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In presence of grain boundaries (GBs), the grain size effect (GSE) is traditionally described as τGB=τ0+kHPdg-1/2 [11,12], where τ0=τCRSS for an infinitely large grain and kHP the empirical Hall-Petch (HP) parameter.
Simplified calculations with straight dislocation segments permit varying the number of dislocations in the pileup and the GB and the degree of dissociation, for different geometries of slip plane and GB.
Dislocation pileups in small grains. 
Dislocation interactions with grain boundaries.
Grain boundaries and interfaces in slip transfer. 

There are some grains with very low internal grain misorientation (in blue as indicated in Fig. 5(a)) and these grains are likely to be recrystallized grains in the midst of the deformed grains.
(b) (a) Fig. 8 (a) EBSD IPF map at the non-isothermal heating zone and (b) fraction of different grain diameters However, from the internal grain misorientation measurements, as seen from Fig. 9(a), only a few grains located near the larger grains have low internal misorientation, which indicates that they were possibly recrystallized grains.
The other larger equiaxed grains though have larger internal misorientation indicative of strain within the grains.
Dynamic recovery occurred during deformation and produced a large number of low angle grain boundaries within the grains.
These recrystallized grains were identified with having very low internal misorientation unlike the deformed grains.

In the model, it is assumed that each material point contains a number of crystal grains and the properties of a material point ( )• are given by the averaging of all grains; ( ) ( )∑= •=• M k k M 1 1 (7) wher M is a number of crystal grain at each material point.
In each case, the results converge almost same response with increasing of number of elements or grains per element.
Fig. 4 Flow stress of FCC material with different numbers of grains per element (extended Taylor model with 8(2x2x2) elements is utilized). extended Taylor model presents stiffer response when the number of grains increases as shown in Fig. 6.
Meanwhile, the results in Fig. 8 show that 0.2% proof stress increases respect to the number of grains per element.
The effects of the number of elements and the number of grains in the extended Taylor model are discussed.

The average initial grain size before deformation was about ∼140 µm.
Their number and the boundary misorientations increase with further deformation, finally leading to the development of new fine grains surrounded by HABs at large strains.
The mechanism of gradual increase in the boundary misorientation in the last stage, i.e. 4≤ε≤12, can be associated with increase in the number of lattice dislocations evolved by usual intrinsic slip and the absorption of accommodation dislocation that originates from incompatibility between neighboring grains.
ECAP results in grain refinement at all of the pressing temperatures.
Sakai: Ultrafine grained Materials IV, edited by Y.T.

Large grain on the film surface hardly is found.
At low temperature, nucleation free energy declines and the number of the core increases.
This is helpful for grain to grow up.
On the other hand, it is considered that residual stress develops when newly deposited grains are attracted to one another during deposition, causing grain coalescence or “zipping” of the grain boundaries.
Thus, a number of microstructure variables are expected to influence the magnitude of residual stress generated by the grain size and coalescence mechanism.

When cold deformation, using the control deformation degree and the annealing temperature to refine the grain, the grain is finer and the grain boundary is more, and the grain boundary has the effect of obstructing the slip deformation [4].
It could be agree with that the 4 kinds of new zirconium with the same of the original grain size .
Compared with process 1 and process 3, it can be seen that the heat treatment temperature is invariable, the larger the cold-rolled shape variable, the finer the grains, the greater the grain boundary area, the more winding grain boundary, the more unfavorable the crack expansion, the higher the yield strength of the material.
Which showed that the effect of increasing the deformation of cold rolling on the fine grain enhancement was more obvious when the original grain size of the material was the same.
The comparison process 3 and process 4 also found the same rule, the increase in annealing temperature resulted in grain coarsening, grain size increased, the less the grain boundary, the material yield strength decreased.

N= turn number.
N= turn number.
N= turn number.
N= turn number.
N= turn number.

The experimentally measured values of stress (maximal force in particular pass divided by cross section) and microhardness are presented in Fig. 2a, as a function of the ECAP pass number.
For particular pass number two factors influence the microstructure evolution of the AA3104 alloy.
As for recrystallized grains (Fig. 7c), some preferences in selection of recrystallized grains orientation were clearly visible.
In the microstructure resulting from the ECAP processing the average size of the microstructure elements slightly decreases with the pass number.
It is well documented that for new, well-developed grains their diameter reaches 3-15 µm, independently of the applied number of passes.

The acicular ferrite grains formed in the austenite grains were trigged by the intragranular ferrite grain(s) formed around TiN.
The pole figure from the ferrite grain and the particle in Fig. 3(a) show that the (001) plane of a ferrite grain is parallel to the (001) plane of a TiN, and the (011) plane of a ferrite grain is parallel to the (001) plane of a TiN.
Fig. 4 shows an inclusion surrounded by a number of ferrite grains corresponding to Fig. 2(a).
The acicular ferrite grains formed in the austenite grains were trigged by the ferrite grains formed around TiN.
The acicular ferrite grains formed in the austenite grains were trigged by the intragranular ferrite grain(s) formed around TiN.

We found that, with increasing temperature, Zr impurities become more stable and prefer to segregate at the interface of ∑5 (310)[001] grain boundary.
Several preliminarily calculations were made in order to estimate the required number of layers.
Following these energy convergence calculations, it was estimated that 20 layers parallel to the grain boundary plane were required.
Further information about the modeling of the ∑5 grain boundary can be found in [12].
The calculated impurity formation energies for substitutions at the grain boundary interface ∑5 (310) [001] are given in Fig. 3.