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Metals that undergo DDRX exhibit a number of characteristics that are well established by experiment [1,2].
The driving force for both nucleation of new grains and grain growth is the stored energy.
(1) dei is the strain increment experienced by grain i, σi is the flow stress of grain i.
The number of subgrains able to nucleate from each grain (Nnuc,i) is given by the product of the fraction of subgrains able to nucleate (Fsub,i) and the number of subgrains lying on the grain boundary (Nsub,i) (Eq. 4): (4) For model implementation, each new grain nucleates from a randomly selected grain and has an initial size equal to that of its instantaneous critical radius rc,i.
The initial grain size distribution consists of grains that are normally distributed with a standard deviation of Do/3.

The fraction and average spacing of HAGBs as functions of number of ARB cycles are plotted in Fig 2.
Also, shear bands spanning across a large number of grains are observed.
Fig. 3 Fraction of prominent texture components versus number of ARB cycles.
Fig. 2 Fraction and average spacing of HAGBs versus number of ARB cycles.
With the increasing number of ARB cycles, S component increases and reaches saturation after the sixth cycle.

The main effect that is expected is their influence on the increase in the number of nucleation sites [2-4].
An increased number of inoculants means a larger number of grains, that is, a finer microstructure in the weld metal.
Therefore, the coarse grain ferrite types such as Widmanstaetten, intragranular idiomorphic and grain boundary allotriomorphic ferrite can be partially replaced with finer grained acicular ferrite [7].
As the number of non-metallic inclusions is higher, a finer grained ferrite microstructure can be obtained, resulting in improved mechanical properties of weld metals.
· The increase in mechanical properties of welds is the result of an increased number of non-metallic inclusions

An A3003 alloy was modified by Ti addition, grain refiner.
The finer grains were uniformly distributed in the modified A3003 alloy billet.
The grain refiner was added to the aluminum alloy for the modification of the A3003 alloy. 2.
In the simplest and dominant model, numerous potent heterogeneous nuclei (TiAl3) are dispersed in the melt, and a large number of these sites become active on cooling and nucleate the solid.
Thus TiAl3 particles during the solidification act as a grain refiner in aluminum alloys and the efficiency of grain refinement increase with increasing Ti contents in limited range (0~0.15) [4].

In CNM process, the main principle is to maximize grain density in the melt and promote grain growth in a non- or less-dendritic motion.
On the other hand, in pouring method II (pouring outside the gauze), a huge number of wall crystals will be created by crystal fracture and crystal remelting.
Therefore, the grain size within the gauze is decreased dramatically.
Below 300°C, a fine equiaxed grain structure is obtained and the grain size increases slowly with the mould preheat temperature.
Pouring outside the gauze leads to a large number of "wall crystals" being brougt into bulk melt, forming very fine equiaxed microstructure.

Introduction It has been observed in a number of experiments that grain size exerts a dominant influence on the mechanical behaviour of polycrystalline metals and alloys at the micron and sub-micron scales.
Having updated the lattice spin, we can obtain the reorientation of crystal grain represented by matrix crys T .
The average size of the lattice grain is represented by the dimension of the element, so that the coarse mesh (1455 elements) in Figs.1-2 stands for grains of larger size and the fine mesh(4203 elements) in Figs.3-4 for grains of smaller size.
The comparison of the simulation results of different mesh size, hence grain size, reveals the strong grain size effect in the microforming process and demonstrates the availability of the code developed.
J., Grain-size effect in viscoplastic polycrystals at moderate strains, Journal of the Mechanics and Physics of Solids,48(10),2213-2230,2000

All of the dislocations and subgrain boundaries in the grains, the martensite in the martensite-austenite islands of the grainy bainite structure, the dispersed phases in the grains and at the grain boundaries, and the grain size were observed and studied in our experiments.
The grains belong to fine ones.
Fine grains, long grain boundaries, large numbers of grains with different orientation, all these increase resistance to dislocations movement and improve strength and toughness.
Fine grain is relative to dispersed particles pinning up the grain boundaries.
Investigations indicate that the number of dispersed particles in the hot-rolled-cooled samples is lower than that in the samples tempered at 200～350℃.

It was found that a single grain was easily removed from the material.
The number of abrasive grains on the surface of the wheel was determined through observations using a microscope.
Furthermore, the numbers were evaluated by a calculation using the wheel particle frequency and the degree of concentration.
As a result, the number of abrasive grains on the surface of the wheel was assumed to be approximately 12,800 particles per square mm.
Figure 3 shows the value of Ft (<0.18 mN) on a single abrasive grain.

It is seen that twins can both expand, taking over an entire grain, or shrink, leaving completely untwinned grains.
Introduction During the last few decades, the world has seen a growth of applications of magnesium alloys in almost every field of today's industry, but a number of issues impose barriers to further expanding this market.
The most important one is its limited deformability caused by the hexagonal crystal structure of magnesium, which limits the number of active deformation mechanisms, especially at room temperature.
EBSD measurements showed that a number of untwinned grains are present with the initial orientation (c-axes perpendicular to the compression axis).
Schmid factors were calculated for grains containing expanding twins as well as for grains containing shrinking twins.

Fig. 1(a) shows the total number of dislocation lines with a simplified distribution to calculate the average space of a dislocation array.
Number of dislocation lines in a dislocation cellblock.
The total number of dislocation lines is proportional to the inverse of the average space of a dislocation array, once the applied stress exceeds the friction stress .
From equation (4), the number N of dislocation lines concentrated in a single dislocation cellblock is calculated to be 5929.
It has been formularized that the total number of dislocation lines within a dislocation cellblock is a material constant, and both sizes of dislocation cell blocks and the ferrite grains just after phase transformation are inversely proportional to the square root of dislocation density.