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Micrometric Grains.
In average, the more a grain initially deforms, the larger is the number of active slip systems at  max.
This last effect is due to the increasing number of sources that are activated under an increasing stress and to the production of additional sources by a more active cross-slip mechanism.
It also decreases with an increased number of initial sources and with increased cross-slip activity.
In addition, the number of grains, sixteen in the present case, does not need to be extremely large to obtain a reasonably realistic size effect.

The effect of grain size in creep strength and creep rate comes through the grain boundary sliding and grain boundaries as barrier mechanism.
Table 2 shows the solution treatment conditions and grain sizes number.
Heat treatment and average grain sizes.
If the grain size is small, it becomes more dislocations to pile up at grain boundaries and form cavities at the grain boundaries.
Acknowledgements The authors would like to acknowledge Ministry of Education Malaysia and Universiti Teknologi Malaysia (UTM) for provided financial support under grant number Q.J130000. 2524.03H33.

These particles are termed as abrasive grains at a large number and their size and distribution are very random and therefore it makes the grinding process a very complex machining process to be studied.
Workpiece Grain 1 Grain 2 Grain 3 (a) (b) Fig. 1 The multiple-grain cutting model In high deformation zones close to contact zone between the workpiece and the grains, the SPH method was implemented in the central part of the workpiece as a cuboid of 160 μm × 120 μm × 20 μm with fully taking advantage of this method.
(a) (b) Fig. 3 Total force and chip formation at each grain from 3-D simulations In the model, Grain 2 was arranged right to Grain 1 while Grain 3 was just behind these other two.
Grains 1 and 2 have much closer results during the cutting process compared to Grain 3 since these two grains are located in the upstream.
Pile-ups generated by Grains 1 and 2 were found ahead of Grain 1 while the softening was decreased, thus the cutting force of grain1 became larger than those from Grains 2 and 3.

In a micro metal forming process, it is possible that only a small number of grains are directly involved.
To investigate the effect of grain size on the CWR of micro copper rod, the study employed annealing techniques to enlarge grain size and the equal channel angular extrusion (ECAE) to refine the grains.
Grain Refinement Equal Channel Angular Extrusion.
Grain Size and Hardness.
The grain refinement clearly increased the strength of the copper.

The method of grain refinement is described which is used to obtain titanium and zirconium base alloys in an ultra-fine grain state.
The microdiffraction pattern contains a great number of reflections of different intensities that are arranged in a circle, which is an indication of increasing misorientation angles at the grain boundaries (Fig. 2a).
However, the original coarse grain counterpart has plasticity, which is almost twice that of the ultra-fine grain counterpart (cf. 15% and 8.5%, respectively).
The work hardening stages observed for the test samples of titanium and zirconium, are found to differ in number.
Otherwise, the ultra-fine grain zirconium counterpart has the same mode of fracture as the ultra-fine grain titanium counterpart.

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 various grains are depicted with different colors.
If one compares the size of both systems to a perfect lattice containing the same number of atoms, one can Fig. 4 System temperature and size evolution with time.
Diffusion at grain boundaries.
A distinction has been made between atoms located at grain boundaries (less than 8 Å from a grain boundary) and bulk atoms.
This preliminary study will be extended further with other configurations (number of atoms, grains) to confirm the observed trend.

In the present work, the net pressure on the grain boundaries is based on the summation of the two major driving forces associated with stored energy and grain boundary curvature (different models of grains boundary curvature are presented in the next chapter), but it can be additionally complemented with the possible influence of precipitates [22]: , (3) Then, the equation (2) is considered for each CA cell which is located at the recrystallization front in tth time step: , (4) where: - recrystallization volume fraction in ith CA cell in the t-1 time step, – velocity of the recrystallization front in jth cell from eq. (2), rx - number of recrystallized neighbours, - physical cell size.
In this case, the grain boundary curvature value is determined based on the CA cells states within the extended Moore neighbourhood (Fig. 1a) and is expressed by the following formula: (6) where: a - the side length of the cell in the CA model, N - the sum of the number of neighbours of a given cell, Ni - the number of neighbouring cells that belong to the same grain as the considered cell, A - the aspect ratio depending on the cell shape (rectangular or hexagonal), Kink - a constant equal to 15 for 2D space and 75 for 3D space, respectively.
In this case, the driving force associated with the grain boundary curvature is the primary factor controlling grain growth.
But at the same time, the role of the crystallographic orientation of grains on grain boundary mobility is also considered.
Huang, Grain boundary curvature based 2D cellular automata simulation of grain coarsening, J.

The recrystallized grain size in the easy deformation zone is reduced with the number of forging passes, and the area of recrystallize grains increase with the number of forging passes. 1.
With the number of forging passes is increased to 6 and 9 (true strain of 3 and 4.5), the hardness along the center line of the samples is similar to that of the 3 forging pass ingot, while, the maximum hardness value near the edge increases with the number of forging passes.
The cumulative true strain increases both in easy deformation zone and stagnant zone with increase the number of forging passes.
Although there are no recrystallized grains in the stagnant zone as the true strain increase to 1.2 (3 passes), 2.4 (6 passes) and 9 (passes), the hardness of the stagnant zone decreases with the number of forging passes indicating that dynamic recovery has happened. 5.
(3) The recrystalized grain size in the easy deformation zone is reduce with increasing number of forging passes, and the area of recrystallized grain get larger increasing number of forging passes.

Introduction Ultrafine-grained materials (UFG) are widely known as polycrystals having very small grains with average grain size less than ~1 μm [1].
This can be explained by the restricted number of slip systems at low temperatures, and therefore results in poor ductility.
But instead, an island like microstructure (some coarse grains are surrounded by fine grains) was developed after 4 passes.
Grain refinement proceeded with increasing pass numbers and the grain size after 4 passes was much finer (L=100~500 nm) in comparison with the same alloy receiving ECApress without back pressure. 2.
However the maximum texture intensity decreased as the pass number increased from 0 (maximum; 12.9) up to 4 passes (maximum; 7.0~7.1), which indicates that the increase of yield stress is mainly due to the refinement of grain size. 4.