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A fine grain structure with an average grain size of 3–17 mm was obtained by static recrystallization.
The average grain size of the specimens used in the previous studies was approximately 80 mm.
The notation used to refer to the specimens is summarized in Table 2, where the numbers following “d” represent the average grain size of the alloys.
Regardless of grain size, the value of fe was decreased by LTHT.
Acknowledgements This study was financially supported by the Japan Society for the Promotion of Science KAKENHI [Grain number: JP 19K23580, 18H01718 and 16J04279] References [1] F.

The modification has obvious refining effect on primary silicon and eutectic silicon grains, electromagnetic stirring has refining effect on primary silicon grains, and eutectic silicon grains appear coarsening phenomenon.
Thus, eutectic silicon grains change from coarse needle flake to fine dot shape.
It can be seen from the figure that with the increase of the constant temperature time, the primary silicon grains in the aluminum silicon alloy increase and the number decreases.
Electromagnetic stirring can refine and passivate the primary silicon grains, but coarsen the eutectic silicon grains.
Räbiger, et al., Grain size control in Al–Si alloys by grain refinement and electromagnetic stirring, J.

The grain size increased dramatically in the center of fusion zone and the grain grew perpendicular to the fusion line at the boundary of the fusion zone that compared to the base metal.
The coarse grain zone of the base material was near the interface to the fusion zone.
Adjacent to the coarse grain zone was the fine grain zone.
Lower the heat input by means of increasing the welding speed conduced to the reduction of grain size in the fusion zone and coarse grain zone, which was beneficial to the improvement of the microstructure of the joint.
HAZ FZ BM Fig.5 Microhardness profile of the joint Table 4 Welding parameters used in the experiment Sample number 1# 2# Tensile strength(Mpa) 280 301 Summary A good appearance and defect-free joint of QCr0.8 bronze can be obtained by electron beam welding.

While both grain sizes and density of sintered samples were found increased from 1.4 μm to 2.46 μm and 90% to 98%, respectively.
The quantitative analyses were carried using the Rietveld method in Xpert Highscore Plus software to further clarified the number of phases formed accurately (as per Table 2).
The average grains size were observed 2.46 um.
Fig. 4: Average grain size of YAG with different sintering hour Density measurement: The relative density and grain growth of sintered YAG at various sintering temperatures and is shown in Fig. 5.
It is generally known that both the average grain size and density proportionally increased with longer holding times.

This value decide about number of generated defects, which are with increase deformations changing theirs localization, which leads to creating new nanometric size grains.
When deformation value are bigger fragmentation grain process is much more slower and strives to specified grain size limit.
Increased number of passes to obtain required results, samples were subjected up to 9 ECAP passes.
As much as grain size and type of grain boundary depend on material properties and process conditions.
To compare grain sizes after the same number of passes and the same section (Figure 1c, 1d, 1e and 1f) are shown.

And for stable Goss oriented grain, the orientation gradient increased slightly, but for meta-stable cube oriented grain, the orientation gradient increased dramatically.
And in spite of the same Taylor factor for both oriented grains, the dissipated averaged energy for cube oriented grain was higher than for Goss oriented grains, and the distribution width of dissipated work in cube oriented grain was also wider than that in Goss oriented grain.
With quaternion as orientation representing parameters [10, 12], the parameter mθ for describing intra-granular inhomogeneous deformation can be defined as following: ( )( ),i m i n θ θ =∑ q a (1) where ()iq is quaternion of the ith part in the grain, a is the quaternion of average orientation, n is total number of parts in the grain, ()( ),iθ q a is the misorientation between the ith part and average orientation. θm=0 means that the grain orientation is absolute uniform.
And even some parts of the grain rotated along two opposite directions, i.e., grain subdivision occur during plain strain compression.
The distribution width of PD in cube oriented grain is wider than that in Goss oriented grain.

By contrast, in the work of Xia et al. [11] the nanostructured martensite in Cu-Al alloys obtained by high-pressure torsion (HPT) decomposed to an ultrafine-grained duplex equiaxed grain structure more quickly than in conventional martensite with large lath widths.
The present investigation was conducted to examine the evolution of the structure and the phase composition of the Cu-Al alloy subjected to HPT under different numbers of rotations.
Figure 1(a) shows the as-received sample with an average grain size of ~1 mm.
For the HPT-processed samples, the microhardness becomes higher because HPT leads to a refinement of the grains [12, 14].
It means also that decomposition of the nanostructured martensite includes inhomogeneous nucleation and grain growth.

According to [10-13] the optimal values aopt, mopt, hopt are determined by the equation: aopt = 2.1×(1+nSdS/dCS)3–1.1; (1) mopt = 2.1×(1+nCdC/dS)3–1.1; (2) hopt = 2.1×(1+dH/dC)3–1.1, (3) where dCS, dS and dC are average grain sizes of coarse and fine aggregate and cement particles, respectively, mm or μm; nS, nC are the number of densely packed rows of grains of fine aggregate and cement particles, respectively, between grains of coarse and fine aggregate; dH is the width of the densest layer of cement hydration products between clinker insoluble particles, μm.
Let us suppose that the densest structure of the hydration product layer between clinker insoluble parts with the maximum number of electro- heterogeneous contacts s contacts consists of two rows of ettringite crystals, grown towards each other on the surfaces of cement particles or aggregate grains (Fig. 2, d), dG in (3) can be taken as 2×0.5 = 1 μm.
а) b) Fig. 4 Study into crack resistance of concrete under dynamic effects: the test sample of the rail base mounted in the testing machine MUP-50 The vertical loading on a rail had a frequency of 8 Hz, a force range of 100-235 kN, and the total number of cycles was 1.5 million.
A value of m specified corresponded to a width of the cement stone layer between fine aggregate grains of 20 μm according to equation (5).
The actual coefficient of grain separation of coarse and fine aggregate, and water-to-cement ratio to the optimal values aopt = 1.30, mopt = 1.27, W/Copt = 0.23, respectively, and a width of the cement stone layer between grains of fine aggregate 20 μm in C40/50 concrete provided the maximum values of physical and mechanical properties of concrete.

It can be seen that the number of cleavage planes of Alloy Ⅰ is higher than Alloy Ⅱ.
However, the number of dimples shows the opposite trend.
The curves of crack length versus the number of cycles (a-N curves) are presented in Fig. 3(b).
It can be seen from Fig. 5(a, c) that fine recrystallized grains ( the green part in the picture ) are scattered in the alloy and the number is small.
In general, the FCP rate is smaller for alloys with coarse grain size than for those with fine grain size.

The present study was undertaken to explore the possibility of further grain refinement by increasing the number of passes and lowering the temperature of deformation in subsequent passes, and the associated texture development.
After 1 pass of ECAE, the grain size reduced to 6 µm.
The grain size distribution was found out to be unimodal.
The strength of texture fibers was analyzed through f(g) vs. number of ECAE passes (Fig. 7).
Editors, Ultra fine grain Materials II, Warrendale, PA: TMS, 2002, 643