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Three scales are thus considered namely: macroscopic (aggregate), mesoscopic (grain) and microscopic (slip system).
Using the incremental formulation (D), the stress – total strain relation at the grain scale is given by:
(2) where is the elasto-plastic tangent modulus (fourth rank tensor) at grain scale for undamaged material.
Moreover, grain rotation is calculated at each step in order to actualize the grain orientations (texture).
Calculations of this model have been performed with a stress step of 4MPa and a number of 20000 grains.

Power facilities being in operation and the ones that are newly introduced are characterized by a large number of welding works.
The proportion of grains with microtwins is 90%.
It should be noticed that in grains without microtwins sS = 425 MPa and sL = 325 MPa, in grains with microtwins sS = 410 MPa and sL = 315 MPa.
The volume fraction of the first type grains in the material bulk is 10%, grains of the second type – 5%, of the third type – 65% and of the fourth – 20%.
Dislocation structure in all grains of g-phase is polarized.

Therefore the remaining heat that is not utilized in track formation is transferred to the grains and grain boundaries by phonons.
Finally the number of atoms displaced is D= Ni(nRpA) ξ(z)av (12) where Ni is the number of ions that strike the surface; nRpA is the number of atoms directly affected.
Considering small grain volumes of the nanocrystals we suppose that the heat gets confined within the grain volume.
Further milling leads to large number of interfaces and reduction in size.
This happens as an increasing concentration of grain boundaries are being created while the grain size is reduced to smaller sizes.

The average grain sizes were determined by using the mean linear intercept method.
The raw data were obtained by measuring the grain sizes over 300 grains.
So, it can be inferred that this composition lies in the MPB, where the rhombohedral and tetragonal phases coexist, which could be matched with JCPDS file number 36-0339 and 36-0340 and corresponded to previous work [1,3].
The gas-filled pores combined and grew because of the grain growth [9].
The range of the average grain size increased with the increase of sintering temperatures.

The grain size of each sample was determined based on the average of 20 grain diameter measurements, aided by the MOCHA Jadell software program.
In sample A0 (Fig. 3a), note the homogeneous microstructure consisting of small approximately hexagonal grains with sizes ranging from 0.12 to 0.74 µm, and an average grain size of 0.31 ± 0.15 µm, as well as the presence of very small intergranular pores.
The micrographs in Fig. 3b and 3c, which correspond to samples A20 and A30, respectively, show a fine-grained morphology with low intergranular porosity, composed of irregular shaped grains.
This behavior can likely be attributed to the decrease in grain size in response to the introduction of HAp into the alumina matrix.
This introduction led to an increase in the number of grain boundaries (Fig. 3), thus increasing the barrier mechanism against applied stress and significantly reducing the intensity of this stress over the applied area by dividing it into a series of lower stresses.

Besides, more water and lower pH value led to larger grain of TiO2 sol.
Two kinds of grain shapes, fine particles of about several nanometers and large needle-like grains can be recognized.
The number of needle-like particles decreases with increasing pH (Fig.7a-c) and increases with decreasing R (Fig.7c-e).
It accounts for the decreasing number of needle-like grains with increasing pH.
The results indicate that the number of generated photoelectrons in the as-prepared TiO2 film is larger than that of the commercial sol film.

Introduction When an undamaged metallic material is subjected to cyclic loading, surface microcracks nucleate in slip bands or at grain boundaries, and with continued cycling the microcracks can growth crossing barriers and form cracks longer than one grain diameter.
Experimental procedure The material studied is the high nitrogen DSS SAF 2507 supplied by SANDVIK in the form of bar containing approximately equal volume fractions of austenite and ferrite as well as homogeneous grain structure with a grain size of approximately 10 µm in both phases, Fig. 1.
The cyclic tests have been performed with an incremental step test procedure until about 90% of the fatigue life (0.9Nf) and the surface damage has been monitored at different numbers of cycles by optical microscopy.
Finally, microcracks nucleate mainly in the austenitic grains after 9000 cycles (N/Nf=0.6).
In this process of losing edge dislocations, a rough surface is developing, which turns into extrusions and intrusions with the number of cycles.

By analyzing the metallographic structure we known that Local pressurization could refine Casting organization grain and make the grain more dense.
When the injection speed is too low, mold-filling capacity descend[2].when pouring temperature is excessive, the castings solidification shrinkage rate is large, this phenomenon predispose castings to cracks and make castings grain coarse inside. when pouring temperature is too low, leading to cold shut and surface crack defects[3].
Deriving the die casting of the entity model through STL pattern from UG7.5,in order to reduce the computing time , the casting are meshed by variable meshing module. the model grid nodes is 373194, the unit number is 3452544.
As be seen from the figure 10,many white petals dendrite are primary α solid solution, interdendritic is (α+ Si) eutectic, gray eutectic Si display small strip, the dark grey deformation small block is primary Si, the light gray small block is Al2Cu , a small number of black needle is β phase.
It is a project supported by the Guizhou technology committee industrial public relation project (project number: Guizhou province 2012, NO.3004) and Guiyang Industrial Public Relation Project (project number: Guiyang 2012, NO.101-2-13) References [1] Jincheng Chen, Chunquan Zhai: Special Casting And Nonferrous Alloys.

The sintering temperatures and samples number are separately shown in Table 3 and 4.
The grains in (a) and (b) are smaller and more uniform in size, while in (c) large grains appears.
Therefore, the grains are large.
（2）With the increase of CaO content, large amounts of liquid is produced, promoting the crystal growth and uniform grains.
Sintering and grain-growth kinetics of MgAl2O4.

From XRD and SEM results, all samples have a crystal structure delafossite-typeand a large grain boundary more than 15 μm by electrical conductivity corresponds to grain boundary and lattice parameter: a increases.
The first step, the polycrystalline of CuFeO2 samples examined by XRD measurements, the XRD patterns of all CuFeO2 exhibited in the Fig. 1 shows phases of 3R-CuFeO2 type by confirmed by standard JCPDS card number 39-0246.
The grain size and lattice strain are given in Table. 1.
Firstly, electrical conductivity dependent to grain boundaries, namely electrical conductivity increases with the growth of grain boundaries.
Firstly, electrical conductivity depends on grain boundaries.