Computer simulations of two-dimensional and three-dimensional ideal grain growth

Kim, Seong Gyoon; Kim, Dong Ik; Kim, Dong-Won; Park, Yong Bum

doi:10.1103/physreve.74.061605

Cited by 276 publications

(254 citation statements)

References 57 publications

Supporting

Mentioning

233

Contrasting

Unclassified

Order By: Relevance

“…Within the multi-phase field model, [13,14] grain growth in polycrystalline materials is described by the temporal evolution of phase field, φ i (r, t), which represents a probability of finding a grain with an orientation, i, at given spatial point, r, and time, t. The temporal evolution of φ i is described by the following equation, [14] ( ) . In the present study, σ is set to σ = 0.79 J m -2 [15] and W is given to be W = 6·Δx with the square grid spacing,…”

Section: Computational Detailsmentioning

confidence: 99%

“…The FCG cannot grow along its short axis direction because of the pinning effect of liquid phase which also prevents the FCRB from moving. [11] In the light of these facts, we omitted the initial formation process of FCG and we dealt with only the grain growth starting from already formed FCG structure during cooling as detailed below.Within the multi-phase field model, [13,14] grain growth in polycrystalline materials is described by the temporal evolution of phase field, φ i (r, t), which represents a probability of finding a grain with an orientation, i, at given spatial point, r, and time, t. The temporal evolution of φ i is described by the following equation, [14] ( ) . In the present study, σ is set to σ = 0.79 J m -2 [15] and W is given to be W = 6·Δx with the square grid spacing,…”

mentioning

confidence: 99%

See 1 more Smart Citation

Austenite Grain Growth in Peritectic Solidified Carbon Steels Analyzed by Phase-Field Simulation

Ohno

Tsuchiya

Matsuura

2012

Metall Mater Trans A

View full text Add to dashboard Cite

Formation of coarse columnar grains (CCG) in as-cast austenite structure of peritectic carbon steels is one of the serious problems in continuous casting processes. It was recently elucidated that the formation of CCG is ascribed to a discontinuous grain growth.Furthermore, the critical condition for the discontinuous growth to occur was elicited on the basis of phase field simulations and a theory of grain growth. In this study, by means of the phase field simulations, the detailed investigation is carried out for grain coarsening of as-cast austenite structure. It is demonstrated in the two-dimensional simulations that the coarsest grain structure emerges by the discontinuous growth in the vicinity of the critical condition. In addition, a model for predicting the upper limit of grain size during the discontinuous growth is proposed. The model successfully describes the experimental result with reasonable accuracy. 2 I. INTRODUCIONAs-cast γ-austenite structure in continuously cast slabs of peritectic carbon steels consists of coarse columnar grains (CCG) in the vicinity of the slab surfaces. Since the size of CCG is closely related to the occurrence of surface cracking and low ductility of the slabs, [1][2][3][4] the precise description and prediction of the as-cast γ grain size are quite important issues in the field of casting of steels.A number of attempts have been made for the description and prediction of size of the CCG during continuous casting processes. [5][6][7][8][9][10] In the early works, the CCG structure has been supposed to originate from continuous grain growth which occurs during cooling below a temperature for completion of transformation to γ single phase, T γ . [5][6][7][8] However, our recent study by means of rapid unidirectional solidification experiment revealed that the formation of CCG structure is actually ascribed to a discontinuous grain growth. [11] Figure 1 shows the as-cast γ grain structure observed in a 0.2 mass% carbon steel quenched during the unidirectional solidification. The CCG develop from the mold side to the upper part.Importantly, fine columnar γ grains (FCG) exist ahead of the CCG region. The boundary between FCG and CCG regions, which in this paper is termed the FCG/CCG region boundary (FCRB), is identified in Figure 1. From temperature measurements, it was found that the temperature at FCRB is always T γ during the solidification and, hence, the FCG region corresponds to liquid + γ two phase field, while the CCG region is γ single phase field. 3Although the FCG always form ahead of the growing CCG during the solidification, the FCG near FCRB shrink with the growth of CCG. More specifically, coarse γ grains, which formed in the vicinity of the mold wall, preferentially develop along the temperature gradient below T γ at the expense of FCG, finally growing to CCG. This process is characterized by vertical motion of FCRB in Figure 1 and is classified as a discontinuous grain growth. Since the liquid phase in FCG region prevents the migration of FCRB, the FC...

show abstract

Section: Computational Detailsmentioning

confidence: 99%

mentioning

confidence: 99%

Austenite Grain Growth in Peritectic Solidified Carbon Steels Analyzed by Phase-Field Simulation

Ohno

Tsuchiya

Matsuura

2012

Metall Mater Trans A

View full text Add to dashboard Cite

show abstract

“…In order to understand the relationship between the polycrystalline microstructures and Li diffusivity, four different microstructures of polycrystalline LiCoO2 were prepared using the phase field method, as described in [10,11]. The method describes the ideal grain growth with isotropic grain boundary energy and mobility.…”

Section: 1mentioning

confidence: 99%

“…The method has been applied to predict the evolution of the grain size and grain orientation distribution of a given grain structure [11,12]. It has also been used to simulate the anisotropic electrochemical strain microscopy (ESM) response of polycrystalline LiCoO2 [13].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional phase field based finite element study on Li intercalation-induced stress in polycrystalline LiCoO2

Zhang

Jung

et al. 2015

Journal of Power Sources

View full text Add to dashboard Cite

In this study, the stress generation of LiCoO2 with realistic 3D microstructures has been studied systematically. Phase field method was employed to generate the 3D microstructures with different grain sizes. The effects of grain size, grain crystallographic orientation, and grain boundary diffusivity on chemical diffusion coefficient and stress generation were studied using finite element method. The calculated chemical diffusion coefficient is about in the range of 8.5×10 -10 cm 2 /s to 3.6×10 -9 cm 2 /s. Stresses increase with the increase of grain size, due to more accumulation of Li ion near the grain boundary regions in larger grain size systems, which causes a larger concentration gradient. Failure is more likely to occur in large grain systems. The chemical diffusion coefficients increase with increasing grain orientation angle irrespective of grain boundary diffusivity, due to alignment of global Li ion diffusion path with high grain orientations. Grain boundary diffusivity has opposite effect on the hydrostatic stress. As small grain boundary diffusivity, the stress increases with increasing grain orientation angle, due to

show abstract

“…In some of the models, the interface dynamics has been shown to be curvature driven, in close parallel with the dynamics of cosmological domain walls [23][24][25] or non-relativistic interfaces in condensed matter systems [26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

String networks in ZN Lotka–Volterra competition models

Avelino¹,

Bazeia²,

Menezes³

et al. 2014

Physics Letters A

View full text Add to dashboard Cite

In this letter we give specific examples of Z N Lotka-Volterra competition models leading to the formation of string networks. We show that, in order to promote coexistence, the species may arrange themselves around regions with a high number density of empty sites generated by predator-prey interactions between competing species. These configurations extend into the third dimension giving rise to string networks. We investigate the corresponding dynamics using both stochastic and mean field theory simulations, showing that the coarsening of these string networks follows a scaling law which is analogous to that found in other physical systems in condensed matter and cosmology.

show abstract

Computer simulations of two-dimensional and three-dimensional ideal grain growth

Cited by 276 publications

References 57 publications

Austenite Grain Growth in Peritectic Solidified Carbon Steels Analyzed by Phase-Field Simulation

Austenite Grain Growth in Peritectic Solidified Carbon Steels Analyzed by Phase-Field Simulation

Three-dimensional phase field based finite element study on Li intercalation-induced stress in polycrystalline LiCoO2

String networks in ZN Lotka–Volterra competition models

Contact Info

Product

Resources

About