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Two neighbouring grains are considered, cf.
Fig. 1, where the grain boundary between the two grains, GB1, is modelled as a low angle grain boundary [5].
Grain boundary modeling The first grain boundary GB1, cf.
Fig. 1, is considered as a low angle grain boundary while the second grain boundary, GB2, is assumed to be a high angle grain boundary.
Number of dislocations piling up against GB1 before breakthrough and b.

These models consider inter-granular deformation, grain boundary sliding, grain boundary diffusion and grain growth.
Finite element simulation has reduced the number of trial forming experiments in these processes.
Grain boundary mechanisms include: grain boundary sliding (GBS), grain boundary diffusion (GBD) and grain growth.
(5) The superscript indicates the number of assumed boundary planes which ranges from one to 12 in this case.
Grain boundary mechanisms include: grain boundary sliding (GBS), grain boundary diffusion (GBD) and Grain growth.

Introduction Unique combination of physical-mechanical properties of tungsten makes it an irreplaceable material for the most important units of a number of devices and instruments of space, rocket, aircraft, nuclear and electronic engineering [1].
These additional reflections are observed in EDPs of a number of specimens studied, though the oxide particles themselves are not seen in the electron micrographs.
Grain boundaries are mainly wide and curved.
The EDPs are still ring-wise, but the number of reflections on the Debye rings decreases, and they are no longer uniformly distributed along the rings, but form several groups of closely located 2-3 reflections.
Thus, in Fig. 8 anomalously large grains practically dislocation-free surrounded with much finer grains can be seen.

In each element of that grid, the average impact velocity of all impacts is calculated, as well as the impact number and the maximal velocity (see also Fig. 5).
If we consider now the impact numbers, we can note that as one gets closer to the borders, the number of impacts increases (Figure 6).
Constitutive model for ultra-fine grained materials The third step consists of using the above results in order to predict the grain refinement.
In the first step, by simulating multiple impacts, statistical studies for impact number and velocity have been performed.
It could be noted that the impact velocity is higher in the centre of the sample and the number of impacts increases near the borders.

Figure 1 presents a transmission electron micrograph of ECAP processed Cu showing the evolution of the microstructure with strain (number of passes).
Equiaxed grains separated mostly by high angle grain boundaries were observed almost in all areas investigated.
These boundaries are obviously closer to an equilibrium state than after smaller numbers of ECAP passes.
Two populations of grains were found.
The average grain size of bigger grains was approximately 500 nm while that of the population of finer grains ranged between 200- 300 nm.

In addition, the grain size is decreased when the number of cycles is increased.
When the number of cycles increased up to eighth cycle, the dislocation density at grain interior was lower than those after fourth cycle.
In addition, the SAD pattern became more ring-like with increasing the number of ARB cycles, indicating the increment of a portion of high angle boundary.
After the first cycle (Fig. 4(a)), a large number of dislocations can be observed and grain boundaries are not clear.
With increasing the number of ARB cycles up to 6 (Fig. 4(c)), the fraction of the ultrafine grained increases and the microstructure was filled with the small and equiaxed continuous recrystallized grains containing nano scale twins (white lines in the micrograph).

Systematics of Grain Boundary Diffusion and Solute Segregation in Copper Poly- and Bicrystals Sergiy Divinski Institut für Materialphysik, Universität Münster, Wilhelm-Klemm-Str. 10, D-48149 Münster, Germany divin@uni-muenster.de Keywords: Copper, grain boundary diffusion, grain boundary segregation.
The results on grain boundary diffusion and segregation are analysed in relation to the solute - solvent binding and solute - vacancy interaction in the bulk and in the grain boundaries.
Recently, a large number of such measurements were carried out with several representative solutes in the same high-purity polycrystalline copper.
With increasing group number the solute diffusivity P is increased.
McLean: Grain Boundaries in Metals, (Clarendon Press, Oxford, 1957).

(ii) The number of grains Ni in the observed area (viz. region surrounding 748 grains) at the i-th deformation is counted.
(iii) We express the true grain size di at the i-th deformation by using Ni as follows, , (1) where d0 and N0 are the initial true grain size and the initial number of grain (before superplastic deformation).
Fig.6 Change in the number of grains Ni.
As shown in Fig.6, the number of grains Ni gradually decreases as superplastic deformation advances.
This corresponds to that there are two big domains in Fig.11(a), and also that the number of domains is increased but the size of each domain becomes smaller in Fig.11(b)-(d).

The application case proved that the proposed method can improve the feasibility of the program in grain production, and it is suitable for on-line grain production control for food system.
The grain production system is the gray original character systems influenced by multi-factor, and the major factors of affecting the grain production can therefore be established.
It makes the annual grain production（y） to the series of the system feature .
The results of quantitative analysis showed that the sequence of influencing factors and the behavior characters of the system have higher relevance.So grantee the number of input vector for six, the paper establishes the mapping relationship between the input vector and the output vector. represents embedding dimension.
By the above analysis, the model is a effective tool for grain production forecast.

The EBSD grain orientation mapping demonstrates that the grains are rather equiaxed with an average grain size of 550 ± 170 nm.
Most grains are separated by high angle grain boundaries, while there are also clusters of grains with small angle grain boundaries (close color in Fig. 2a).
Along the crack path, it is however noted that there are only a small number of substantially coarsened grains and that many grains still remain original small sizes.
However, only a few grains within this plastic zone exhibit substantial grain growth, in contrast to homogeneous grain coarsening in the near-threshold regime.
Lee, Grain growth in ultrafine grain sized copper during cyclic deformation, J.