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Although many studies have been conducted in recent years to analyze the grain flow, the analyses and applications of grain flow with roughness effects are still insufficient.
Thus, the authors [4-5] derived an average lubrication equation for grain flow between two rough surfaces and then discussed grain-grain collision elasticity ranging from perfectly elastic to perfectly inelastic.
He treated individual grains as the molecules of a granular fluid.
The Peklenik number is simplified as an isotropic (i.e. ).
The flow factors, expressed as functions of surface characteristics (roughness orientations, Peklenik numbers and standard derivation) and particle size, contribute to the modification of volume flow rate and surface roughness effects.

Therefore, those simulations were limited to small grains in order to keep the number of grains adequate for statistically analysis.
Number of faces vs. grain size.
One important topological feature of the microstructure is the correlation between the number of faces s per grain and the relative grain size x (cf.
Figure 1: a - Number of faces vs. relative grain size for all grains together with quadratic leastsquares fit; b - Number of faces vs. relative grain size divided into size classes for three different time steps.
Figure 1a shows the number of faces of the individual grains as a function of the relative grain size for the 500 th MCS.

The phenomena of grain boundary diffusion and grain boundary segregation play major roles in determining the properties and behavior of a wide variety of materials.
Even though the basic principles have been known for a long time, the field continues to yield a number of very challenging questions.

Note that the initial number of grains are 50 in all cases, and the results for Ks > 3.0 were mostly the same as that shown in Fig. 3 (e), because the grain separation, i.e. increase in the number of grains, never occurs in this model.
(a) Grain distribution (b) Variation of grain number Fig. 4.
Effect of the initial number of grains and the size of calculation domatin on the steady state grain size.
identification numbers, large-number grains depicted in yellow-red color show decaying tendency, and vanish at last, as shown in Fig. 5 (a).
On the other hand, when the small-number grains are weighed, large-number grains survive, as shown in Fig. 5 (c).

The size of grains at the top and bottom of the rolled plate converged to 0.65µm, while that of grains at the center of the plate increased with the number of ARB cycles.
The size of grains at locations of NT and NB ranges from 0.7µm to 0.8µm and remains more or less unchanged with the ARB cycle number.
However, the grain size at the NC position varied a lot with the cycle number.
The grain size increased continuously from 0.56µm to 1µm as the cycle number increased from 3 to 6.
However, the size of grains at the center of the processed plate increased with the cycle number.

Under this condition, the two low energy grain boundaries replace the high energy grain boundary and the grain with the low energy grain boundaries grows by penetrating into the high energy grain boundary.
If a grain has an inward grain boundary curvature, the grain grows in the direction to flatten the curvature.
It can be said that the low Journal Title and Volume Number (to be inserted by the publisher) 3 mobility boundary has a strong pinning effect on the high mobility boundary through the kinetic coupling at the triple junction.
These trapped grains are called island grains.
Journal Title and Volume Number (to be inserted by the publisher) 5 On the other hand, MC simulation shows that island grains are easily formed by solid-state wetting [7].

Variation in the distributions of the number of face, Nf, for individual grains of the simulated microstructures at different time step is shown in Fig.4.
The average face number with time.
The average face number approaches to a constant value of about 13.7 in the isotopic system [11, 12].
Variation in the relation between the average number of faces of neighbor of N-face grain, m(Nf) and the face number, Nf at different time step in simulations with two texture component A and B of different initial volume fraction (fA0=0.97, fB0=0.03) and a mobility ratio of 1:5.
Pinning force in 3-d is much smaller than that in 2-d [18] 0 200 400 600 800 1000 1200 0 20 40 60 80 Number of faces per grain (Nf) m (N f)xN f t=100 t=800 t=1000Dislocation density near grain boundary is also major factor also considered to be related to the grain boundary mobility.

To analyze compression deformation characteristics of coarse-grained soil under different moisture content and different grain compositions conditions, influence pattern of moisture content and grain compositions was researched through uniaxial compression test.
Table 1 Experiment of variable moisture content sample number M1 M2 M3 M4 M5 M6 moisture content (%) 0.69 2.22 4.43 6.31 8.60 10.32 dry density (g/cm3) 2.10 2.08 1.98 2.03 2.07 2.11 Table 2 Experiment of variable grain compositions number the occupation of the mass under a certain size among the whole mass (%) 60mm 40mm 20mm 10mm 5mm 2mm 0.075mm M1~6 100 79.1 46.7 30.8 20.7 12.3 2.9 N1 100 92 32 24 16 8 0 N2 100 92 84 76 68 60 10 N3 100 88 76 36 24 12 2 N4 100 100 80 60 40 20 5 N5 100 80 80 60 40 20 5 N6 100 88 48 36 24 12 4 N7 100 40 32 24 16 8 0 N8 100 80 60 40 30 20 5 Influenced Factors Analysis of Compression Deformation Select uniaxial consolidometer of Φ280 mm×230 mm and conduct creep test with gradation loading method of 50→100→200→400→800kPa according to the distributing character of the filling layer.
Through the study of grading analysis, mass percentage of soil sample’s certain grain takes up too much or too little, with N1, N2, N3, N6 and N7 containing more than 40% of certain grain and N4, N5 missing in another grain, resulting in a uneven grain size distribution.
Table 3 Testing parameters and results of variable grain compositions sample number N1 N2 N3 N4 N5 N6 N7 N8 dry density (g/cm3) 1.80 1.88 1.92 1.99 2.00 2.02 2.04 2.06 final deformation (mm) 13.56 11.77 9.32 7.56 5.80 5.07 4.13 3.93 Analysis on Compressive Deformation Characteristics After applying axial load, read number every 15 seconds in the first 15 minutes and then read once every 15 minutes until compressive deformation becomes stable. 14 groups of data with similar deformation characteristics were acquired.
Secondly, only considering influence of grain composition on compression deformation, the filler, with a good gradation and 70% coarse-grain partial contained, is recommended to be applied.

The typical rolling textures after deformation are not strong and a large number of low-angle grain boundaries are found.
The grain of as-cast copper ingot is visible to naked eyes except for fine grain area, and the grain size is at the level of millimeter.
Coarse grain can be transformed to fine gain, as shown in Fig. 2(b), small equiaxed grain with an average grain size of about 100μm is obtained.
The grain size is about 17.9μm.
The typical rolling textures after deformation is not strong and a large number of low-angle grain boundaries are found.

The Brandon criterion [13] was used to classify Σ3n boundaries, both as a length fraction and as a number fraction, with n≤3, i.e.
In a heavily twinned material, as a 'rule of thumb' the length to number ratio is close to 3:2 [14].
Although the relative number of Σ3s is less than their relative length, the opposite is true for Σ9 and Σ27 boundaries.
Proportions of Σ3, Σ9 and Σ27 boundaries as (a) length fraction and (b) number fraction for each specimen.
The rate of increase of Σ9 number fraction from the asreceived to the pre-treatment stage is greater than the accompanying rate of increase of Σ3 number fraction.