Effect of the Degree of Prior Cold Work on the Grain Volume Distribution and the Rate of Grain Growth of Recrystallized Aluminum

Rhines, F. N.; Patterson, Burton R.

doi:10.1007/bf02643395

Cited by 160 publications

(56 citation statements)

References 9 publications

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“…Meanwhile, Abbruzzese-Compopiano's quadratic model [7] also agrees well with the experimental results of Liu et al [9] when the sphere equivalent radius is used for grain size instead of mean tangent diameter. The Abbruzzese-Compopiano's [7] and Thorvaldsen's [8] quadratic models are also consistent with the experimental results of -titanium alloy [10] and aluminum alloy [11] as well as the results of surface evolver simulation [12]. These studies considered a mean field approach in describing topology-size relationships while neglected the effects of the neighboring grains.…”

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confidence: 64%

Neighborhood topological effect on grain topology-size relationship in three-dimensional polycrystalline microstructures

et al. 2013

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A new grain topology-size relationship in three-dimensional (3D) polycrystalline microstructures has recently been established by considering the effects of non-random first nearest neighbor grains. In this contribution, a generalized form for this relationship is presented by considering the interactions of kth (k=1, 2, 3…) nearest neighbor grains, and large scale Monte Carlo-Potts model simulation is used to investigate the general neighborhood topological effect on the topology-size relationship. The results show that, unlike their first nearest neighbors (k=1), the topological correlations of 3D grains with their kth layers (k2) of nearest-neighbors may have trivial effect on the topology-size relationship. Many macroscopic properties such as mechanical, thermal, magnetic and conductive properties of the material can be directly linked to microstructure; therefore, it is very important to predict the grain microstructure and its evolution [1][2][3][4]. The size and the shape of grains and their spatial correlation are likely to play a significant role in the microstructural evolution. Therefore, the grain topology-size relationship is of fundamental importance for a better understanding of polycrystalline materials. In 1985, by applying the methods of statistical mechanics to the structure of random, space-filling cellular structures, Rivier [5] revealed that the maximum entropy inference under a few constraints yields structural equations of state, relating the topology of cells to their size. These equations of state are namely Perimeter law (for metallurgical grains) and Lewis's law (for ideal soap froths). According to Perimeter law, the average radius of grains is proportional to the number of their edges. While, in three dimensions (3D), a parabolic relationship exists between the grain size and grain topology. DeHoff and Liu [6] have proposed a linear relationship between the number of grain faces and the mean tangent diameter of individual grains in 3D. Thereafter, Abbruzzese and Compopiano [7] and Thorvaldsen [8] proposed two independent forms of quadratic relationships between the number of grain faces and the sphere-equivalent radius of grains in 3D. The DeHoff-Liu's linear model has been verified experimentally by Liu et al. [9] and strongly recommended it when the mean tangent diameter is used for grain size. Meanwhile, Abbruzzese-Compopiano's quadratic model [7] also agrees well with the experimental results of Liu et al. [9] when the sphere equivalent radius is used for grain size instead of mean tangent diameter. The Abbruzzese-Compopiano's [7] and Thorvaldsen's [8] quadratic models are also consistent with the experimental results of -titanium

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confidence: 64%

Neighborhood topological effect on grain topology-size relationship in three-dimensional polycrystalline microstructures

et al. 2013

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“…In the case of isotropic materials, three dimensional computer simulations have been used to demonstrate the scale invariance of the network topology [13]. These simulations compare favorably to results from Al, where boundary properties are naturally anisotropic [14]. Recent three dimensional grain growth simulations have verified that microstructures with anisotropic grain boundary properties remain scale invariant during grain growth [15].…”

Section: Assumptionsmentioning

confidence: 99%

A Model for the Origin of Anisotropic Grain Boundary Character Distributions in Polycrystalline Materials

Rohrer¹,

Gruber²,

Rollett³

2008

Ceramic Transactions Series

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“…Figure 11 shows the relationship between the mean value of R V / R V for grains with f faces and f , as determined from our simulation data. We also compare with measurements made by Rhines & Patterson (1982) on aluminium, by Zhang et al (2004) on a-iron, and with simulation data generated by Anderson et al (1989), using a Potts model and kinetic Monte Carlo techniques. The fit, particularly to the data for aluminium, is quite good and appears to describe the experimental data better than the linear fit posited by Anderson et al (1989).…”

Section: (D) Topologymentioning

confidence: 99%

“…The relationship between the number of faces f and the mean value of R V / R V for grains with f faces is plotted (solid circles) and compared with (a) measurements for Al (Rhines & Patterson 1982), reproduced from Anderson et al (1989), (b) measurements reconstructed from serial sections of a-iron (Zhang et al 2004), (c) simulation data of Anderson et al (1989). In (d), all three are shown for comparison, with Al data marked by triangles, a-iron data by stars and Anderson et al (1989) where m f is the variance of f .…”

Section: (D) Topologymentioning

confidence: 99%

Large-scale simulation of normal grain growth via diffusion-generated motion

2010

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Diffusion-generated motion is used to perform a very large-scale simulation of normal grain growth in three dimensions with high accuracy. The method is based on the diffusion of signed distance functions and shares similarities with level-set methods. The Herring-angle condition at junctions and topological transitions are naturally captured with this formulation. This approach offers significant advantages over existing numerical methods and allows for accurate computations on scales not previously possible. A fully resolved simulation of normal grain growth, initially containing over 130 000 grains in three dimensions, is presented and analysed. It is shown that the average grain radius grows as the square root of time and the grain-size distribution is self-similar. Good agreement with other theoretical predictions, experimental results and simulation results via other techniques is also demonstrated.

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Effect of the Degree of Prior Cold Work on the Grain Volume Distribution and the Rate of Grain Growth of Recrystallized Aluminum

Cited by 160 publications

References 9 publications

Neighborhood topological effect on grain topology-size relationship in three-dimensional polycrystalline microstructures

Neighborhood topological effect on grain topology-size relationship in three-dimensional polycrystalline microstructures

A Model for the Origin of Anisotropic Grain Boundary Character Distributions in Polycrystalline Materials

Large-scale simulation of normal grain growth via diffusion-generated motion

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