Large-scale simulations and parameter study for a simple recrystallization model

Elsey, Matt; Esedoḡlu, Selim; Smereka, Peter

doi:10.1080/14786435.2010.546377

Cited by 25 publications

(15 citation statements)

References 32 publications

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“…We have demonstrated that this algorithm is useful for simulations of normal grain growth -an important problem in computational materials science. The algorithm can be extended to include other physical effects, for example, the addition of bulk energy terms for modeling recrystalization can be incorporated using the approach proposed by Elsey et al [6]. Further generalizations, for example to anisotropic surface energies, are currently under investigation.…”

Section: Discussionmentioning

confidence: 99%

“…This procedure will be discussed in more detail below. In [6], we further extended this algorithm to models of recrystallization. The schemes have thus proven their mettle in very large-scale, fully resolved, accurate simulations in both two and three dimensions, handling hundreds of thousands of topological changes along the way.…”

Section: Distance Function Diffusion Generated Motionmentioning

confidence: 99%

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Simulations of anisotropic grain growth: Efficient algorithms and misorientation distributions

2013

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An accurate and efficient algorithm, closely related to the level set method, is presented for the simulation of Mullins' model of grain growth with arbitrarily prescribed surface energies. The implicit representation of interfaces allows for seamless transitions through topological changes. Well-resolved large-scale simulations are presented, beginning with over 650,000 grains in two dimensions and 64,000 grains in three dimensions. The evolution of the misorientation distribution function (MDF) is computed, starting from random and fiber crystallographic textures with Read-Shockley surface energies. Prior work had established that with random texture the MDF shows little change as the grain network coarsened whereas with fiber texture the MDF concentrates near zero misorientation. The lack of concentration about zero of the MDF in the random texture case has not been satisfactorily explained previously since this concentration would decrease the energy of the system. In this study, very large-scale simulations confirm these previous studies. However, computations with a larger cutoff for the Read-Shockley energies and an affine surface energy show a greater tendency for the MDF to concentrate near small misorientations. This suggests that the reason the previous studies had observed little change in the MDF is kinetic in nature.In addition, patterns of similarly oriented grains are observed to form as the MDF concentrates.

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Section: Discussionmentioning

confidence: 99%

Section: Distance Function Diffusion Generated Motionmentioning

confidence: 99%

Simulations of anisotropic grain growth: Efficient algorithms and misorientation distributions

2013

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“…As h → 0, the two interfaces h 12 and h 23 merge into one interface, 13 , between Phases 1 and 3. Therefore the measure of | h 13 | jumps up in the limit h → 0 although the total interfacial energy converges due to the choice of surface tensions Lemma 2.8 (Implications of convergence assumption) The convergence assumption (8) ensures that for any pair i = j and any…”

Section: Figmentioning

confidence: 99%

“…Multi-phase meancurvature flow models the slow relaxation of grain boundaries in polycrystals (called grain growth), where each grain corresponds to a phase. Elsey et al have shown that (a modification of) the thresholding scheme is practical in handling a large number of grains over time intervals sufficiently large to extract significant statistics of the coarsening (also called aging) of the grain configuration [11][12][13]. In grain growth, the surface tension (and the mobility) of a grain boundary is both dependent on the misorientation between the crystal lattice of the two adjacent grains and on the orientation of its normal.…”

Section: Contextmentioning

confidence: 99%

Convergence of the thresholding scheme for multi-phase mean-curvature flow

2016

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We consider the thresholding scheme, a time discretization for mean curvature flow introduced by Merriman et al. (Diffusion generated motion by mean curvature. Department of Mathematics, University of California, Los Angeles 1992). We prove a convergence result in the multi-phase case. The result establishes convergence towards a weak formulation of mean curvature flow in the BV-framework of sets of finite perimeter. The proof is based on the interpretation of the thresholding scheme as a minimizing movements scheme by Esedoglu et al. (Commun Pure Appl Math 68(5):808-864, 2015). This interpretation means that the thresholding scheme preserves the structure of (multi-phase) mean curvature flow as a gradient flow w. r. t. the total interfacial energy. More precisely, the thresholding scheme is a minimizing movements scheme for an energy functional that -converges to the total interfacial energy. In this sense, our proof is similar to the convergence results of Almgren et al. (SIAM J Control Optim 31(2):387-438, 1993) and Luckhaus and Sturzenhecker (Calculus Var Partial Differ Equ 3(2):253-271, 1995), which establish convergence of a more academic minimizing movements scheme. Like the one of Luckhaus and Sturzenhecker, ours is a conditional convergence result, which means that we have to assume that the time-integrated energy of the approximation converges to the time-integrated energy of the limit. This is a natural assumption, which however is not ensured by the compactness coming from the basic estimates.

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“…Coupling of a crystal plasticity finite element model with a level set formulation of recrystallization is presented in [140]. A level set approach is also taken in [141,142] where a finite difference scheme is used on fixed grids, also in both two and three dimensions. In these publications, some simplifications are made, for example in terms of the boundary mobilities and the boundary energies not being dependent on the misorientation between adjacent grains.…”

Section: Level Set Modelsmentioning

confidence: 99%

Approaches to Modeling of Recrystallization

Hallberg

2011

Metals

157

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Control of the material microstructure in terms of the grain size is a key component in tailoring material properties of metals and alloys and in creating functionally graded materials. To exert this control, reliable and efficient modeling and simulation of the recrystallization process whereby the grain size evolves is vital. The present contribution is a review paper, summarizing the current status of various approaches to modeling grain refinement due to recrystallization. The underlying mechanisms of recrystallization are briefly recollected and different simulation methods are discussed. Analytical and empirical models, continuum mechanical models and discrete methods as well as phase field, vertex and level set models of recrystallization will be considered. Such numerical methods have been reviewed previously, but with the present focus on recrystallization modeling and with a rapidly increasing amount of related publications, an updated review is called for. Advantages and disadvantages of the different methods are discussed in terms of applicability, underlying assumptions, physical relevance, implementation issues and computational efficiency.

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Large-scale simulations and parameter study for a simple recrystallization model

Cited by 25 publications

References 32 publications

Simulations of anisotropic grain growth: Efficient algorithms and misorientation distributions

Simulations of anisotropic grain growth: Efficient algorithms and misorientation distributions

Convergence of the thresholding scheme for multi-phase mean-curvature flow

Approaches to Modeling of Recrystallization

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