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Furthermore, the Betti numbers b0 and b1 decreased with crack growth, and especially the Betti number b1 had a strong correlation with stress intensity factors [8].
Fig. 6 Relation between the Betti number, b1 and cut-off threshold value.
This result is applicable to the fracture surface whose asperity colony is larger than the original grain size.
This analysis was carried out where the asperity colony size is larger than the material original grain size.
Nakane, The Betti number of prior austenite grain of repeated quenching bearing steels (JIS, SUJ2), Advanced Materials Research, Vol. 1082, pp 191-196. (2015) [8] M.

The results showed that the cellular dendrite of the general cast-rolling magnesium strip was coarse, the grain structure was heterogeneous and the average grain diameter was between 50μm~60μm.
However, the grain structure became more homogenize after the ultrasonic treatment for cast-rolling magnesium strip, the grain was refined and the average grain diameter was between 20μm~30μm.
Table 2 Experimental parameters Number Ultrasonic power /W Melt temperature /℃ The former case temperature /℃ Casting speed /(m·min-1) Thickness /mm 1# 0 690 675 2.7 3.8 2# 500 690 675 2.7 3.8 In order to obtain the appropriate mechanical properties, the two states of cast-rolling magnesium strip tensile specimen were intercepted from the horizontal, vertical and 45º direction.
Therefore the nucleation rate was enhanced, which conducive to grain refinement.
Fig5(b) shows that some of dendrites are peeled off, the grain is fined, the grain is elongated in the rolling direction, plastic deformation is very obvious.

The high shear solidification resulted in a fine and uniform grain structure with b-TCP particles evenly distributed in the matrix in clusters of 5-20 mm in size.
A fine and uniform grain structure was obtained after casting with an average grain size of ~23 mm (Fig. 1a), largely attributable to the high shear prior to casting.
After 1 pass ECAE, the initial grains were subdivided due to simple shear flow along the extrusion die shear plane.
The characteristic dimension for overall subgrain/grain structure was estimated as to be ~2.3 mm after 4 pass ECAE, facilitated by the formation of grain boundaries due to dynamic recover during ECAE.
ECAE samples exhibited higher values than that of the as-cast state and the hardness increased with increasing number of ECAE passes.

The number of primary Si increases obviously and the average grain size of primary Si decreases largely, less than 50μm.
Also the number of the primary Si particles increased significantly and the average grain size of primary Si decreased substantially(shown in Table.3）.
This is because that a large number of AlP compound had formed in Al-Fe-P master alloy, which has a lower melting point.
So the average grain size of primary Si maintains 40μm or less in 5 hours.
The number of primary Si increases obviously and the average grain size of primary Si decreases less than 50μm respectively.

Alemdag et al. [1] observed that the higher strains and the number of passes used, the better the material properties became.
Temperature affected the grain growth while the strain affected the deformation and the dislocation of the grains, resulting in a reduction in the size of the grains.
At the initial stage of deformation, the grains were large, as the deformation took place the large grains were broken down into small-sized grains.
These cumulative strains caused grain refinement and redistribution of the grains, sub-grains and phases, altering the hardness [12].
When an original sample of AA 7075 was tested for hardness experimentally, its average Brinell Hardness Number (HBN) was found to be 153.43.

He concluded that the annealing of PbS thin film modifies its grain boundaries and consequently increases the grain size.
The increase of solution concentration enhances the reaction rate and contributes towards the increase of number density of planes in all orientations especially towards the preferential orientation (200).
As the deposition time was increased, grains grew bigger while reducing the grain boundaries and overall affecting the mobility of the carriers, thus dropping the resistance.
This variation in results could be attributed to large grain sizes.
It was observed that optical band gap is sensitive to thermal annealing and grain size, it decreases with annealing and increasing grain size.

The number of electropulses (N) was either 50 or 100, while the applied current (I), pulse duration (t) and frequency (f) were kept constant.
Vicker's hardness vs. number of applied electropulses.
Conrad, Colony (grain) size-reduction in eutectic pb-sn castings by electropulsing Scr.
Wang, Grain refinement by means of phase transformation and recrystallization induced by electropulsing, Trans.
Guo, Grain refinement and formation of ultrafine-grained microstructure in a low-carbon steel under electropulsing, J.

Still, the fraction of recrystallized grains is very small and no significant grain refinement takes place.
Grain size is rather homogeneous, although still some large initial grains remain present.
It can be seen that no twinning takes place clearly in all the grains; recrystallized grains are visible along some grain boundary areas.
The average grain size of the small grains is about 3μm (see Fig.4d).
The smaller grain size observed in the sample with 2.38 effective strain in comparison with that with 2.07 effective strain is attributed to the larger number of dislocations generated in the former due to the larger strain imposed.

The cause of this agglomeration is assumed to be grain boundary grooving, driven by the difference between the interface energy and grain boundary energy.
Firstly, one can observe that the agglomeration of NiSi is accompanied by abnormal grain growth: the fraction of grains that exhibit the axiotaxy texture increases, both during agglomeration, as well as during prolonged anneals of thick NiSi films [7].
Figure 2: Effect of grain morphology on the interface matching.
In summary, the complex epitaxial texture of CoSi2 was found to originate from a limited number of axiotaxy texture components.
In the case of Co/Si(100), it was shown how a complex microstructure consisting of a large number of epitaxial components could be understood from the underlying axiotaxy texture.

According to rough statistics, the number of cooling holes in single advanced aero-engine has reached hundreds of thousands.
The crystalline grain size of 2 # sample is more uniform and 33.32μmin diameter on average, while other crystalline grain size between 40.36μmand74.83μm.
On the contrary, when the addition amount of La3+ was over high, the probability of grain nucleus growth was increased, which lead to a coarse-grain and a loose structure of coating layer.
Fig.7 Affection diagram of grain size, micro-hardness and electrode loss rate number of tube electrode electrode loss ratθ（%） average grain size（μm） microhardness（HV） measurement (HV) value Fig.8shows the surface micro-morphology of 1#copper and 5# electrode after EDM machining.
The material micro-structure mainly included three parts: the grain size, the uniformity degree of the grain distribution and grain orientation.