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The homogeneous body was created by assigning to each element a random orientation created from random numbers.
We investigated the relationship between the number of elements and the mode of deformation.
However, the number of elements placed in the wall thickness direction differs from one to the other, depending on whether the centrally placed grains are almost convex or smooth.
Relation between number of elements in the thickness direction and deformation in the inner surface direction.
Acknowledgement This study was supported by JST SPRING, Grant Number JPMJSP2128.

Microstructural examination showed the grain sizes of both alloys were reduced to the range of ~0.3-0.5 µm through ECAP.
The Al-7034 billets were pressed at 200°C and rotated by 90° in the same direction between consecutive passes in the processing route termed BC and the Al-2024 billets were pressed at room temperature using route Bc-C where they were rotated by 90° after odd-numbered passes and by 180° after even-numbered passes.
The as-received Al-7034 alloy contained a fairly equiaxed array of grains with an average grain size of ~2.1 µm and there was a low density of dislocations [7].
These peaks move slightly to higher temperature with an increase in the number of ECAP passes, and they occur at 376, 380 and 394°C for 2, 6 and 8 passes of ECAP, respectively.
This effectively reduces the number of obstacles available to impede the movement of dislocations.

Microstructure investigation displayed an increment in average grain size of LSMO due to the grain growth promotion as the sintering temperature increased.
For polycrystalline manganites, their magnetic and electrical properties are strongly depend on the microstructure condition such as grain size, grain boundaries and grain porosity [6-9].
All samples showed high grain porosity.
At low sintering temperature, the average grain size is very small and thus leads to a large number of grain boundaries.
The increment of average grain size from LS650 to LS950 reduced the grain boundaries region and enhanced the grain connectivity.

The results showed that the cellular dendrite of the general cast-rolling magnesium strip was coarse, the grain structure was heterogeneous and the average grain diameter was between 50μm~60μm.
However, the grain structure became more homogenize after the ultrasonic treatment for cast-rolling magnesium strip, the grain was refined and the average grain diameter was between 20μm~30μm.
Table 2 Experimental parameters Number Ultrasonic power /W Melt temperature /℃ The former case temperature /℃ Casting speed /(m·min-1) Thickness /mm 1# 0 690 675 2.7 3.8 2# 500 690 675 2.7 3.8 In order to obtain the appropriate mechanical properties, the two states of cast-rolling magnesium strip tensile specimen were intercepted from the horizontal, vertical and 45º direction.
Therefore the nucleation rate was enhanced, which conducive to grain refinement.
Fig5(b) shows that some of dendrites are peeled off, the grain is fined, the grain is elongated in the rolling direction, plastic deformation is very obvious.

But the impact property obviously decreased with the increase of quenching temperature, that is due to the grain coarsening.
A number of studies about the steel are reported so far.
On the one hand, carbides dissolved and more alloy elements diffused into austenite grains with the quenching heating temperature increased and heating time prolongated, that enhanced the solution strengthening and the grain boundary strength.
On the other hand, the grain and the martensite lath grew up with quenching heating temperature increased and heating time prolongated, that weakened the grain strengthening.
Fig.3 shows the average grain size after quenching at different parameters.

In the present model, both the number of potential nucleation sites per unit volume and the rate at which solute atoms from the matrix join the nucleus depend on the nucleation site and are either related to the lattice parameter (homogeneous nucleation), to the grain size (nucleation at grain boundaries) or to the dislocation density (strain induced nucleation) [5].
Grain Structure Model.
In [4] a nucleation rate RN is derived by the number of dislocations per critical nucleus that recover with time.
The grain orientation spread was used to discriminate between the original and the recrystallized grains [13].
Only in case of samples with negligible recrystallization during the compression, the crack propagates along the whole grain boundaries of the deformed grains, tearing apart the grains, often singling out individual grains (Fig. 2 right).

Fig. 1 Kinetics of austenitic grain growth Kinetics of austenite grain growth.
Austenite grain then coarsens irregularly.
At the temperature of 850°C number of particles is comparable in both steels microstructure.
Generally the monitored grain size is comparable or finer then austenite grain before deformation.
Grain size corresponds to initial austenitic grain before deformation or is smaller.

Introduction During welding of HSLA steel, austenite grain growth will inevitably results in poor toughness of the coarse grained heat-affected zone (CGHAZ).One method of alleviating this problem is to introduce fine dispersed particles, such as TiN, TiNb(C,N) into the steel.
These stable second phase particles are expected to pin the grain boundaries, thus restricting austenite grain growth [1-4].
More than 150 fields were examined and the number of particles analyzed was at least 1000 for every specimen.
The particle number per unit area changes from 42.88 to 3.144, the average particle diameter changes from 14.2nm to 24.6nm, see Fig.2b.
Effect of Ti addition on austenite grain growth kinetics of medium carbon V-Nb steels containing 0.008~0.18%N.

The high shear solidification resulted in a fine and uniform grain structure with b-TCP particles evenly distributed in the matrix in clusters of 5-20 mm in size.
A fine and uniform grain structure was obtained after casting with an average grain size of ~23 mm (Fig. 1a), largely attributable to the high shear prior to casting.
After 1 pass ECAE, the initial grains were subdivided due to simple shear flow along the extrusion die shear plane.
The characteristic dimension for overall subgrain/grain structure was estimated as to be ~2.3 mm after 4 pass ECAE, facilitated by the formation of grain boundaries due to dynamic recover during ECAE.
ECAE samples exhibited higher values than that of the as-cast state and the hardness increased with increasing number of ECAE passes.

The K2O isometric replaces Na2O at the same time the Al2O3 isometric to replace SiO2, reduced the grain size.
In contrast, the content of [AlO4] will increase by 4No, which further result in a significant decrease of the number of discontinuous points in the glass network.
It is found that the main crystalline phase are Na4Ca4 (Si6O18), in addition to a small number of Na6Ca3Si3O18 and Ca3Si2O7 crystals, which indicates that K2O and Al2O3 don’t affect the species of the main crystalline phase.
As show in Fig.4 (c), small equiaxed grains formed in the AA samples , which is because the glass viscosity increase due to the replacement of part of SiO2 by Al2O3, so that crystal growth rate slowed down, and the more smaller equiaxed grains easily form, the average grain size is about 0.3μm.
Fig.4 (d)show that the large amount of small equiaxed grains formed in the AKA samples, there are many kinds of crystalline in the AKA samples by the XRD analysis, many kinds of crystal grow at the same time in the certain space, which make the probability of collision with each other increase, the collision of these crystals hinder the fast growth of crystals, so that the crystal cannot develop into flakes or needle, but form equiaxed grains, the average grain size is about 0.43μm, the grain size of glass-ceramics samples are listed in Table5.