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According to [10-13] the optimal values aopt, mopt, hopt are determined by the equation: aopt = 2.1×(1+nSdS/dCS)3–1.1; (1) mopt = 2.1×(1+nCdC/dS)3–1.1; (2) hopt = 2.1×(1+dH/dC)3–1.1, (3) where dCS, dS and dC are average grain sizes of coarse and fine aggregate and cement particles, respectively, mm or μm; nS, nC are the number of densely packed rows of grains of fine aggregate and cement particles, respectively, between grains of coarse and fine aggregate; dH is the width of the densest layer of cement hydration products between clinker insoluble particles, μm.
Let us suppose that the densest structure of the hydration product layer between clinker insoluble parts with the maximum number of electro- heterogeneous contacts s contacts consists of two rows of ettringite crystals, grown towards each other on the surfaces of cement particles or aggregate grains (Fig. 2, d), dG in (3) can be taken as 2×0.5 = 1 μm.
а) b) Fig. 4 Study into crack resistance of concrete under dynamic effects: the test sample of the rail base mounted in the testing machine MUP-50 The vertical loading on a rail had a frequency of 8 Hz, a force range of 100-235 kN, and the total number of cycles was 1.5 million.
A value of m specified corresponded to a width of the cement stone layer between fine aggregate grains of 20 μm according to equation (5).
The actual coefficient of grain separation of coarse and fine aggregate, and water-to-cement ratio to the optimal values aopt = 1.30, mopt = 1.27, W/Copt = 0.23, respectively, and a width of the cement stone layer between grains of fine aggregate 20 μm in C40/50 concrete provided the maximum values of physical and mechanical properties of concrete.

The grain to which the cell belongs.
The setting of this property for each cell of the system identifies unambiguously the grain–boundary cells, which have neighbours that belong to a different grain. 2.
The growth length, , for each grain boundary cell, i.
The number of nuclei formed, , is given by , (4) where V is the volume of non–recrystallised ferrite for ferrite recrystallisation and the volume of pearlite regions for austenite formation.
Acknowledgement This research was carried out under the project number MC5.06257 in the framework of the Research Program of the Materials innovation institute M2i (www.m2i.nl).

We have covered three different grain sizes of particles.
The possible solution of these problems can be the plating of the SiC grains.
A number of common reducing agents have been suggested for use in electroless copper baths, like formaldehyde, sugars, hypophosphyte.
The copper deposit is light, and there is on the dark grey grains.
If the coating time increases, the numbers of the particles and the plating rate increase, as well.

This procedure can be generalized by removal of an arbitrary number �e of subcubes.
This is obtained by iterating the generating process an infinite number of times.
We then randomly remove a fixed number of subcubes �e = (33 − �f ).
In general, the number of subcubes will be equal to 2l( ) d, where l is the number of iterations and d = 3.
Snow grain-size measurements in Antarctica.

The stress of 400 MPa at the crack end in the columnar grain region was about two-fold larger than that of 180 MPa in the equiaxed grain region.
The plane consisted of a columnar and an equiaxed grain region.
The maximum size of the columnar grains was 5 mm.
The collimator size and oscillation range were optimized to obtain a continuous Debye-Scherrerring from a sufficient number of grains.
Debye-Scherrer ring from a sufficient number of grains in an area of 9 mm2.

Except temperature distributions, the macro-micro models can offer more information about solidification process, such as undercooling, grain size, grain density etc.
Except temperature distributions, the macro-micro models can offer more information about solidification process, such as undercooling, grain size, grain density etc.
For the macro-micro models, since grains are assumed to be spherical, the local volume fraction of solid, fs, can be given by ( ) 3 ( ) ( ) 4/3 ( )   =   sf t N t R tπ (6) where N(t) is grain number per unit volume and R(t) is grain radius.
In general, it is thought that the higher cooling rate (dT/dt) yields the larger grain density since the higher cooling rate leads to the greater undercooling, which causes the larger number of nuclei [18].
From the figure, it can be found the grain sizes are strongly related to the undercooling.

These models are applied for optimization of the grain size and % volume of recrystallization.
The equations proposed for recrystallized grain size by Sellars are employed by the researchers at Kawasaki Steel for their model [3].
Grain size of the developed microstructure was determined using Clemex Vision Image Analyzer.
Table 1 GA Based FLC for Hot Deformation Process Process Parameters GA Parameters Process Ke Kce Ku Population Size 20 Crossover Probability 0.7 1.0267 0.9928 135.0964 Mutation Probability 0.005 10 1 18.20 Number of Generations 50 Fig.2 Closed Loop Response of Grain Size (SP=30µm) Fig.3 Closed Loop Response of Vol.
However there are number of parameters to be chosen in advance, to ensure the effectiveness of the controller.

This value decide about number of generated defects, which are with increase deformations changing theirs localization, which leads to creating new nanometric size grains.
When deformation value are bigger fragmentation grain process is much more slower and strives to specified grain size limit.
Increased number of passes to obtain required results, samples were subjected up to 9 ECAP passes.
As much as grain size and type of grain boundary depend on material properties and process conditions.
To compare grain sizes after the same number of passes and the same section (Figure 1c, 1d, 1e and 1f) are shown.

Experimental Material and Procedures The starting material used in this investigation was an extremely coarse grain (grain size ∼ 5 mm) high purity (99.99%) aluminium.
The edge lengths and volumes of the "mean" subgrains and grains Spatial grain intensity NV, surface and grain junction intensities SV, LV.
The structure independent stereological relations are SV = 2NL and LV = 4NA (the mean number of profile vertices per unit area in a random planar tessellation is 6 and any vertex belongs to the three profiles meeting in it, hence the number of profile vertices per profile is 2; the vertices compose together the point processes induced in the section planes by their intercepts with the fibre process of triple grain junction and its intensity is one half of the fibre process length intensity LV).
Lowe (editors): Utrafine Grained Materials II.
Lowe (editors): Ultrafine Grained Materials III.

In many applications, such as milling or percussion drilling, they are subjected to fatigue with considerable loading cycle numbers.
Thus S-N curves (so called Wöhler plots) are determined to limited number of loading cycles < N= 107.
The data indicate a continuous decrease of fatigue life without any horizontal section even up to 1010 number of loading cycles.
Fig.5: Normalized S-N curves of hardmetals with 10% Co content and grain sizes of 2µm and 0,4µm Fig. 6 shows as an example the pronounced influence of residual stresses on fatigue life which decrease with increasing number of loading cycles, possibly due to changes in fracture morphology.
Both curves are steadily decreasing, and pronounced difference was observed between the stress amplitudes of the two curves at 107 numbers of cycles.