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Blut and Ebdon [9] proposed the reasonable sampling intervals Dx and Dy, which should be located at: (2) Where dm is the average grain size of the abrasive grain and can be estimated as follows: (3) Where: Gs is the abrasive grain size number.
The density D of the abrasive grain is the number of abrasive grains per unit area, which determines the number of abrasive grains involved in the grinding process.
In the evaluation of the wear degree of the abrasive belt, it can estimate the pull-off phenomenon of the abrasive grain on the abrasive belt, which is expressed as follows: (4) Where: n is the number of abrasive grains in the sampling area; M is the number of rows of the measured area data; N is the number of columns of the measured area data; Dx is the sampling interval at x direction; Dy is the sampling interval at y direction.
This is because that only a few abrasive grains contact with the workpiece, severe wear or pull-off are the majority of wear patterns at the initial wear stage, so the maximum value declines significantly, but the number is small enough to affect the mean height change.
Abrasive grain pull-off is the main reason for the changes of abrasive grain density.

UFG structure with an average grain size of ~0.3 µm was produced in Cu billets by TE processing.
There were also wellshaped grains.
The Summary of mean values of mechanical properties with number of TE passes increasing is shown at Fig. 8 a. 0 1 2 3 4 0 100 200 300 400 0 20 40 60 80 100 YS UTS YS and UTS, MPa Number of TE passes Elongation Reduction in area Elongation and Reduction in area, % 0 2 4 0 2 4 6 8 V, % Number of TE passes YS UTS Elongation Reduction in Area (a) (b) Fig. 8.
Valiev: Nature Materials, Vol. 3 (2004), p.511 [2] Ultrafine Grained Materials III.
Varyukhin: Ultrafine Grained Materials III.

The integration must be able to support complex authorization specifications and the fine-grained resources access requirements that the various parties may have.
In this paper, we use a fine-grained policy based on RBAC in which roles are used to simplify authorization management and views are to control services and resources by fine grains.
In summary, the main advantages of the policy are fine-grained, reusable, type-checked specifications of access policies.
There are three kinds of constraints when a role is defined: Base number constraints; Leading role constraints; Mutual exclusion constraints.
Views also serve as basis elements for fine-grained access control policy.

The same length is applied to calculate the fatigue-effective stress and strain (averaged over ao length), the fatigue damage parameter PSWT, and finally the number of load cycles Nin for the growth step n.
At the weld notch, coarse-grained HAZ was observed.
Consequently, the grain size at 99% probability level is significantly larger, as is the volume-weighted average grain size dv.
The Hybrid has a pronounced peak at low grain sizes.
Figure 4: Relation between Martens hardness and different grain sizes: a) volume-weighted average grain size [7], b) grain size at probability level of 99% (PF = primary ferrite, P = pearlite, AF = acicular ferrite).

The eutectic lamella phase was refined by the extrusion; the grain size of the α and β phase was measured to be a few micro-meters.
Then, direct extrusion was carried out at 573 K to obtain the extrusion composed with fine matrix grains.
Refined matrix grains and dispersion of β phase were confirmed by microstructure observation and XRD analysis. 3.
Acknowledgement This work was partially supported by the Funding Program for Grant-in-Aid (Grant Number 25246012) for Scientific Research from the Japan Society for the Promotion of Science (JSPS).
Sherby, Low Stress Creep of Fine-Grained Materials at Intermediate Temperatures: Diffusional Creep of Grain Boundary Sliding?

The number of the acid centers of the carrier fixed loading became larger and the combination turned more firm.
Analysis of specific surface area, grain size and sulphur content .
The average grain size of the catalyst SZ samples was 148 nm and the average grain size of the catalyst SZ-C samples was 99 nm.
The smaller the grain size, the larger the specific surface area of the catalyst with the same mass, the more the number of the acid centers, the higher the catalytic activity.
While the grain size of the catalyst SZ-C was small and even.

The chord length l of a grain is the length of the intersection of the grain with a test line.
In traditional stereology, the number of intersections Nis of a (random) test line of length L with grain boundaries is counted.
The number density NL = Nis/L of intersections is the inverse of the mean chord length ¯l = 1/NL.
From the number Ncr of such occurrences and the total line length L = N∆x the intersection density NL = Ncr/N∆x and the average chord length ¯l = N∆x/Ncr can be inferred.
The accumulated frequency distribution Pθ(θcr) = 1− Ncr N (1) is intimately linked to the number Ncr of incidences of point pairs with angles above the critical angle.

Grain refinement and precipitation hardening are the main reasons for high strength, and toughness improvement can be attributed to grain refinement and particular microstructural characteristics of AF.
Large number of nanometer particles distribute in X80 pipeline steel, which is given in Fig.4.
Grain refinement can be achieved through repeated recryatallizaiton of austenite during hot rolling.
Sub grain and high density dislocations are characterization of acicular ferrite.
Large number of nanometer particles exist in experimental steel.

For the latter case, even if the number fraction of larger grains in the nanostructure is low, their volume fraction can be sufficiently high to contribute to dislocation-based plasticity in the material [2].
The material was processed using the so-called route Bc, as detailed in [18], but for number of passes as high as 16.
It is clear from Fig. 2a that the strength of the material increases gradually with the number of passes from 1 to 8.
(a) 10 µm 5 µm (b) 5 µm 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 0 10 20 30 40 50 60 70 80 90 100 100 Above 1000 nm 500-1000 nm 100-500 nm Number of grains (%) Grain diameter (nm) milled with Y milled without Y atomized Figure 4: Graph showing the number of grains and their average size within the +100/-500 nm, +500/-1000 nm and +1000 nm grain size fractions for different types of initial powder (atomized FeAl powder, milled FeAl powder, milled FeAl powder with Y2O3 addition).
Fig. 4 gives a plot showing the number of grains contained within the +100/-500 nm, +500/-1000 nm and +1000 nm grain size fractions for the case of the processing of different types of FeAl powders.

Nowadays, the main manufacturing method for most magnesium components is still die casting, because most magnesium alloys have a limited number of slip systems related to the HCP crystal structure, resulting in poor processing capabilities [1].
A large number of DRX grains appeared around the grain boundary.
A large number dislocations generated inside the grains during the deformation process.
The intergranular LPSO and fine a-Mg grains located at the boundaries of the coarsely deformed grains.
The nucleation of DRX-ed grains at the kink bands and a-Mg grain boundary may be achieved by forming sub-grains and increasing their misorientation (i.e., CDRX mechanism).