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Then, from each ODF, a new list of discrete orientations is generated, and the ratio between the absolute numbers of entries in these lists is chosen equal to the respective volume fractions of the recrystallized and the deformed grains.
The total number of grains in this new list is chosen to fulfill the standard input for the GIA and CORe grain pool.
The median of the size distribution of the previous grains after a CORe calculation is assigned to the reconstructed grain list as the new grain size.
Generally, the simulated grain structure is consistent with experimental observations with respect to both the recrystallized volume fraction and the grain size.
Acknowledgement This research was carried out under the project number M42.5.09375 in the framework of the Research Program of the Materials innovation and institute M2i (www.m2i.nl).

Grain refinement is a promising technique for improving the strength and ductility of metal materials due to the strong influence of grain size on the mechanical properties.
Some twin crystals can be as long as 300um, which formed from the grain boundary, and finally at the grain boundary and many twins parallel to each other and with other twins stable at a certain angle range.
For large grains, stress concentration near the grain boundary is more obvious than the small grains, and thus a large number of twins and the volume fraction within the grains should be larger.
It is clear that annealing treatment also induces an unobvious grain growth in AZ31 alloy.
And with the increase of annealing temperature and time, the size of grains grows.

The size of recrystallized grains having orientations of the rolling texture was considerably smaller than the size of grains having other crystallographic orientations.
Such grains were, on average, smaller than grains of other orientations (see Fig.4).
The largest average size was recorded for P- and CubeND-oriented grains.
The larger number of nucleation sites in the A6.4 sample resulted in a smaller average recrystallized grain size, 13 µm, compared to that in the recrystallized A3.6 sample, 19 µm (see Fig.4).
Once formed, P and CubeND grains were able to grow to a significantly larger average size than grains of other orientations (see Fig.4).

It is evident that increasing the SiC content reduces the area fraction of pullout, fpo, and that this reduction accrues both through a reduction in the number of pullouts per unit area, and through a reduction in the diameter of the individual pullouts.
Figure 9 shows the effect of moving some of the SiC particles in composites containing 2% SiC from within the grain to the grain boundary.
The resulting lack of grain growth removes the mechanism by which SiC particles are enveloped within the grains (Fig. 10).
Plot of %po vs. % of SiC particles on the grain boundary for 2% SiC composites with grain and particle sizes shown. 2 µm2 µm2 µm Figure 10.
Acknowledgements Some of this work was supported by the Mexican Government through the National Council for Science and Technology (CONACyT) with grant number 70668/118089.

However, as known form other materials, these properties are significantly influenced by the grain size [2,3,7,8] because during magnetization the movement of Bloch Walls is hindered at grain boundaries due to the change of the preferred direction of magnetization which is related to the grain orientation.
Average chemical composition, grain size and used temperature of recrystallization, TR.
The number of revolutions was chosen in such a way, that the von Mises equivalent strain gvM = 2rrn/(-3 t) [10] was 32 at a radius of 3 mm for all produced samples.
Thus, the captured micrographs depict the grain and subgrain morphology of the severely deformed microstructure because in a single phase material, the energy and intensity of BSEs (brightness) depends among other things (order number of elements, topography) on the orientation of the crystallites with respect to the direction of the incident electron beam.
Pippan, Proc. of Symp. of Ultrafine grained materials III, TMS (2004), p. 629-634

Evolution of crater density with pulse number.
These micro-irregularities can be grain boundaries, small precipitates or phase boundaries.
It has the finest structure and contains more grain or phase boundaries.
Evolution of crater density with the number of pulses.
Craters nucleate in the sub-surface at grain boundaries as well as precipitates and burst through the melted surface.

It seems that the final size of the colonies at the end of the transformation is correlated to the number of α-alumina seeds in the starting γ-alumina powder.
But the above observations suggest that a grain rearrangement process is coupled with the phase transformation.
Unfortunately, at the end of the sintering, the microstructure is always composed of micrometric grains.
For higher contents, the excess of the dopant has to be rejected to the surfaces and grain boundaries of α-particles which grow at the expense of γ-grains.
To benefit from this effect and with the goal of producing sub-micrometric grain size dense ceramics using isothermal sintering, further work with controlled density of nucleation sites and co-doping to limit grain growth is planned.

However, increasing the number of grains leads to longer computational time.
The VPSC-FLD predictions based on the IF steel texture represented by various numbers of grains, i.e., spanning from 100 to 20000, are demonstrated in Figure 3.
As shown in the previous Section, the predicted FLD is affected significantly by the number of sampled grains in the statistical population.
Results shown in Figure 5b also indicate that the computational speed reduces when increasing the number of CPU cores in use (in this case a population consisting of 100 grain was used for 10 different ψ0 for 7 paths.
Note that the re-0 5000 10000 15000 20000 Number of grains in the population 0 5 10 15 20 25 30 35 40 Computation time [hour] (a) Various numbers of grains in the population (b) Number of CPU cores in use 0 10 20 30 40 50 Number of CPU cores in use [N] 0 2 4 6 8 10 12 14 Speed-up Time(1)/Time(N) 100 grains with 70 independent runs (c) Linear scaling of the results in (b) Fig. 5: Computation time spent for VPSC-FLD calculation sults illustrated in Figure 5a may be significantly sensitive to the technical specifications of computing hardware.

Little coarsening of grains were observed below 1060℃ during annealing treatment, whereas grains coarsened obviously over 1080℃.
Nomenclature ultimate grain size (μm); recrystallized grain size, or initial grain size before annealing (μm); annealing holding time (s); annealing temperature (K)； grain growth activation energy (J/mol)； , , and are constants.
For instance, the increase in the number of dislocations is a quantification of work hardening; yield strength is increased in a cold-worked 690 alloy.
Sellars includes the effect of initial grain size.
Initial grain size,, is defined by the average value that grains grow to for 3mins exposure.

These mould properties depend upon different process parameters like percentage of clay and water, additives, grain fineness number and number of strokes made to prepare a mould.
It can be controlled by a number of parameters such as shape and size of sand grain, moisture and clay contents of the sand mould.
The silica sand grain’s shape is shown in Fig. 1.
AFS grain fineness number for the silica sand used for present work was found to be 55.
Permeability number: - Permeability number is calculated as the rate of flow of air passing through the standard rammed green sand specimen under standard pressure.