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The strain-free partially-melted specimen exhibited complicated grain morphology of the primary α-Al grains.
In Fig. 2 (B) and (C), fine secondary α-Al grains and eutectic structure surrounding the primary α-Al grains are observed.
The cold compression deformed dendritic α-Al grains and introduced large number of dislocation.
And then the eutectic structure surrounding spherical α-Al grains begins to melt and the liquid penetrates along grains’ boundaries.
This devides α-Al grains into small pieces.

Making use of uncertain number, triangular fuzzy number method can overcome the ambiguity of index attribute and its value, as well as the limitations of human thinking.
The Concept of Triangular Fuzzy Number.
The definition of Triangular Fuzzy Number is as follows: if , and , then is called triangular fuzzy number.
Each element of judgment matrix is the triangle fuzzy number.
When calculated the number, a new matrix can be formed by the intermediant value() of the triangle fuzzy number.

The optical microscope Leica was used for determining the grain number.
As one can see from table 1 the average grain number in the metal before its deformation by the present day and the proposed technologies corresponds to 5-6 numbers.
The microstructure of U-8 steel after its deformation in the flat dies corresponds to the structure of sorbite - a variety of pearlite, the grain size in the longitudinal direction corresponding to 6-7 numbers in the axis zone and 7-8 numbers in the surface zone.
In the cross direction the grain size in both the axis and the surface zones is 7-8.
During deformation of billets by the proposed technology, i.e. in the tool with elastic elements realizing the and the longitudinal shear in the billets the grain size in all the directions corresponds to 9-10 numbers with noticeable equiaxity both in the surface and the axial zones.

The typical samples were numbered according to its transparency, semi-transparent, sub-transparency and opaque, respectively.
The polished samples and the respective number were shown in Fig. 1.
If the crystal grain arrangement is not close, there is some porosity between crystal grains.
The grain arrangement of No. 7 is rather disorder while the grain arrangement of No. 15 is very close.
The better grain arrangement leads to the less porosity between grains and the better transparency.

The TSS prevented the grain growth keeping your submicrometer grain size. 1.
The monoclinic structure of the zirconia phase can be stabilized in the tetragonal or the cubic form by the addition of dopants such as CaO, MgO, Y2O3, Sc2O3, Yb2O3 and a number of additional rare earth oxides[7].
At medium and lower temperatures, e.g. 550–800ºC, the YSZ electrolytes with a submicrometric grain size, have higher conductivities than others with a micrometric grain sizes [9].
Materials with submicron grain structure can be obtained from nanometric powders.
As shown in Fig. 4 all the samples presented grain size below 1 mm.

The decline in plasticity is significantly supported by the precipitation of (FeMn)S particles and their distribution along the boundaries of austenite grains, which are thus weakened [10,11].
Particles occurring at the grain boundaries act as nuclei for the formation of cavities.
According to [16], the main problem of material embrittlement is the precipitation of sulphides (Fe, Mn) S and oxisulphides in globular form along the borders of austenitic grains.
Plasticity was assessed by counting the number of turns to failure Nf.
Fig. 1 Temperature dependence of number of turns to failure for TiNb IF steel samples after hot torsion test Other minimum plasticity point with the number of turns to failure 6.2 (sample X7) was also observed at 946°C.

As the strain rate increases (or as the temperature is reduced), the number of peaks on the stress-strain curve decreases, and at high strain rates, the stress rises to a single peak before settling at a steady-state value.
With an increase in the strain rate, however, the difference in stress between recrystallizing and old grains diminishes, resulting in reduced driving force for grain growth and rendering smaller grains in the alloy.
There are a number of non-linear differential equations which may provide similar oscillatory behavior in their solutions, and thus it doesn't seem terribly meaningful to draw physics from Eq. (5).
If we take l as d/2, d being the mean sub-grain size, and D ~ 7.7x10-16 m2/sec (for γ-Fe at 1100 oC [16]), the incubation times from 0.09 to 45.5 sec suggest mean sub-grain sizes from about 17 to 374 nm.
One scenario could be that the sub-grain boundaries produced during hot working are strain-rate sensitive and thus the average sub-grain size may increase with an increase in strain at certain strain rates [18].

The grain size distributions follow a normal logarithmic distribution with a positive skew, i.e. there are smaller grains than large ones12.
The intrinsic coercivity is a logarithmic function of the average number of surface defects per grain and, hence, on the average grain size13.
Table 2 lists the mean grain size, elongation, roundness and respective deviations used to analyze the homogeneity of the Pr15FebalCo8B7Nb0.05Mx HD sintered magnets varying atomic number (Z) of the addition elements.
Table 2 - Mean grain size, elongation, roundness and respective standard deviations for the sintered Pr-Fe-Co-B-Nb-M permanent magnets varying atomic number (Z).
Figure 4 shows the variation on the various squareness factors as a function of the atomic number (Z) of the addition element.

It is concluded that the HTBD is related to the microstructure observed inside the grains and does not dependent on grain size.
The ultrafine grained or nanograined structures formed from SPD are a granular type structure containing mainly high-angle grain boundaries (HAGBs).
The number of atoms involved in relaxation process may be increased when temperature is raised.
Therefore, the HTBD should be related to the inner parts of grains and independent of grain sizes, which is in agreement with the results reported in [10].
The HTBD is related to the inner parts of grains and is grain size-independent.

Pinus sp.specimens: (a) parallel, (b) 45º and (c) normal to the grains.
Number of specimens, for each situation, is denoted by x.
Embedment strength fe0 fe45 fe90 x 12 12 12 Xm 22 13 7 Sd 4,50 3,30 2,60 CV [%] 23 28 43 Result analysis shows higher values ​​of strength in the direction parallel to grain, and lower in the parallel to the grain.
Failure modes: (a) crushing in hole wall of wood piece; (b) cleavage in grain direction.
The direction parallel to grain led the greater wood strength to embedment of bolts, and perpendicular to the grain the smaller, considering Pinus sp.