A vertex dynamics simulation of grain growth in two dimensions

Weygand, D.; Bréchet, Y.; Lépinoux, J.

doi:10.1080/13642819808206731

Cited by 113 publications

(92 citation statements)

References 39 publications

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“…According to experimental observations and numerical simulations, the value of " r r 3 is in the range 0:2 $ 0:4. 8,10,11,14) This indicates that the applicable range of the function FðrÞ ¼ ar m is about r < 0:1. For reference, when the Hillert's and Rayleigh functions are approximated by 3 2 r=4 and 3 2 r around r ¼ 0, as in Section 4.1, the error at r ¼ 0:1 is 9.2% and 1.2%, respectively.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…The linear distribution is illustrated in Fig. 2, where the size distributions FðrÞ in the following simulations depend linearly on r for small grain sizes: the vertex model, 6,10) 2D Monte Carlo model, 7) variational principle, 8) Surface Evolver program 9) and atomic jump model, 11) where n ¼ 2 has been obtained. A slightly increasing m-value with decreasing r in the 3D vertex model 6) may occur from insufficient data for such small grains.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Although the physical basis of the model is ambiguous, the obtained size distribution shows good consistence with some numerical simulations. 10,11) The Rayleigh function Hðr c Þ is represented as 21) Hðr…”

Section: Theoretical Modelsmentioning

confidence: 99%

“…On normal grain growth, there have been extensive studies including the curvature-driven growth model, 1) diffusion-like growth model, 2) statistical analysis, 3) stochastic model 4) and numerical simulations. [5][6][7][8][9][10][11][12] Despite a variety of the analyzing methods, most of the studies predict an n-value of 2, and thereby n ¼ 2 has widely been recognized as the theoretical grain growth exponent for normal grain growth. In those studies giving n ¼ 2, however, the obtained size distributions of grains in a steady state are various.…”

Section: Introductionmentioning

confidence: 99%

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Kinetics of Normal Grain Growth Depending on the Size Distribution of Small Grains

2003

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A theoretical relationship is derived between the kinetics of normal grain growth and the size distribution of small grains. When the distribution of the normalized grain size r is proportional to r m around r ¼ 0 in a steady state, the grain growth exponent n is revealed to be m þ 1. The same relationship is also derived from the analysis of the mean field model for particle growth. The validity of this relationship is confirmed from the consistence with existing grain-growth models and numerical simulations. Experimental consistence is observed for the size distribution on sectional surface. It is found that a log-normal function is not a steady-state size distribution for normal grain growth with n ¼ 2, even though it may approximate experimental size distributions. The obtained relationship is also shown to be applicable to particle coarsening by Ostwald-ripening.

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Section: Numerical Simulationsmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Theoretical Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kinetics of Normal Grain Growth Depending on the Size Distribution of Small Grains

2003

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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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Dynamic and Static Recrystallization

Montheillet¹,

Lépinoux²,

Weygand³

et al. 2001

Adv. Eng. Mater.

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Thermomechanical treatments basically aim at refining the grain size and controlling the crystallographic texture of metallic materials. First developed for the austenitic rolling of C±Mn steels, they are now being extended to a wide range of metals, e.g., aluminum, titanium, and nickel-based alloys. Dynamic or static recrystallizations are certainly the main mechanisms responsible for the microstructure and texture changes occurring during or after deformation. It is therefore not surprising that several teams of the Rhône-Alpes Federation are currently involved in parallel or converging investigations in that field. These researches take advantage of the availability of new experimental devices to produce large strains (Equal Channel Angular Extrusion, ECAE) and investigate the microstructures (orientation mapping by EBSD (Electron Backscattering Diffraction)), as well as the development of analytical modeling and numerical simulations. Some recent results are briefly summarized in this paper.Dynamic recrystallization (DRX), which occurs during straining, has long been considered to be restricted to low stacking fault energy materials, such as copper, c-iron, and the austenitic steels. In high stacking fault energy metals (aluminum, a-iron, ferritic steels), where the dislocation mobility is much larger, dynamic recovery was assumed to be the only operating mechanism. However, it is now well established that two types of DRX can take place: (i) discontinuous or ªclassicalº dynamic recrystallization (DDRX), occurring by nucleation and growth of new grains consuming rapidly the surrounding strain hardened matrix, and (ii) continuous dynamic recrystallization (CDRX) involving the generation of new grain boundaries by the progressive misorientation of neighboring subgrains.The main differences between DDRX and CDRX are the following: ± While the flow curves associated with DDRX switch from single to multiple peak behavior with increasing temperature and/or decreasing strain rate, such transition has never been observed for CDRX.± CDRX leads to strong crystallographic texture at large strains, whereas texture formation is hindered by DDRX. ± The temperature dependence of the flow stress (ªapparent activation energyº) is generally reported to be larger for DDRX, with some exceptions. Recent investigations involving large to very large strains imposed by torsion (i.e., monotonic simple shear) or ECAE (i.e., ªcrossedº simple shear) have shown that DDRX and CDRX combine the same elementary mechanisms, but with different kinetics. When grain boundary migration is slow, CDRX takes place; by contrast, in the case of large grain boundary velocity, the subgrain boundaries are swept by moving boundaries before they themselves transform into large angle grain boundaries. When DDRX takes place, the steady state microstructure is established quite rapidly (e<1). It displays strong heterogeneities, due to the coexistence of ªyoungº and ªoldº grains exhibiting low and high dislocation densities, respectively (Fig. 1). [1] CDRX is ...

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A vertex dynamics simulation of grain growth in two dimensions

Cited by 113 publications

References 39 publications

Kinetics of Normal Grain Growth Depending on the Size Distribution of Small Grains

Kinetics of Normal Grain Growth Depending on the Size Distribution of Small Grains

Lattice Boltzmann models for the grain growth in polycrystalline systems

Dynamic and Static Recrystallization

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