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When the grain boundary is rough, normal grain growth occurs with a moderate rate.
On the other hand, for faceted boundaries, either abnormal grain growth or grain growth inhibition occurs resulting in a duplex grain structure or fine-grained structure, respectively.
Journal Title and Volume Number (to be inserted by the publisher) 3 essentially no movement of faceted boundaries is expected [3,4].
Grain growth is inhibited when the driving force for grain growth is below a critical value, while abnormal grain growth occurs when the driving force is above a critical value for some large grains.
Journal Title and Volume Number (to be inserted by the publisher) 5 The formation and thickening of intergranular amorphous films also affects the growth kinetics of the single crystal.

Furthermore, it was found that Δρ of grains unrelated to crack initiation increased continuously with the number of cycles, whereas that around the crack initiation site decreased with crack initiation.
In both materials, the number of grains with small β (shown in blue) decreases and the number of grains with large β (shown in red) increases as the number of cycles increases, except (j), indicating that the number of grains reconstructed immediately before fracture is significantly reduced.
In the homogeneous and harmonic materials, the filling ratio decreased with increasing number of cycles, reaching about 25% immediately before fracture.
The intensity of diffraction spots decreased and eventually disappeared as misorientation increased, which was found to be the cause of the decrease in the number of reconstructable grains and the decrease in filling ratio with increasing number of cycles.
Δρ in the homogeneous material shown in (a) is almost constant after 1.00×103 cycles for grains larger than 20 μm, whereas it increases with the number of cycles for grains smaller than 20 μm.

Results and Discussion Figure 1 shows the hardness variations with respect to the number of ECAP passes for 4N-Al and 5N-Al.
The hardness of 3N6-Cu increased continuously with increasing number of ECAP passes as shown in Fig.2.
Fig.2 Hardness variation with respect to number of ECAP passes for 3N6Cu and 7N-Cu.
Fig.3 Hardness variation with respect to number of ECAP passes for 4N-Al and 5N-Al.
The fine-grained structure in 5N-Au suggests that the coarse grains in 5N-Al are not due to grain growth at the ECAP temperature.

The results show that, in the grain growth process, most of the spherical second-phase particles located at triple junctions, while the stick SPPs located at the grain boundaries along the grain boundary.
The SPP acts as obstacles to grain boundary movement to retard grain growth.
Phase field model The microstructure of grain growth in phase field model [10] for polycrystalline materials is described by a set of orientation field variables, in order that distinguish different orientations of grains; here P is the integer number of possible orientation.
The average radius of SPPs r=3.3 g.p. , the orientation number P =36, and other parameters m==1.0, =2.0, =1.0.
Then particles appear as black spot, grains are bright and grain boundaries gray.

To clarify this notion, the grain’s shape is characterized using the fractal dimension (Df), which is a number measuring the degree of irregularity or the fragmentation of a grain.
These numbers constituted the size of the object.
The method is based on a theory that the number of grains smaller than the predetermined size can be made exponentially: NX>x=KxDf (4) Such that x is a predetermined particle size; X is the linear dimension of the grains bigger than x’s dimension, N is the number of grains (fragments), K is a proportionality constant; and Df is the fractal dimension of fragmentation [5, 6].
In dealing with a graph showing the size of the boxes representing the grain’s fragment size according to the number of the boxes (number of grain fragment), the fractal dimension is obtained by the slope given by the equation (Df =-m).
The differences are quite close to the grain of 5 mm and 4 mm as they are important for grains of 3.14 mm.

For face-centered cubic (FCC) metals, a considerable number of experimental studies have demonstrated that the efficiency of grain refinement varies with not only the processing route and also the die angle.
Statistic data in terms of the average number of active slip systems per grain was then computed for each increment, i, by comparing the simulation results at that increment and those of the previous one, (i − 1).
It is therefore reasonable to infer the relative efficiencies 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Pass number a Average number of slip systems Nall Nnew Nrev 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Pass number b Average number of slip systems 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Pass number c Average number of slip systems Figure 2.
(3) 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Pass number a Average number of slip systems Nall Nnew Nrev 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Pass number b Average number of slip systems 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 Pass number c Average number of slip systems Figure 3.
A higher number of newly activated slip systems is found for the experimentally identified optimum route for grain refinement in FCC metals.

As will be seen in more detail below, the number of γ-fibre grains nucleated at grain boundaries and in-grain interiors was higher in the finer grained steel.
The effect of initial grain size on the number of in-grain shear bands in the present samples warm rolled at selected temperatures is illustrated in Fig. 1.
There are also a number of references that relate the amount of in-grain shear bands to the final formability [15-17].
As mentioned above, the finer HBGS sample yielded a higher number of γ grains nucleated at grain boundaries, as expected; it also had the higher number of SBN belonging to the same fibre.
Finer HBGS's yield higher numbers of γ-grain boundary nuclei.

And the insulation process after high temperature hot rolling can make a large number of the Cu2S diffusion precipitation, There was no significant effect on the precipitation of Cu2S after low temperature hot rolling, still remain in the precipitate state after hot rolling. 1 Introduction Grain-oriented electrical steel has high performance of high magnetic sensitivity and low iron loss.
Hot rolling temperature and thermal maintain time of the experimental steel plate number Hot rolling temperature(℃) thermal maintain time (seconds) number Hot rolling temperature(℃) thermal maintain time (seconds) 1-1 1050.2 30 2-1 966.9 30 1-2 1103.6 300 2-2 978 300 1-3 1083 600 2-3 975.8 600 2.2 Experimental Method.
During the hot rolling process, the ferrite grain were dynamically recrystallized, after hot rolling, during the postrolling maintain process, the ferrite grain did not grow up significantly with the extension of the insulation time, This is because if there are diffusion-distributed second-phase particles in the ferrite matrix, these particles can hinder crystal boundary moving and grain growth, It makes the grain difficult to grow up normally in the thermal maintain process [5].
The high temperature hot rolled grain of about 1100℃ is larger than the size of about 950℃, in the rolling surface normal longitudinal section from the surface to the center grain size is getting smaller and smaller; this is due to the deformation shear pressure of the surface layer, making the surface grain size larger than the central layer
Developments in the production of grain-oriented electrical steel.

Current issues concerning the characterization of grain boundary networks via five-dimensional (5D) grain boundary distributions are considered.
It is clear that the number of boundary data needed for evaluating the distribution depends on the number of distinct boundary types (number of bins), the acceptable error level and the distribution itself.
With ng denoting the number of grains, the corresponding number of complete boundaries is roughly 13ng/2.
Approximate number of grains (ng»2N/13) which need to be investigated to reach the given error level D for c=1 and f0=1 versus the number of equi-volume bins (1/v).
The integration can be done in a number of ways.

Three-dimensional position of grains was detected by grain-boundaries visualizing method.
Grains deform inhomogeneous, because slip deformation is not continuous on grain boundary.
The number of 74 grains was found in this study.
A grain contains the number of 10 - 100 particles.
The tensile strain in the whole sample was measured from the number of slice by counting 1 pixel as 0.5 mm.