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In present model, deformation in macroscale is transferred to meso-scale, where a representative element contains several, score or hundreds grains, and then is applied in micro-scale to each grain.
Deformation in macroscale is transferred to meso-scale, where representative element contains several, score or hundreds grains, and then is applied in micro-scale to each grain.
The microstructural part calculates the grain refinement during the cold deformation.
Each cell represents small volume that contains many dislocations and number of dislocations or their density is used as parameter of the cell.
For the other slip direction 1D CA is decomposed on such number of 1D CA how many parts were cut by LABs.

In addition, the final texture in the microstructure depends strongly on the number of template particles [4].
Randomly-oriented polycrystalline KSN ceramics show inferior electrical properties compared to KSN single crystals due to abnormal grain growth that inhibits densification [9], limited number of polarization directions [8] and averaging of electrical properties.
There are limited number of results on textured KSN ceramics.
A duplex microstructure consisting of mm-sized grains together with smaller grains develops in the N1-T0 (Fig. 5a).
Template particles controlled matrix grain growth and, therefore, no cracking or abnormal grain growth were observed in the samples textured by TGG.

Optimum Pass Design of Bar Rolling for Producing Bulk Ultrafine-grained Steel by Numerical Simulation Tadanobu Inoue National Institute for Materials Science, 1-2-1, Sengen, Tsukuba, 305-0047, Japan INOUE.Tadanobu@nims.go.jp Keywords: Rolling, groove design, finite element analysis, ultrafine-grained structure, strain distribution, low-carbon steel Abstract.
The groove design for creating ultrafine-grained low-carbon steel through a caliber rolling process was studied from the viewpoint of the large strain accumulation and cross-sectional shape variation in a bar.
The optimum pass schedule to fabricate a 13mm square bar of ultrafine-grained steel from a 24 mm square bar by caliber rolling at warm working temperatures was proposed.
Introduction Refinement of crystal grains is an effective method for developing toughness and strength in steels without the addition of alloying elements by controlling the thermomechanical treatment.
Since a large strain is needed for creating ultrafine-grained (UFG) structures, various severe plastic deformation processes have been proposed [1].

Multiple scattering theory for acoustic waves, proposed by Foldy [5], was represented following heuristic integral equation by Lax [6], , (1) where is conditional number density of scatterers at if a scatterer is known to be at , and is a T-matrix.
Grain size distribution of each sample of S3 and S5 Table 1.
For the bimodal grains, however, dispersions are slightly different.
And the attenuation of larger size grains increase more steeply.
For, grains can be considered as scatterers.

Optimization of Process Parameters for Unidirectional Solidification of Magnesium Alloy Ming Chen1,a Xiao-Dong Hu1,b Hong-yang Zhao1,c Dong-Ying Ju1,d University of Science and Technology Liaoning, Anshan, China 114051, 1a:cchen552@163.com,1,b:hulinas@sohu.com,1,c:zhy@ustl.edu.cn,1,d: dyju@sit.ac.jp Corresponding author: Dong-Ying Ju, E-mail: dyju@sit.ac.jp, Phone:86-412-5928052, Fax : 86-412-5929554 Keywords: unidirectional solidification, finite element method, phase field, columnar grain Abstract: The unidirectional solidification process of magnesium alloy needs to establish a specific temperature gradient in casting mold, the direction of crystal growth and heat flow are in the opposite direction in the unidirectional solidification.
The process can better control the grain orientation, and eliminate the horizontal grain boundary to obtain excellent performance of magnesium alloy.
(5) (6) The parametermeans the strength of anisotropy and is a mode number of anisotropy, for the magnesium alloy we assign the value of 6 to.
For the constant value of , which is according to the macro analysis result when cooling intensity is ~5000W/m2k and pulling speed is 0.1mm/s, we can see the developed columnar grain structure.
For the constant value of , it can be seen that the columnar grain structure is more developed, through the comparison of different value of , it can be known that the higher cooling intensity is, the more developed the columnar grain structure is, but it is hard to make the value less than 1.5 in the actual process, that needs very large cooling intensity.

Results Grains will grow up gradually and be well spheroidized during the resting process after stirring, but long time resting may make the grains coarsening.
Concave parts of the grains were filled up due to atom diffusion.
The reason is tiny grains with low melting point melted and disappeared, and large grains survived and grew.
Fig. 3 Micrographs of semi-solid slurry with different resting time (a) 0s (b) 30s (c) 60s (d) 90 s Discussion Large numbers of well-ordered clusters will be formed in the melt because of structure and energy fluctuation existing in molten metal.
At last, spherical grains were formed.

The number of “effective” crystallization contacts is determined from the correlation of approached particles sizes and a number of particles of different size in a dispersive system.
The optimal structure providing maximum of contacts is formed under the condition of one grain of small size being placed between grains with greater sizes.
Small sized grains fill in porous space like liquids since they easily pass through big-sized.
The optimal granularity ensures the most compact packing in a unit space with maximum of contacts of varying-sized grains(see Fig. 8 a).
The equations for the coordination number in disordered systems.

Four of the packets exist along the prior austenite grain boundaries and one packet grows from the boundary edge into the prior austenite grain.
White broken lines indicate the austenite grain boundaries.
Figure 3 shows 3D images of incipient-formed lath martensite regions in a prior austenite grain, corresponding to the prior austenite grain in Fig. 1.
The prior austenite grain shown in Fig. 3 has five packets in the prior austenite grain.
The number of incipient blocks with rule 1, which is the same as rule i+ii in Ref. 2, was consistent at a ratio of three over seven.

Effect of dip coated speed, number of coated cycles and annealed temperature on films properties were investigated.
The optimum condition for film preparation was at dip coated speed of 0.12 cm/s, number of coated cycles of 20 cycles and annealed temperature of 500 ºC.
Surface morphology of the TiO2 films formed grain that look like knobby shape.
Each grain was separate off and showed sharp grain boundary trace.
Surface morphology of TiO2 film formed grain in nano-grain size in the range of 10-50 nm.

Introduction At present, the earth experiences a large number of earthquakes every year, causing huge damage to human life and property.
The grain size of ferrite was coarse, with some hybrid crystal phenomena, and the average grain size was only 5.0.
This was due to the relatively low reddening temperature after the roll, which increases the cooling rate of the sample, and the fact that the grains were too late to grow, and therefore more fine grains were obtained.
The internal structure of rolled 1 # steel contains a large number of mixed crystals, and normalization at different temperatures will still lower the overall mechanical properties of the material.
The grain sizes were 8.0-8.5 grades, respectively.