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The grains that are intersected by the domain boundary S and the internal grains that are not intersected by S.
Each grain is bounded by a boundary uj,wherej =1]p§ and p§ denotes the number of grains.
The boundary of each grain is divided into the contact boundary uj¢ , indicating the contact with a neighbour grain boundary and into the free boundary ujfl¢, indicating the grain boundaries that coincide with the domain boundary S.
Hence for every grain:Figure 1: Artificial microstructure generated by a quasi-random generator with randomly distributed material orientation for each grain.
uj = ujfl¢ } uj¢ (1) For the internal grains ujfl¢ = a and thus uj = uj¢ .Thereforeujfl¢ exists only on boundary grains resulting to p§S j=1 ujfl¢ = S.

the strain tensor, the texture development and the grain subdivision mechanisms.
The reduction of shear flow stress in the band from Gτ to ( )NG DB 1 δ−τ=τ can be estimated from the local modified Taylor factors in the grain and the DBs by G DB N M M =δ , where the modified Taylor factors are based on the minimum number of simultaneously acting slip systems necessary to accommodate the actual strain.
Where DG is the size of the grain in which the DB may form.
It is also clear that by reducing Mr by creation of Σboundaries, deformation banding may still be a deformation mechanism at very high strains when the grain size has reached sub-micron sizes, i.e. one can expect to observe an increasing number of twin configurations and CSL boundaries at very high strains (from 2 to 8 ECAP passes) [3].
The number of twin boundaries and other CSL configurations are observed to increase with accumulated strain (and increased shear stress)[3,++zuh twins].

When adding 5wt% Mg, the mean grain size is the smallest, 0.712 mm, while the biggest grain size is 1.115mm in raw steel.
Table 2 Designed calcium and magnesium contents of experimental steel The number of the furnace 1 2 3 4 5 6 7 Ca (wt%) 0 1 3 5 0 0 0 Mg (wt%) 0 0 0 0 1 3 5 The steps of smelting the experimental steel are as follows
Then we measure the size of the grains in the figure and convert into the specific size of the grains.
The thick austenite grains have the heredity, that is to say, the thick austenite grains lead to the thick ferrite grains after the phase transformation.
When adding 5wt% Mg, the mean grain size is the smallest, 0.712 mm, while the biggest grain size is 1.115mm in raw steel.

With the increase of the distance from the bottom of the starter block, the number of grains is gradually reduced, and the size of the grains gradually becomes larger.
With the increase of section height, the number of grain with an included angles that less than 15° between the <001> direction and the heat flux direction is increased.
The height of the starter block should be designed in the 13-36mm, which can ensure a certain number of grains to enter into the spiral part.
The number of grains in the spiral block is drastically reduced by the initial selection at (f) to (g) segments.
With the increase of the distance from the start block bottom, the number of grain decreases and the size of the grains become larger.

Four evaluation indexes including the mean protrusion height of abrasive grains Hm, the standard deviation of grain protrusion height Hv, the standard deviation of the distance between two adjacent grains Dv and the number of micro cutting edges per square millimeter Nm were put forward to assess wheel topography and grinding performance.
According to the above three aspects, several statistically indexes of the wheel topography were calculated and a dominant evaluation index was grain number including static cutting edge number and dynamic cutting edge number[4].
Considering the randomness of grain shapes and their distribution, four evaluation indexes were proposed to estimate the grinding performance of the wheel based on correlative literature, which were mean protrusion height of the abrasive grains Hm, standard deviation of the grain protrusion height Hv, standard deviation of the distance between two adjacent grains Dv and the number of the micro cutting edges per square millimeter Nm.
The grit number and concentration of the grinding wheel were 80 and 100% respectively.
Furthermore, the number of micro cutting edges indicated that the dressing process could make the abrasive grain sharper.

The dielectrics used in MLCCs are polycrystalline ceramics, which contain many grain boundaries (GBs).
As mentioned above, the Coulombic energy acting to the O 2- ion at the low Ti4+ density site is smaller than that in the grain interior.
This implies that the number of low Ti4+ density sites, i.e., the number of negative- GBVOE − sites, is correlated with the GB energy.
Figure 4 shows the GB energy dependence of the number density of the negative GBVOE − sites per a unit area on the GB plane.
The number density linearly increased with the GB energy.

The measurements showed that achieving the same deformation with the same number of deformation cycles and same heat treatment temperature, the application of shorter heat treatment holding time was advantageous in aspect of grain boundary structure comparing to the thermo-mechanical treatments with longer holding time.
Grain boundaries.
The grain boundary is the surface, where two dissimilarly oriented grains meet, thus the grain boundary is a discontinuity in the crystal.
Grain boundary engineering (GBE).
The aim of our investigation is to clarify the effect of varying the length of the heat treatment processes applying the same temperature, same deformation rate and same number of cycles during the thermo-mechanical treatment.

The creep property of sandy slate coarse-grained soil under different moisture conditions is analyzed through uniaxial compression creep test on influence rule of moisture content on creep of coarse-grained soil.
It turns out that moisture content is the important factor that affects creep property of sandy slate coarse-grained soil and using dry or saturated coarse-grained soil is able to decrease long-term settlement of embankment.
Limited by topographic condition, a large number of high fill subgrades are emerging continually.
When moisture content is in a low level, coarse-grained soil consists of solid-gas phase.
Fig.5 Stabilizing time constant α of sandy slate coarse-grained soil The Nonlinear Creep.

Grain boundaries of approximately 500 grains were delineated manually with Adobe Illustrator software on digitised TEM bright field images to determine the grain size distribution.
Larger grain size can be obviously seen in sample A.
It is clear that high current densities promote the grain refinement.
As oxide nucleation in the grain boundary region is easy, decreasing the grain size increases the number of surface oxide nucleation centers, resulting in an increase in the nucleation rate of NiO.
The scales on various grains grow at significantly different rates.

Also, the coarse grained cBN layer was put on the WC-16wt%Co substrates, and the fine grained cBN layer was put on the coarse grained cBN layer.
Besides, we choose the coarse grained cBN layer can provide fewer obstacles for Co and WC to infiltrate in the fine grained cBN layer.
From the figure 2a, the grain size is about 1-2µm, which is as large as the initial grain size.
When the temperature increase to 1600℃, there are large number of cBN-to-cBN bonding which we strive to fabricate by HPHT sintering process.
SEM examination showed that the PcBN compacts had number of cBN-to-cBN bonding among cBN grains.