodynamic description of phase transitions. As with structural transitions, most applications require one to consistently take into account the role of strain. If temperature drives the transition, the relevant strains are, as a rule, small enough to be treated as infinitesimal, and therefore one can get away with linearized elasticity theory. However, for transitions driven by high pressure, strains may become so large that it is absolutely mandatory to treat them as finite and deal with the nonlinear nature of the accompanying elastic energy. In this paper, we explain how to set up and apply what is, in fact, the only possible consistent Landau theory of high-pressure phase transitions that systematically allows us to take these geometrical and physical nonlinearities into account. We also show how to incorporate available information on the pressure dependence of elastic constants taken from experiment or simulation. We apply our new theory to the example of the high-pressure cubic-tetragonal phase transition in strontium titanate, a model perovskite that has played a central role in the development of the theory of structural phase transitions. Armed with pressure-dependent elastic constants calculated by density-functional theory, we give an accurate description of recent high-precision experimental data and predict a number of elastic transition anomalies accessible to experiments.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Landau Theory Coupled To Nonlinear Elasticitymentioning

confidence: 99%

Fully Consistent Finite-Strain Landau Theory for High-Pressure Phase Transitions

et al. 2014

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“…When the melting of an elastic solid was considered ), additional surface stresses were not introduced. Surface stresses have been ignored until very recently in the phase field theories for multivariant martensitic and reconstructive PTs and twinning (Artemev and Khachuaturyan (2001); Chen (2002); Clayton and Knap (2011a,b); Denoual et al (2010); Finel et al (2010); Hildebrand and Miehe (2012); Jin et al (2001a); Levitas et al (2004); Levitas and Lee (2007); Lookman et al (2008); Salje (1991); Vedantam and Abeyaratne (2005)). …”

Section: Introductionmentioning

confidence: 99%

“…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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“…6 and 20. Similar developments can be applied for various phenomena described by the phase field approach, such as various phase transformations (martensitic, 1,6,20 reconstructive, 21 and electromagnetic phase transformations, 22 melting-freezing, 7,23 amorphization), diffusive phase transformations described by Cahn-Hilliard theory (e.g., spinodal decomposition, segregation, separation, and precipitation), 24 twinning, 20,25 grain evolution, 26 dislocations, 27 fracture, 28 and interaction of defects (cracks and dislocations) and phase transformations. 29 Finally, the expression obtained for the surface stresses can be included in commercial multyphysics codes, like COSMOL, 30 instead of the current simplified expressions.…”

Section: Discussionmentioning

confidence: 99%

Interface stress for nonequilibrium microstructures in the phase field approach: Exact analytical results

Levitas

2013

Phys. Rev. B

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An exact expression for the temperature-dependent interface stress tensor (tension) and energy is derived within a phase field approach. The key problem, of which part of the thermal energy should contribute to the surface tension, is resolved with the help of an analytical solution for a nonequilibrium interface. Thus, for a propagating interface at any temperature, the interface stress tensor represents biaxial tension with magnitude equal to the temperature-dependent interface energy. Explicit expressions for the distributions of interface stresses are obtained for a nonequilibrium interface and a critical nucleus. The results obtained are applicable for various phase transformations (solid-solid, melting-solidification, sublimation, etc.) and structural changes (twinning, grain evolution), and can be generalized for anisotropic interface energy, for dislocations, fracture, and diffusive phase transformations described by Cahn-Hilliard theory. An exact expression for the temperature-dependent interface stress tensor (tension) and energy is derived within a phase field approach. The key problem, of which part of the thermal energy should contribute to the surface tension, is resolved with the help of an analytical solution for a nonequilibrium interface. Thus, for a propagating interface at any temperature, the interface stress tensor represents biaxial tension with magnitude equal to the temperature-dependent interface energy. Explicit expressions for the distributions of interface stresses are obtained for a nonequilibrium interface and a critical nucleus. The results obtained are applicable for various phase transformations (solid-solid, melting-solidification, sublimation, etc.) and structural changes (twinning, grain evolution), and can be generalized for anisotropic interface energy, for dislocations, fracture, and diffusive phase transformations described by Cahn-Hilliard theory.

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Phase-Field Reaction-Pathway Kinetics of Martensitic Transformations in a ModelFe3NiAlloy

Cited by 32 publications

References 26 publications

Fully Consistent Finite-Strain Landau Theory for High-Pressure Phase Transitions

Fully Consistent Finite-Strain Landau Theory for High-Pressure Phase Transitions

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

Interface stress for nonequilibrium microstructures in the phase field approach: Exact analytical results

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