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So it leads to less hardening and lower resistance against deformation of surface grains and makes the surface grains deform easier than those grains inside because dislocations moving through the grains during deformation pile up at grain boundaries but not at the free surface [2].
With the decreasing specimen size and invariant grain size, the share of surface grains increases, which leads to increasing ratio of free surface grain to all grains (Fig. 1).
The function can be differentiated as (4) The surface layer model has the limitation that the number of grains in the thickness or radial directions must be more than two, i.e..
For easier understanding, we give the definition as follows (5) Here, for micro sheet, N is the number of grains in the thickness direction.
For micro cylinder, N is the number of grains in the radial direction.

Monte Carlo simulation, of recrystallization and grain growth [1, 2].
Monte Carlo simulation of recrystallization and grain growth.
A number termed as Si was assigned to each lattice site.
Following the Saito and coworker’s research on the basis of diffusion-controlled mechanism of grain growth to convert simulation time (MCS) to real time (sec) [10-12], one can write: (8) where DGB is the grain boundary diffusion coefficient, d, the simulation lattice constant considered to be 5 µm in this simulation, and Q the number of all orientations in the simulation.
Acknowledgments This research was carried out under the project number MC 4.04203 in the framework of the Research Program of the Materials Innovation Institute M2i (www.m2i.nl), the former Netherlands Institute for Metals Research.

At the same times, the 0.125mm grain diameter raindrop speed was about at 0.6-1.4m/s, the 0.25mm grain diameter raindrop speed was about at 1-1.4m/s, the 0.375mm grain diameter raindrop speed was about at 1-1.4m/s, the 0. 5mm grain diameter raindrop speed was about at 1-3.4m/s, the 0.75mm grain diameter raindrop speed was about at 3.4m/s, the 1mm grain diameter raindrop speed was about at 4.2m/s, the 1.25mm grain diameter raindrop speed was about at4.2-5m/s, the 1.5mm grain diameter raindrop speed was about at5m/s.
Researchers carried out a large number of research about soil erosion on the Loess Plateau (Tang Keli, 2004; Chen Lei, 2002), both prototype test model test a large collection of information, and achieved fruitful results.
At abroad, soil erosion observation experimental had start early on 1915 in Utah, United States, observed the amount runoff and soil loss; 1917, Head of soil department University of Missouri, M.F.Miller imitation of the early German research built a number of experimental plots to study the factor quantitative work firstly.
At the same times, the 0.125mm grain diameter raindrop speed was about at 0.6-1.4m/s, the 0.25mm grain diameter raindrop speed was about at 1-1.4m/s, the 0.375mm grain diameter raindrop speed was about at 1-1.4m/s, the 0. 5mm grain diameter raindrop speed was about at 1-3.4m/s, the 0.75mm grain diameter raindrop speed was about at 3.4m/s, the 1mm grain diameter raindrop speed was about at 4.2m/s, the 1.25mm grain diameter raindrop speed was about at4.2-5m/s, the 1.5mm grain diameter raindrop speed was about at5m/s.
At the same times, the 0.125mm grain diameter raindrop speed was about at 0.6-1.4m/s, the 0.25mm grain diameter raindrop speed was about at 1-1.4m/s, the 0.375mm grain diameter raindrop speed was about at 1-1.4m/s, the 0. 5mm grain diameter raindrop speed was about at 1-3.4m/s, the 0.75mm grain diameter raindrop speed was about at 3.4m/s, the 1mm grain diameter raindrop speed was about at 4.2m/s, the 1.25mm grain diameter raindrop speed was about at4.2-5m/s, the 1.5mm grain diameter raindrop speed was about at5m/s.

Post-mortem material characterization of the grain structure was also performed.
Calculating the grain area along the length of the simulated results showed that when the number of seeds (No) was 100, the CET was observed at 14.3cm (143 mm in fig. 3(i)).
When the number of seeds was increased to 500 in the simulation, the CET occurred at approximately 13.7cm (137 mm in fig. 3(ii)).
The number of seeds used in the simulations was approximated.
The seed data used in the simulation was selected to demonstrate the qualitative effect of increasing the number of seeds (that is, the effect of adding a grain refiner).

Multiple grain reorientation as the distinguishing feature of ECAP.
Fragmentation of grains under ECAP.
The longer is the trajectory of grain reorientation, the higher misorientation accumulates within grains due to their non-uniform deformation and the more intense is resulting grain fragmentation.
A probability of grain fragmentation with formation of high-angle boundaries increases with the number of ECAP passes.
These displacements of grains result in their accidental rotations.

The microstructure of the material evolved during the process vary from columnar grain along the thermal gradient in the melt pool to fine equiaxed grains.
In their study, the number of Si particles were observed to have decreased with increasing solution temperature.
Material and Process Average Grain Size (μm) Hv0.05 LBPF Al [1] 6.0 ± 2 127 ± 1 FSPed Al 2.57 ± 1 64 ± 1 For specimens that underwent FSP, fine equiaxed grains were observed with significant grain refinements.
Recrystallisation and recovery of the material could have led to an increase in the number of sub-grain boundaries as observed in the EBSD images (Figure 3).
Material and Process Mean grain Misorientation Fraction of high-angle grain boundaries (>15°) Fraction of low angle grain boundaries (<=15°) Number of samples (1-5°) (0-15°) LBPF Al [1] 7.07 0.14 0.83 0.86 99709 FSPed Al 15.10 0.34 0.55 0.66 120740 Microhardness.

The quality of the grain by electrograining influences the quality of anodic oxide layer and photosensitive layer directly, and decides service performance of final product in the end.
The Evaluation Theory of Grain Quality of PS Plate At present, there are two kinds of the detection technology of grain quality: the one is to measure the situation of the grain on the surface by means of surface roughness dictator and surface outlook tester as shown in Table 1 and Fig. 1. the other is to check the grain surface visually by means of SEM and AFM [1]or metalloscope. the first method has been adopted by International Organization for Standardization(ISO), Deutsche Industrie Normen(DIN), Japanese Industrial Standards（JIS）and the Chinese relevant standards for its objectivity, and the other one has only been regarded as the additional means of auxiliary analysis in productions and Experiments on account of its more subjective effects.
Therefore the below article analyses the influencing factors of electro graining quality of PS plate by means of the detection technology which is the combination of the surface roughness tester and metalloscope.
Table 2 Factor levels of orthogonal experiment of electrograining Level Factor Electrolyte Concentration A [g/L] Electrolysis Temperature B [℃] Electrolysis Time C [min] Current Density D [A/dm2] 1 2.5 25 20 0.8 2 3.0 30 25 0.9 Table 3 Design of 4-factors L16(215)orthogonal table head Number of column 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 A B A×B C A×C B×C D A×D B×D C×D Experimental Results and Analysis The orthogonal experiment has had 16 times electrograining, and there have been 2 pieces of aluminium sheet in the same factor level.
That is to say, it can change depth but spacing of grain.

The synthesis of ultrafine-grained (UFG) materials is very attractive because small grains lead to excellent creep properties including superplastic ductility at elevated temperatures.
However, the maps have complications for construction due to the difficulties of estimating the curved field boundaries which require special calculation procedures to prepare a very large number of datum points in stress-temperature space.
This grain size was selected because, although the creep data came from the earlier published results demonstrating successful grain refinement of the high-purity Al from 1 mm to 1.3 µm through ECAP for 4 passes at room temperature, there is grain growth during tensile testing at 473 K [20].
Principles of superplasticity in ultrafine-grained materials, J.
Langdon, Deformation mechanism maps based on grain size, Metall.

Grinding process becomes very complex and difficult to analyze, because the distribution of abrasive grains is stochastic and abrasive grain geometrical shape is anomalistic.
Because the number of cutting points is large, cutting point geometrical shape is anomalistic, grinding velocity is high, every abrasive grain's cutting depth is small and inconsistent, especially the spark eject from grinding wheel, all of these make the process become elusory.
We know there are large numbers of cutting points whose geometrical shapes are inconsistent arrange irregularly on the surface of grinding wheel and their positions and directions are stochastic, So the cutting geometries of abrasive grains are different each other.
In order to make the simulation close to true grinding process, we should get a universal ubiety (abrasive grain 1 and 2. in Fig.2), the height of abrasive grain 1 is higher than the height of abrasive grain 2 and the abrasive grain 1 locate top left direction of the abrasive grain 2.
From Fig.5 we can see the area ABCE is cutting volume of abrasive grain 1 and the area BCD is cutting volume of abrasive grain 2.

The relatively large initial grain size permitted the identification of the fine DRX grains nucleated at the TJs of the original grains.
It is notable in Fig. 3 that TJ nucleation was already detectable at ε = 0.1 and that the number of new grains increased monotonically with strain.
In this strain range, no nucleation was observed either on grain boundaries or in the grain interiors.
Nature of grains nucleated The crystallographic orientations of the grains nucleated at the TJs at a strain of 0.2 were analyzed using OIM.
This revealed that more than 90% of the new grains had Σ3 relations with one of the surrounding grains, irrespective of the testing temperature.