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As the intergranular stress is dependent on grain orientation, we also called this stress as grain-orientation-dependent stress.
This is mainly due to that the chosen micro-mechanical model cannot accurately capture the interactions of grain-to-grain.
If the grain-orientation-dependent stress for a given grain at ( )ϕθ,,0 , i.e
Grain-orientation-dependent stresses.
Analysis of the micro-stresses using the present SODF method will provide more information on interactions of grain-to-grain.

Moreover, it is found that the recrystallization temperature of the Al-0.6%Cu alloy samples decreases with increasing the number of ECAP passes.
%Cu alloys subjected to different number of ECAP passes were annealed at different temperature.
The numbers of ECAP passes are 1, 2, 4, respectively.
(1) The grains of Al-0.6%Cu alloy are refined to sub-micron level after multi-pass ECAP
(2) The recrystallization temperature of the Al-0.6%Cu alloy decreases with increasing the number of ECAP passes

The Barium Titanate PTCR phenomenon is a grain-boundary (GB) resistive effect.
But for BaTiO3 PTCR ceramics have been studied only by a limited number of investigators [4-5].
An equivalent circuit consist of intra (grain), inter-grain (grain boundary) and electrode interface regions of a BaTiO3 PTC thermistor which is proposed by Maiti and Basu [6].
Electrical behavior and Grain-boundary potential barrier.
The total resistance of the sample is shown to be composed of at least two, grain boundary (GB) and grain (G), components as shown in Fig. 3.

A commercial spray-cast aluminum alloy, having a composition of Al-11.5% Zn-2.5% Mg-0.9% Cu-0.2% Zr, was processed by equal-channel angular pressing (ECAP) to give an ultrafine-grained microstructure with a grain size of ~0.3 µm and a fracturing of the rod-shaped MgZn2 precipitates.
Introduction Equal-Channel Angular Pressing (ECAP) has now become established as an effective method to achieve an ultrafine-grained microstructure [1-3].
Firstly, processing by ECAP, for example by 6 passes at 473 K, significantly reduces the grain size from ~2.1 µm to ~0.3 µm [6].
It is also noted that an increase in the number of passes from 6 to 8 leads to a shift in the optimum strain rate so that the maximum elongation occurs at a faster rate.
Fig. 2 Elongation to failure versus initial strain rate for the Al-7034 alloy at 673 K after processing by ECAP at 473 K for different numbers of passes.

The total mass loss of each group divided by the sample number got the mass loss of each sample in as-welded and heat-treated conditions.
In this manner the formation of a continuous network of chromium-rich phase at the grain boundaries is prevented.
But in the heat-treated sample, the number of fine carbonitride precipitates (<1μm) are in the majority.
However, the number of large particles (>1μm) are not big fluctuation in the two samples.
Table 4 Wear rate of samples Sample Wear rate(10-10g mm-3N-1) As-welded 2.41 Heat-treated 1.32 Conclusions Carbonitride particles in the haidfacing alloy were complex MX precipitate (M= Nb, Ti; X=C and N) distributing on grain boundary and dislocations of the hardfacing alloy with different number and size in as-welded and heat treated conditions.

For those film with a greater grain size, the remagnetization processes take place due to the non-coherent magnetization vectors rotation and DW displacement in the grains.
The films thickness D was calculated using the value of the mass per unit area of the deposited material , where ρ is Ni density, I is a current density, t is a deposition time, M is Ni molar mass, z is valence number of ions, F is Faraday constant.
The grain size influences the roughness of a surface.
Thus, in films with grains less than 400 nm the magnetization reversal processes are carried out by incoherent rotation of the magnetization vectors in different grains.
If grain size becomes more than 400 nm, the magnetization reversal is mainly due to the domain wall motion in the grains.

Formocorund grains were used as cutting material.
In case of grain included into solid metallopolymer inclusion, inclusion particles can stick to this grain resulting in cutting, performed by this inclusion.
Inclusions metric parameters calculation results Parameter Belzona 1321 Devcon Ceramic L Diamant Ceramic FL Leo- Ceramic Grains quantity 282 1.149 24 2.064 Grains quantity for 1 mm2 31.869 4.800 152.012 8.902 Average grain area, [µm2] 31 208 7 112 Minimum grain area [µm2] 2.01 1.05 2.02 2.11 Maximum grain area [µm2] 1790.38 9416.36 26.50 9.060 Average grain diameter [µm] 5.60 14.43 2.56 10.60 Grain number [G] 12 9 14 10 Grain number G mode 9 7 12 6 Grain number G and its frequency in the frames of the effective 85% range 6 (20.2%) 7 (10.3%) 8 (4.6%) 9 (23.2%) 10 (6.7%) 11 (10.4%) 12 (10.5%) 13 (5.0%) 14 (4.3%) 15 (3.6%) 4 (15.4%) 5 (18.4%) 6 (19.2%) 7 (19.9%) 8 (12%) 9 (7.3%) 10 (3.6%) 12 (33.4%) 13 (11.1%) 14 (27.6%) 15 (19.8%) 16 (8.2%) 3 (11.4%) 5 (14.1%) 6 (21.5%) 7 (19.1%) 8 (13.8%) 9 (8.7%) 10 (4%) Coefficient of material volume filling with filler particles [%] 4.6 12.4 0.4 8.3 Metric parameters of inclusions calculation results are indicated in Table
For display purposes Fig. 4 shows diagram of grains numbers in the frames of the effective range, indicating mode value.
Diagram of grains numbers distribution within effective range, indicating mode Mathematical expectation on grains size is indicated in Table 3.

Modeling of Heat and Solute Interactions upon Grain Structure Solidification Ch.
Due to the small value of the Biot number, the temperature could be assumed uniform in the thickness.
Figure 6 presents the simulated grain structure.
The grains appear much coarser than the experimental grain structure.
In the simulated grains structure, after nucleation in the undercooled liquid, grains remain fixed in space and can only grow.

At higher strains the microstructure refines by the break-up of the ribbon grains into lower aspect ratio submicron grains.
This could be simply because of the greater element distortion that results from the higher strain with the 90° die, for the same number of cycles, but may e a result of differences in die friction effects.
Cell bands can also develop HABs in regions near grain boundary surfaces and triple points, in the original grain structure, due to high local orientation gradients resulting from grain-grain interactions [8].
This leads to an increase in grain boundary area simply due to the geometric shape change imposed on a grain [18].
Acknowledgements The authors are grateful to the continued support and insight of Professor John Humphreys over a large number of years and for funding from University of Manchester EPSRC Light Alloys Portfolio Partnership (EP/D029201/1).

The main advantage of such modifiers is a great number of particles per the melt volume unit.
Phase Composition and Structural State of Unmodified High-Manganese Steel The quality of railway arrow samples was evaluated in terms of austenite grains, phase composition, number, shape, and distribution of nonmetallic inclusions.
However, the MM introduction into the melt had an impact on the grain size, number and distribution pattern of nonmetallic inclusions in the railway arrow samples.
Figure 3 a shows the optical image of a modified sample, which demonstrates that the number of nonmetallic inclusions has significantly reduced both in the grain body and along the grain boundaries.
The comparison of microstructure in unmodified and modified samples by means of SEM revealed that the MM introduction significantly reduced the number of nonmetallic inclusions inside the grain and along their boundaries (Figs. 2 and 4).