Phase field methods: Microstructures, mechanical properties and complexity

Finel, A.; Bouar, Y. Le; Gaubert, Anaïs; Salman, Oğuz Umut

doi:10.1016/j.crhy.2010.07.014

Cited by 78 publications

(54 citation statements)

References 27 publications

(36 reference statements)

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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%

“…The main property of the thermodynamic potential, which allows such a solution is that in some temperature and stress ranges it possesses minima in the space of the order parameters corresponding to austenite and each martensitic variant, separated by an energy barrier (Barsch and Krumhansl (1984); Chen (2002); Jin et al (2001a); Levitas and Lee (2007); Lookman et al (2008); Vedantam and Abeyaratne (2005)). However, potentials developed in material science and physical literature (Barsch and Krumhansl (1984); Chen (2002) ;Finel et al (2010); Jin et al (2001a); Lookman et al (2008)) did not take proper care of the mechanics of martensitic PTs and did not have sufficient degrees of freedom to incorporate all material properties of A and M i (see Levitas and Preston (2002a,b); ). Also, PTs criteria should follow from the material instability conditions (Salje (1991); Toledano and Dmitriev (1996); Toledano and Toledano (1998); Umantsev (2012)), which never were implemented in physical and material literature for multivariant martensitic PTs.…”

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%

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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%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…On the other hand, the phase-field approach has proved to be an efficient method to model the motion of interfaces and growth of precipitates based on a sound thermodynamical formulation including non convex free energy potentials [13]. The effect of microelasticity on the morphological aspects and kinetics of phase transformation is classically studied but the occurrence of plasticity is recent [19,20,38].…”

Section: Introductionmentioning

confidence: 99%

Micromorphic vs. Phase-Field Approaches for Gradient Viscoplasticity and Phase Transformations

Forest

Ammar

Appolaire

2011

Advances in Extended and Multifield Theories for Continua

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Abstract. Strain gradient models and generalized continua are increasingly used to introduce characteristic lengths in the mechanical behavior of materials with microstructure. On the other hand, phase-field models have proved to be efficient tools to simulate microstructure evolution due to thermodynamical processes in the presence of mechanical deformation. It is shown that both methods have strong connections from the point of view of thermomechanical field theory. A general formulation of thermomechanics with additional degrees of freedom is presented that encompasses both applications as special cases. It is based on the introduction of additional power of internal forces introducing generalized stresses. The current knowledge in the formulation of physically non-linear constitutive equations is used to develop strongly coupled elastoviscoplastic material models involving phase transformation and moving boundaries.

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“…Discontinuous variables like plastic strain in conventional plasticity can be smoothed at boundaries and interfaces to better reproduce physical deformation mechanisms, or in strain localization bands in the case of softening mechanical behaviour. Sharp interfaces are replaced by smooth interfaces in phase field models to simulate moving boundaries and thus avoid complex front-tracking methods [4][5][6]. The regularization is used in the two latter cases to obtain discretization-objective simulations results, i.e.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

Forest¹

2016

Proc. R. Soc. A.

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International audienceThe construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the Helmholtz free energy function of the constitutive material model. The combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator. Within the small strain framework, the choice of a quadratic potential w.r.t. the gradient term provides the widely used Helmholtz operator whose regularization properties are well known: smoothing of discontinuities at interfaces and boundary layers in hardening materials, and finite width localization bands in softening materials. The objective is to review and propose nonlinear extensions of micromorphic and strain/damage gradient models along two lines: the first one introducing nonlinear relations between generalized stresses and strains; the second one envisaging several classes of finite deformation model formulations. The generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling. Two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach: additive split of some Lagrangian strain measure or choice of a local objective rotating frame. Three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient. A new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable

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Phase field methods: Microstructures, mechanical properties and complexity

Cited by 78 publications

References 27 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

Micromorphic vs. Phase-Field Approaches for Gradient Viscoplasticity and Phase Transformations

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

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