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The grain size was less than 1 μm via RPW process due to its severe plastic working on raw powder.
With increase in the number of cycles (N) in RPW process, the magnesium matrix grains are gradually refined.
The mean grain size at N=200 is 0.9 μm, and much smaller than that at N=1 (9.3 μm), that is, RPW is suitable for in-situ grains refinement.
On the other hand, when employing RPW at N=200, Fig.4 (b) indicates that fine β phases with 1~2 µm exist not only at the grain boundaries but within the grains.
UTS Fig.5 Dependence of tensile strength of H/E ZAXE05613 on number of cycles in RPW.

The internal grains havealso been refined.
The edge grain of solidification ingot gradually shifted from the dendrite to the ellipsoid, spherical grain
In addition, under the atmospheric pressure with the same cooling rate, crystallization starts when the number of crystallization centers is little and when the line-speed is large.
Hence, the relatively coarse grains were got.
And the internal grains have also been refined

With biaxial deformation, grain boundary slide occurred more frequently than with uniaxial deformation, causing grain boundary separation and formation of micro-voids between the grains.
Observation of a vertically sectioned surface showed an initial grain size of 17 µm and equiaxial grains.
In addition, the Mg alloy, which as a small number of slip systems, has a high strength coefficient F which enhances the difficulty of deformation in sheet thickness.
In uniaxial deformation elongated grains are observed at έ = 2.7 ×10-1 and equiaxial grains at 2.7×10-4 s-1.
Grain rotation is hardly observed, and microvoids are formed at the grain boundaries

Birmingham parameters were used to characterize the performances of grinding wheel, in items of grain density, grain shape and grain sharpness.
Density of abrasive grains.
The Birmingham parameter of Sds is the number of summits of a unit sampling area.
Its expression is: number of summits ( 1)( 1) Sds M N x y      (2) where M and N are the number of data points in x and y directions; Δx and Δy are the sampling interval in x and y directions.
With a smaller sampling interval, a larger number of peaks will be counted.

Brittle intergranular failure in grain aggregates.
Within that approach, the material is assumed to consist of grains bonded to one another.
The crack propagation corresponds to the transition from the state with a lower number of broken bonds (configuration with less ones) to the state with a higher number of broken bonds (configuration with more ones).
Then the decrease in elastic strain energy can be expressed as: ∆Eelastic = − C × (number of broken parallel-to-loading chains of grains) 3/2.
The basic idea is to represent each bond between two grains by a binary variable.

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.

During recent years, a significant number of studies have been carried out to study recrystallization kinetics and texture evolution during hot rolling [1, 2].
The fraction recrystallized is obtained from the number fraction of pixels in grains that have a GOS value less than 3°.
The volume fractions of different texture components in deformed and recrystallized regions were calculated from the average orientation and number of pixels in each grain.
The average orientations of grains are also used to determine the texture component of the each grain and weighted with the number of pixels of that grain to obtain the corresponding volume fraction.
This is also evident from the analysis of the number fraction of pixels of cube recrystallized grains against the deformed grains.

This topic was then restudied in USSR just after World War II but it is only after the seventies that a large number of investigations were focused on superplastic metallic alloys.
What is the contribution of grain boundary sliding?
In the case of HPT processing, strain gradient are of course observed from the disk center to the periphery but appropriate strategies for extracting samples have been developed [36] and reasonable homogeneity can be obtained after a large number of turns [37].
This is not straightforward since it requires to follow a large number of cavities and to deal with local strains and not only with macroscopic ones.
Ma, Superplasticity governed by effective grain size and its distribution in fine grained aluminum alloys, Mater.

Overall，the average ferrite grain sizes in the three tested rebar are fine, which have fine grained strengthened effect and are contribute to improve strength and plasticity.
Ferrite content /% Pearlite content /% Bainite content /% Ferrite grain size /um Ferrite grain grade /grade 1# 59.3 40.7 / 8.5 10.4 2# 49.1 26.8 24.1 8.6 10.6 3# 56.7 36.6 6.7 8.6 10.6 Table 3 Quantitative analysis results of microstructure and ferrite grain size for different microalloyed rebars.
According to the test results of precipitates, a large number of V(CN) and Nb (CN) precipitates with size of 5～30nm are formed and distributed on ferrite matrix, grain boundary and dislocation lines.
The cleavage fracture is composed of a large number of cleavage plane with the size being equivalent of the grain size.
Becauce when crack grow and propagate, it would go through a certain number of parallel cleavage plane with different orientation,which result in grain boundaries become obstacles to crack propagation, grain size effect crack propagation that is the cleavage plane size increases with grain size increasing and grain boundaries crossed by crack propagation is lesser, therefore, the crack easily propagate and propagation rate is also faster, which easily lead to cleavage brittleness fracture.

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.