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In the EBSD grain boundary maps, green lines and red lines show high angle grain boundaries with misorientation angle (q) larger than 15° and low angle grain boundaries having misorientation 2°≤q<15°, respectively.
The mean grain sizes of the specimens are 40 µm ~ 50 µm.
The average grain size of the specimen deformed at 100 s-1 is 10 µm, which is a fairly fine grain size.
The mean grain size (thickness) is 200-300 nm.
The equivalent strain determined by equation (2) becomes much smaller than Hencky strain at high strain regions, so that Hencky strain rate decreases with increasing rotation number in the present torsion test using constant rotation speed.

There are limited number of studies were dealt with examination of the Hall-Petch relationship in Al-Mg alloys.
Distinct areas of fully recrystallized grains with an average size of ~1 mm alternate with unrecrystallized grains (Fig.3b).
The formation of low number of deformation-induced LABs takes place in this strain interval.
Experimental datum points were fitted to straight line with a high accuracy (Fig.6) despite a great difference in dislocation density and density of LABs between deformation structures produced by different number of passes.
Lee, W.J.Nam, Microstructures developed by compressive deformation of coarse grained and ultrafine grained 5083 Al alloys at 77 K and 298 K, Mater.Sci.Eng.

Obviously, the ECAP process refines the grain.
As shown in the Fig. 1, the ECAP processing refines the grain.
On the other hand, the number of grain boundary is increasing with ECAP processing, which lead to the increasing number of sensitive site for pitting corrosion.
Thus, the corrosion resistance of specimen is decided by the competition between the current magnitude of glavanic cell and the number of glavanic cell.
The superiority of grain boundary is weakened.

Multi-fractal theory is used to detect fractal behaviors embedded in grain size distribution ofsinter with low SiO2.
Finally, we sieve the powders, and measure the grain size distribution,as shown in table 1.
Table 1 Effects of SiO2, carbon, basicity, and MgO on grain size distribution Multi-fractal analysis.
Let us consider a large amount of grains with different diameters.
One can filter out the grains whose sizes are less than ε, and record the number of left ones, denoted with N(ε).

The contact area and the applied normal load are used for calculating the hardness number.
The model consists of an indenter, the surface grain in contact with the indenter, and the rest of sample in contact with the given surface grain.
Due to this load the indenter and grain approach a short distance δ1, and the rest of sample and grain approach a short distance δ2.
If the indented surface grain is strongly bonded to the rest of sample, the indentation modulus becomes equal to the Young’s modulus of the grain’s material.
Eg represents the Young’s modulus of the grain’s material.

Takao et al. [7] found two features of slip band in a grain of carbon steel: it was nearly equal to the grain size at early stage of fatigue process; and its length did not change during the fatigue process.
N and Ni mean number of cycles and fatigue crack initiation cycles, respectively.
In this study, fatigue crack initiation is defined when the fatigue crack in a grain reaches a grain boundary and starts growing in Mode I.
Therefore the grain size can be defined as the initial crack size in carbon steels.
(2) Prediction error from empirical σw1 value increase with increase in grain size.

The number of simultaneous cutting edges.
The square endmill used experiment is 8-flute with a diameter of φ6mm (MOLDINO ES8WB0600LN), with the 38degrees Helix angle, TiAlN coating and made of ultrafine grain cemented carbide.
Next, the effect of number of endmill flutes is examined with the constant number of simultaneous cutting edges.
All were in the same condition: φ6mm square end mills, Helix angle 38degrees, TiAlN coating and made of ultra-fine grain cemented carbide.
Secondly, while keeping the number of simultaneous cutting edges, the number of flutes in endmills was changed to examine the number of flutes with the best accuracy.

The fatigue test was interrupted and DCT imaging was conducted at certain number of cycles.
Figure 5(a) shows that mode value of grain spread orientation, where the frequency takes the highest value, stays unchanged against the number of cycles.
To examine the difference of the grain orientation spread by crystallographic planes and grain orientation, changes of the value of Δωdiff with number of cycles is shown in Fig. 5(b), where the plane indicates crystallographically equivalent plane.
Since the number of grain orientation spread in the monotonic tension tests is larger than that in fatigue test, high stress in the monotonic tension test must activate many slip systems on grains, while low stress in fatigue tests induces activate only primary slip system on particular grains.
This work was supported by JSPS KAKENHI Grant Numbers 23360056, 25420017.

The fatigue test was interrupted and DCT imaging was conducted at certain number of cycles.
Figure 5(a) shows that mode value of grain spread orientation, where the frequency takes the highest value, stays unchanged against the number of cycles.
To examine the difference of the grain orientation spread by crystallographic planes and grain orientation, changes of the value of Δωdiff with number of cycles is shown in Fig. 5(b), where the plane indicates crystallographically equivalent plane.
Since the number of grain orientation spread in the monotonic tension tests is larger than that in fatigue test, high stress in the monotonic tension test must activate many slip systems on grains, while low stress in fatigue tests induces activate only primary slip system on particular grains.
Supports of this work by Grant-in-Aid for Scientific Research (B) by the Japan Society for the Promotion of Science under proposal number of 23360056 (Head investigator: Professor Y.

The growth grains is directly related to diffuse mass transport along grain boundaries from the regions under the compressive stress to condensate at the surface and combines with adjacent grains and forms secondary grain growth[4],[5].
With the grains growing, the mean surface roughness has been increasing significantly.
For DC magnetron sputter deposition, substrate is only as a carrier to receive the sputtered atoms, and the number of sputtered atoms is merely relationship with energy and density of Ar+.
That is the characteristic of the substrate, such as substrate temperature, can not determine the number of sputtered atoms.
The grains are growing and the surface is performing rough with heating the substrate.