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The grains misorientation angle was quantified by measuring the orientation of single cleavage facets with respect to its neighbours, hence a number of cleavage facets and their misorientation angle was measured.
For the normalized steel, the number of grains boundaries with misorientation angles between 3° and 10° was about 15%.
Low-angle boundaries, where the angle between the grains is low, may be regarded as arrays of dislocations, the number of dislocations involved in the boundary and the total energy of the boundary increases as the misorientation angle increases.
Furthermore, unlike to low-angle boundaries, where the boundary energy is related the misorientation angle, and thus to the number of dislocations involved in the boundary, the energy of high-angle boundary is rather independent of the misorientation angle.
Kim showed a distribution of misorientation angles where the large number of boundaries are into two ranges of misorientation angles; the ranges were below 10º and between 50º and 60º in a bainitic steel [16].

Modelling grain boundary sliding from first principles Carla Molteni Physics Department, King’s College London, Strand, London WC2LR 2LS (UK), carla.molteni@kcl.ac.uk Keywords: Grain boundary, sliding, migration, density functional theory, first principles methods.
While in germanium sliding is controlled by local stick-slip events involving rebonding of a few atoms at the boundary interface, in aluminium larger numbers of atoms act in concert over extended areas, ultimately limited by boundary defects.
Grain boundary sliding plays a dominant role in the plastic deformation and fracture of polycrystals.
For the (0,0) translation state, the periodicity is that of the DSCL: the energy maxima occur when the atomic “bumps” belonging to each grain sit on top of each other at the interface, while the minima occur when the “bumps” of one grain fit nicely on the “hollows” of the other grain.
In general, in Al a large number of atoms act in concert over extended areas, ultimately limited by boundary defects.

But this method owns a limitation in simulation of high Reynolds number, which is [2], when LB method is used to derive Navier-Stokes equation, one of errors is O (M2), where M is the Mach number.
It permits a reduction in error in exchange for a smaller Mach number which leads to a smaller Reynolds number, but in the engineering application of hydro turbine, turbulent exists in most of the practical flow phenomenon and high Reynolds number is often encountered.
Simulations of high Reynolds number fluid flow based on entropic Boltzmann method.
Stabilization of the Lattice Boltzmann Method Using the Ehrenfests’Coarse-Graining Idea.
Research on Lattice Boltzmann Method with High Renolds Number. 2008, 56-58

Some austenite also nucleated on the ferrite grain boundaries or the carbide particles within the ferrite grain.
A small amount of recrystal grains emerged within the ferrite grain, and the nucleation site is near the grain boundaries of deformed ferrites, as shown in Fig. 1(b).The recrystallized grains were equiaxed and very fine and small.
When the temperature was heated to 690℃{TTP}8451 , a large number of recrystallized grains had been formed.
Here the recrystallized ferrite grains were equaxed, and the size of the grains was uniform.
The recrystallized grains were equiaxed and very fine and small. 2）When the temperature heated to 690℃{TTP}8451 , a large number of recrystallized grains had been formed.

Creep resistance of specimens made of coarse grain material was significantly higher than the resistance of fine grain material.
Images of macro and microstructure of IN-713C superalloy as well as their morphological parameters Heat Evaluation of the structure of superalloy Carbide content in surface area AA Morphological parameters of macrostructure 1 AA = 0.74 % N = 33 -number of grains, A = 0.76 mm2 - mean surface area of a grain 2 AA = 0.92 % N = 14 -number of grains A = 1.93 mm2 - mean surface area of a grain 3 AA = 0.95 % N = 25 -number of grains, A = 0.86 mm2 - mean surface area of a grain 4 AA = 0.86 % N = 10 - number of grains, A = 2.67 mm2 - mean surface area of a grain It comes out from the tests of macrostructure of the nickel superalloy that both with (blue modification filter for heat 2) and without (white filter for heat 4) volumetric modification in the casting experiment, coarse-grained structure was obtained.
Creep resistance vs. selected morphological parameters of structure IN-713C nickel superalloy samples Heat Creep resistance tz [h] Rate of steady-state creep Vu [s-1] Carbide content in surface area AA [%] Number of grains on specimen section N Ratio of carbide content in surface area and number of grains AA/N [%] 1 25.4 3.27*10-7 0.74 33 0.022 2 26.7 3.05*10-7 0.92 14 0.066 3 28.3 2.8*10-7 0.95 25 0.038 4 50.0 1.38*10-7 0.86 10 0.086 In the research of creep relatively lower creep resistance of sample from heat 2 was found (showing coarse-grained microstructure) as compared to sample from heat 4 with similar number of macrograins in the cross section.
This influence is good described by the implemented parameter AA/N, (ratio of carbide content in surface area and number of grains in specimen, Table 2).
With the increase of parameter AA/N both in the close-grained (heat 1 and 3) and coarse-grained (heat 2 and 4) group of the produced superalloys creep resistance tz was higher.

The bending strength of brazed segments without CBN grains is 128MPa, a little higher than that with CBN grains concentration 75% 116MPa.
All the single-crystal grains fractured along the cleavage plane。
Compared with the fracture surface morphology shown in Fig.4, it’s easy to find that the number of fractured CBN grains decreases with the increasing of graphite content.
It implies that the bonding strength inside of copper-tin alloy and between grains and copper-tin alloy are both higher than the grains’ own strength with a low graphite content, so that the poor bonding and fracture happened through the CBN grains.
Moreover, micro-crack on the surface of CBN grains may exist because of the residual stress on the interface of grain and filler.

With the development of nanotechnologies, the number of industrial processes dealing with the production of nanostructures or nano-objects is in constant progress (microelectronics, metallurgy…).
Especially, today’s materials can be both composed of nano-objects as clusters or decorated defects…, and contain a large number of interfaces as in nanometer-thick film stacking and buried nano-wires or nano-islands.
If we consider that not all the grains are growing, the fraction of growing grains fgr can be a fourth parameter.
The B solubilities in grains and grain boundaries were chosen to be the same, as well as the initial profiles (solid line) in grains and grain boundaries.
Grain boundaries.

The initial microstructure with prescribed grain size was generated by a normal grain growth algorithm.
The inherently poor workability of Mg and several of its alloys is due to the limited number of slip systems associated with the hexagonal close-packed (HCP) crystal structure.
Secondly, nucleation of DRX only occurs on grain boundary (including primary grain boundaries and R-grain boundaries), all other nucleation mechanism is not considered.
The grain growth adopts the probabilistic transformation rule, so the growing grains reach approximately globular shape.
The mean radius of primary grain , is defined as (1) where is the side length of hexagonal cellular, is the number of CA cells, and is the number of primary grains.

It concludes that the inclusions create not only a hygro stress concentration around the grains but also the number of inclusions should influence the network in cementitous matrix. 1.
Moreover, we find out that one-grain-cube creates very high stress (~45MPa) merely around the grain at 48h while ten-grain-cube generates less stress (~15MPa).
In the meanwhile, the stress is smoothly distributed among the grains providing one micro-crack network at 48h after mixing up stage.
Hygro-mechanical stress variation at 48h after mixing up created by the number of grains: a) 2 grains b) 3 grains c) 6 grains d) 10 grains at 48h on the left and the micro-crack observation around one sand grain by SEM (A: aggregate; CP: cement paste). 5.
According to the numerical results, it has been found out that the number of inclusion influences the magnitude of hygro-mechanical stresses around the sand grains, the higher number of inclusions inducing the greater stresses.

A majority of the orientations scatter around the main texture component in ODF, which indicates that a number of grains keep similar crystal orientations to the main texture component in grain subdivision during ECAE processing.
Many low angle grain boundaries are produced in the course of grain refinement.
In the meantime, orientation distribution becomes more scattered around main texture component with increasing number of ECAE passes.
The ODF results show that the orientation of a number of grains deviates farther from the main texture component after more ECAE passes.
Ultrafine-grained materials III.