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The number of cycles and corresponding fatigue crack length are recorded.Incremental polynomial is used to determinate the crack propagation rate ().
Grain boundaries play an important role in hindering the further propagation of plastic zone.
Fig. 8 Determination of of the critical points (1#) After determining of the critical points, the fatigue crack propagation length in near-threshold zone can be obtained from the corresponding fatigue crack propagation rate and cycle numbers at different test points in the near-threshold zone.
The equivalent diameters of 3~4 prior austenite grains at each critical point are measured, and the average is taken as the corresponding prior austenite grain size .
Relationship between Size of Plastic Zone and Prior Austenite Grain Size 5.1 Size of Plastic Zone at Critical Points.

The simulation results showed that the greater the restored energy, the greater the number of the recrystallized grains.
In order to simulate grain growth in a single-phase system, only the free energy density function f0 is required to provide a certain excess free energy at the grain boundary.
The parameters of the gradient term K2 and the coupling term K1 have been determined by the grain boundary energy and the grain boundary range.
The smaller grains shrink until they are absorbed by the surrounding grains, and the grain morphology remains relatively stable during the growth process, which is consistent with the main characteristics of grain growth.
On the other hand, the greater the restored energy, the greater the number of the recrystallized grain.

Grain Potential Productivity of Cultivated Land in Baoji, Shaanxi Province, China Tuansheng Lia, Haohao Wu,b , Hongzhi Zhaoc College of Earth Science and Resources, Chang’an University, Xi’an, Shaanxi, 710054, China atuanshen@chd.edu.cn, bwhh_xkp@yahoo.cn, c247911938@qq.com, Keywords: grain potential productivity; agricultural land classification; Baoji Division Abstract.
Many scholars have made a large number of researches about the crop photosynthetic potential productivity, photo-temperature potential productivity, climatic potential productivity and land potential productivity from different angles ever since.
In the agricultural land classification, the natural quality index of a classification unit is theoretical standard grain yield got by land conditions of a classification unit revising the photo-temperature (or climatic) potential productivity of the crops, and converted by grain yield ratio coefficient.
Therefore, the utilization quality index of land is a standard grain yield that can be got by increasing investments and use level.
Result analyses The grain potential productivities of cultivated land of Baoji are shown in table 1.

In grain A, fine cracks and small cleavage steps existed, the cracks were propagated from grain A to grain B, altered the propagation direction at the hindrance of grain boundary, and finally led to increase the steps height in grain B.
The fracture was serrated and the number of mechanical twins in grains at −196 °C was less than at 25 °C.
The low temperature plasticity at −196 °C may have relation to the activation of new slip systems which suppress the occurrence of twinning, because the number of twins at −196 °C was obviously less than at 25 °C(see Fig. 4(a)).
The twinning can easily occur in the pyramidal planes }1110{ or 1}2{11 at beginning of plastic deformation, so that the number of twins at 250°C is the most in the six tensile temperatures, and when the deformation temperature is enhanced to 300 °C or 350 °C and the number of twins decreases or even to zero.
Due to the strength of the interior grain at 400 °C is higher than that of its grain boundary, the deformation can not reach interior grain easily by slip, but the stress can induce the nucleation of twinning on grain boundaries and the twinning further extends to interior grains.

The as-extruded alloy bars retain equiaxed grains with a large number of precipitated phases, β-Al12Mg17 and AlMg2Zn.
The grain size is about 2 mm.
Many small precipitates distribute on the grain boundaries and inner grains.
There exists a large number of dimples, some cleavage steps and small tearing cracks on the fracture surface, which suggests toughness fracture feature.
A large number of precipitates (β-Al12Mg17 and AlMg2Zn) with a particle size of about 200nm occurred during hot extrusion, which distribute along the grain boundaries and throughout the interior of the grains

Brewer's grains is the main by-product of beer industry.
In this work, the waste brewer's grains has been modified through physical and chemical methods to generate suitable biosorption material.
The adsorption conditions was also studied so as to utilize the brewer's grains as the low cost material for Cr(VI) wastewater purification and the brewer's grains reutilization, then the results would be the theoretical basis for the comprehensive utilization of the material.
Material and Methods Reagents and instruments Preparation of modified brewer's grains biosorbent:The brewer's grains was from the bee laboratory in our school, washed with tap water, and broiled in 0.5 mol·L-1 sulfuric acid for 24 h.
And the 60-80 meshes of brewer's grains were selected in further experiments.

Thus, anisotropic grain interaction occurs.
(5) Note that the ( , , )ijF hklψϕ are not components of a tensor since they relate the lattice strain (a number) to the stress tensor (expressed in the S-system).
For the following discussion such an average of (extreme) grain-interaction models will be called an effective grain-interaction model.
The number of grain-interaction models of extreme types of grain-interaction assumptions is two for bulk materials (Reuss and Voigt).
• For extreme grain morphologies (flat discs and needles), the grain-interaction in the EshelbyKröner model exhibits similarities with the grain interaction in the Vook-Witt and inverse Vook-Witt models, respectively.

Work piece for CCB was machined parallel to rolling (RD) with a 300mm length, a 20mm width and a 1.5mm thickness, and then was cyclic-bent continuously up to the maximum number of passes, �CCB=40.
The formation of coarse-grained layers was observed also in A5083Al.
Consequently CCB and annealing enable to make coarse-grained surface layers of controllable thickness with number of the CCB passes.
The coarse-grained layer likely retarded corrosion.
The coarse-grained layers had a high corrosion resistance.

The grain site can be assumed one of those states, qgrain = [1, 2 …Q] where Q is the total number of all sites in the simulation space, and q represents the state of a grain site.
A random number, Rg, which is between 0 and 1, is generated.
While simulation, generate a random number, R, which between 0 and 1.
A random number, Ra, which is between 0 and 1, is generated at random.
The grain size R is defined as the radius of the equal-volume sphere of one grain, the surface of total pores is the summation of the number of grain neighbors of each pore site, and the surface of total grain boundaries is the summation of the number of grain neighbors of each grain site.

Introduction Grain boundaries act generally as diffusion short circuits; consequently, the major part of material transport will occur by grain-boundary diffusion in nanomaterials where a large amount of atoms can lie on grain or interphase boundaries (50% for a grain size equal to 5 nm; 20% for a grain size equal to 10 nm).
It is well known from classical treatments of grain or interface diffusion that there are three different grain-boundary diffusion regimes in coarse grained crystals: type A, B and C.
We will see that there is an increasing number of new experimental evidences that the above diffusion coefficients agree very well with each other, i.e. in most of the cases the structures of relaxed grain-boundaries in nanocrystalline and polycrystalline samples are very similar.
-In A kinetic regime (Dv t)1/2 >> d), the different diffusion zones overlap each other resulting in a macroscopic homogeneous diffusing distribution which appears to obey Fick's laws as for a homogeneous system with an effective diffusion coefficient (Deff) equal to an average of Dv and Db weighted in the ratio of the number of diffusing atoms in the grains to that in GB [6]: Deff = g Db + (1-g) Dv, (2) 4 Title of Publication (to be inserted by the publisher) where g is the grain-boundary volume fraction (g � �/d; the factor of proportionality depends on the grain shape, but is in the order of unity).
In effect, owing to the number of GBs and the synthesis conducted under UHV conditions, the grain boundaries must be purer in the first type of materials if one excepts the contamination during the preparation (specially by oxygen) and supersaturated metastable nanocrystalline solid solutions.