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However, the mechanisms leading to grain refinement in pure Al and aluminium alloys under ECAE processing have only been the object of a limited number of studies [4-10].
This mechanism is based on the assumption that the original grains are deformed as the whole sample due to a limited number of active dislocation slip systems.
Journal Title and Volume Number (to be inserted by the publisher) 5 a b Fig. 2.
The fraction of these grains is low. 50 µµµµm d 100 µµµµm a 10 µµµµm b 50 µµµµm c Journal Title and Volume Number (to be inserted by the publisher) 7 Further strain up to ε∼12 leads to an increased fraction of recrystallized grains (Fig. 4d) outlined by HABs from all sides and an increased proportion of HABs (Fig. 3).
A negligible number of recrystallized grains could result from this type of CDRX.

The grained structure in FG alloy as shown in Figure 1b, is presented by two different grain types, namely, coarse (average grain size 1.9 µm) and small (average grain size ~0.4 µm) grains.
Along with a-Ti phase grains, the type VT1-0 titanium alloy has a small number of b-Ti phase grains possessing a body-centered cubic (BCC) lattice and Im3m space group.
.% The implantation of aluminum ions in the type VT1-0 titanium alloy results in the formation of a number of phases possessing various crystal lattices.
Obviously, it is connected with the phase formation: UFG alloy has the largest number of secondary phases, while the FG alloy has the lowest one (see Table 1).
As is known from the work of Honeycomb [13], the dispersion hardening of the alloy depends on the number of particles, their size, distribution, and distance between them, and also the degree of atomic mismatching between the lattices of the precipitate and the matrix.

The numbers of small grains were seen dominating the microstructural pattern and no specific and uniform grain shapes were observed.
A similar number of pixels was used to ensure that a broad and wide image would be captured, using the same total mapped area of 30x35µm. 6438 grains was successfully mapped with a grain-size average of 0.2661µm, the smallest and largest grains being 0.0564µm and 3.2762µm, respectively.
The number of grains revealed was found to be twice many when compared with the number for CS50.
Due to the grains being heavily deformed, a large part of the mapped area could not be indexed, hence a large number of blanks were observed on the image.
Less force is required and a lesser number of grains has made a larger grain-size material prone to fail a lot more quickly than would a smaller grain-size material.

This temperature range is also where the number of carbide particles per unit area at grain boundaries reaches its maximum.
The high number of particles per unit area increases the rate of crack initiation at grain boundaries under rapid loading; linking of microcracks along grain boundaries which are already weakened by impurity segregation results in TE and intergranular fracture. 1.
Fig. 1c shows numerous small carbide particles, which have reprecipitated along grain and lath boundaries at 520 °C; the number of these particles per unit area is greatest for this tempering temperature.
The high number of particles means that there are many microcracks, and these microcracks can become linked during further loading along the grain boundaries, which are already weakened by the impurity segregation.
In the temperature range where temper embrittlement occurs, the number of carbide particles per unit area reaches a maximum

ρ can be determined from the number of effective grains Nt divided by the evaluation area Ae.
When these values are determined, Nt can be calculate from the distribution Ng(h) as the number of grains existing within the range from the most periphery to the thickness of t (h=0～-t).
Here, assuming k as the supporting stiffness of grain, fh acts on the grain as shown in equation (2).
In order to calculate Fe , the grain supporting stiffness k is given as 3.13 N/μm according to the grain size and bond type.
On the other hand, Fig.5 shows the change in Nt, which means the number of grains within the peripheral layer with thickness of t.

The maximum grain size was 60cm.
Table 1 Representative graduation of three coarse grain soil fillers No.
LµS1/2µV1/3µF1/D (1) After confirming the concept of fractal dimension, Turcotte [2] raised the particle number-particle size fractal model according to the Mandelbrot’s fractal theory.
The coarse grained fillers were formed by the rock crushing.
Three different coarse grained fillers were chosen to find the result.

Copious nucleation applies a high undercooling during pouring and generates a large number of solid nuclei.
Fig.2. also demonstrates that the number of crystals poured at lower temperature is much more than that of high temperature.
So when the crystal nucleus produced during the pouring process move to the crucible, the crystal nucleus will be remelted because of higher liquid temperature, which results in the number of nucleus decreasing.
A large number of retained crystal particles exist in the liquid and prohibit the dendritic growth and thus promote the formation of the desired microstructure, so the grains obtained from slurry preparation are small and round at low pouring temperature.
Effect of grain refiner (0.06% Ti) on the average grain size at different pouring temperature 4.

The austnite grain size also increased.
The distribution of inclusion size and numbers were measured and counted, and the semi-quantity distribution chart was shown in Fig.7.
Size of most inclusions in experimental steel is below 3μm, and the size of less than 1μm account for the majority of total number of inclusions.
At this point, the inclusions (particle size below 1μm) have a larger size and smaller relative number compare to the austenite grain, its effect on retard the grain boundary movement is extremely limited.
However, as the number of these mini type inclusions is still small and the dissolution of some MnS in a higher temperature, the austenite grain growth of experimental steel is still faster with the temperature increasing.

A limiting grain size of the coatings has also been identified in the grain refinement process.
At high nitrogen pressures, poisoning of the magnetron targets and collision and scattering of the atoms and molecules become significant, and thus reduce the number and kinetic energy of the travelling species approaching the substrate.
A higher nucleation rate and a reduction of the self-shadowing effect of the deposition process will occur with an increasing number of depositing atoms/molecules.
Furthermore a limiting grain size in this grain refinement can be determined.
grain size), Ho = (minimum) hardness of the coating at large grain size, and PN = nitrogen deposition pressure.

The mechanism of the MgAlON grains to generate Joule heat was the same as Al grains.
So each grain would form 12 necks.
So, (4) According to geometrical rules, the relationship of r2 and r1 could be expressed by: (5) Based on formula (3) to formula (5), the relationship of h and r1 was: (6) (a) (b) Fig. 2 Schematic diagram of the necks formed between grains: (a) Diagram of 12 coordination number of CPH; (b) Diagram of the necks formed between grains Computing results and analysis Influence of Joule heat on the temperature distribution in Al grains.
In view of process control, if I and B remained unchanged, the contact point number and the heating rate of samples would increase with the particle size decreasing.
The heating and melting process in Al grains would further promote the contact point number increasing and samples heating rapidly, so the materials’ structure and property would be regulated and controlled.