A variational approach to two dimensional grain growth—I. Theory

Cocks, A.C.F.; Gill, S.P.A.

doi:10.1016/s1359-6454(96)00121-8

Cited by 75 publications

(46 citation statements)

References 21 publications

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“…The Variational Principle The variational principle is a well established theoretical tool that has been applied to various physical problems, including diffusional void growth and crack propagation [3] [4], grain growth [5], creep deformation [4] [6], morphological evolution of electronic thin films [7] and solid-state sintering [1] [4] [8]. At a given temperature, if the atoms have enough mobility, they diffuse along free surfaces, grain boundaries and through the lattice, so as to reduce the total free energy.…”

Section: General Frameworkmentioning

confidence: 99%

Sintering Kinetics of Plasma-Sprayed Zirconia TBCs

2007

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A model of the sintering exhibited by EB-PVD TBCs, based on the principles of free energy minimization, was recently published by Hutchinson et al [1]. In the current paper, this approach is applied to the sintering of plasma-sprayed TBCs and comparisons are made with experimental results. Predictions of through-thickness shrinkage and changing pore surface area are compared with experimental data obtained by dilatometry and BET analysis respectively. The sensitivity of the predictions to initial pore architecture and material properties are assessed. The model can be used to predict the evolution of the contact area between overlying splats. This is in turn related to the through-thickness thermal conductivity, using a previously-developed analytical model [2].

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Section: General Frameworkmentioning

confidence: 99%

Sintering Kinetics of Plasma-Sprayed Zirconia TBCs

2007

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“…Vertex, or front tracking, models for simulation of grain growth have been established by a number of authors, e.g., in [121][122][123][124][125][126]. In most models, a two-dimensional grain structure is considered and its geometry is represented by line segments-the grain boundaries-connected at nodes or vertices which are positioned at triple (in 2D) or quadruple (in 3D) junctions and possibly also at intermediate positions along the grain boundary, cf.…”

Section: Vertex Modelsmentioning

confidence: 99%

Approaches to Modeling of Recrystallization

Hallberg

2011

Metals

153

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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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“…Recently, computer simulation becomes indispensable in exploring the details of grain growth and validating the analytical models. Simulation models for this purpose include the Potts model, [4][5][6][7][8][9] the vertex model, [10][11][12][13][14] the phase field model 1,[15][16][17][18][19][20] and others. Though the Potts model has advantages in the simplicity of switching rules, it is still not intuitive to scale the Monte Carlo time to the physical time.…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann models for the grain growth in polycrystalline systems

Zheng

Chen

et al. 2016

AIP Advances

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In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.

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A variational approach to two dimensional grain growth—I. Theory

Cited by 75 publications

References 21 publications

Sintering Kinetics of Plasma-Sprayed Zirconia TBCs

Sintering Kinetics of Plasma-Sprayed Zirconia TBCs

Approaches to Modeling of Recrystallization

Lattice Boltzmann models for the grain growth in polycrystalline systems

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