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At the same time, it permits a reduction in the number of ECAP passes required, which produces a more homogeneous ultrafine-grained (UFG) state, and, finally, in a decrease in the structural anisotropy and enhanced properties.
Microstructure of the asreceived Grade 2 CP-Ti rods has equiaxed grains in both cross and longitudinal section with α-phase grain size of about 75-80 µm (Fig. 1).
Some dark coarse particles, observed at grain boundaries and inside grains, are oxide phases [12].
Effect of the number of ECAP passes on mechanical properties of Grade 2 Ti billets.
The grain/subgrain size is reduced to 150-250 nm.

It is anew nano-surface technology to refine grains to the degree of nanoscale.
The grain size of sample surface is measured by XRD-7000S.
The type of dislocation inside the grains tends to partial dislocation.
Because the grain boundary sliding or crystal rotation is prone to realize when the grain size is nanometer scale from the relationship between grain boundaries sliding and grain size [12-14]. large number of dislocations are very difficult to form in the nanoscale subgrain.
At the time grain boundary can’t absorb large number of dislocations.

By using probability and statistics, the model of cutting depth distribution of grains was obtained. 1 Introduction In the lapping process of multi-cell-disc, the deformation of multi-cell, the processing load, the distribution of abrasive group and other factor have significant impact to the distribution of abrasive group’s cutting depth on multi-cell-disc.
So make the following assumptions to simplify the analysis2 : (1) Particles as a rigid body; (2) Assuming the surface to be processed is an ideal plane before processing; (3) Assuming hardness of the material processing is a constant, and unrelated with the shape of abrasive, pressure and other factors; (4) In the circumstances of the lapping pressure is certain, Each abrasive grain in lapping assumed load is changing at different times, but the total load is a constant3; (5) At a certain moment, abrasive and lapping surface are stable and maintain contact with parallel, the distance between them is a definite value, and can change over time; (6) The amount of overlap has nothing to do with the contact force, Compared with the particle size, the amount of overlap is small.These assumptions are set based on the actual processing conditions, it is realistic. 3 Analysis single abrasive grain stress As the lapping of multi-cell-disc is formed by the number of abrasive particles in the surface
The depth of Single grain pressed into the work piece have a certain relationship with the depth of pressed into the under disc.
In the lapping process, in the role of some lapping press, the force of abrasive give under disc and work piece are P, this time when abrasive are pressed into the work piece also into the under disc. 4 Establish mechanical model between single abrasive and work piece The mechanical relationship between the Single grain and work piece diagram shown in Fig.5.
When not fixed angle is pressed into the specimen, the relationship among the indentation depth, single grain pressure, semi-angle of pyramid pressed into the work piece and the yield point of the work piece materials are4: (2) In the formula, P is the single grain pressure (N); σs is the yield point of the work piece material.

Segregation thermodynamics indicated that the segregation of magnesium to grain boundaries prevented element such as Cr, C from enriching on grain boundary, which was helpful for the reduction of network carbide precipitation.
Sample numbers was shown in Tab. 2.
But a small amount of uncontinuous network carbide precipitated in the grain boundary.
Part of magnesium segregated to grain boundaries in the thermal processing and may reduce the enrichment of other elements in grain boundary.
Grain boundaries in metals[M].

Austenite Grain Refinement in Direct Charging based Thermomechanical Processes J.
The lower total reduction with a lower number of passes introduces some additional complexities that need to be evaluated.
Although the average grain size is about 800 mm, a wide range of grain sizes is observed, with grains as large as 2500 mm.
The applied strain is higher than εc for grains smaller than 800 μm.
Prediction of the grains under DRX conditions in an as cast grain size distribution in a 0.05% Nb steel (pass conditions: 60% reduction, 1070ºC, 5 s-1).

The results showed that β grains with the average size of about 305 μm and the discontinuous grain boundary α phase along the β grain boundary were obtained for the samples deformed at 881℃.
However when the deformation temperature increased to 896℃ the average size of β grain increased to 510 μm, and the continuous grain boundary α phase along the straight β grain boundary were obtained.
The fracture mechanism analysis revealed that the fracture mode of fine β grain and discontinuous grain boundary α phase is the transgranular fracture, while for the coarse β grain and continuous grain boundary α phase is the intergranular fracture.
During deformation at 881℃, the average β grain size of about 305μm and the discontinuous GBα phases along the β grain boundary were obtained.
Fig. 5 shows the fracture surface and crack of TC18 titanium alloy deformed at 896℃. the macro fracture morphology of the sample deformed at 896℃was relatively flat, there were a large number of deep rock sugar block tearing edges in the crack initiation area, and there were also a large number of dimples (Fig. 5a), which is a typical ductile-brittle mixed fracture.

Number of DCAP cycles (N) was varied from 1 to 2.
Number of revolutions was varied from 1 to 15 (strain is e=4.1-6.9).
Increasing of number of revolutions up to 15 (e=6.9) leads to certain coarsening of the structure.
Probably these particles situated on grain boundaries and inside grains deter nanoscaled grain growth and do not restrain active development of dynamic recrystallization.
It is known that shock waves create large number of lineal defects.

It is not possible to create the trajectory of an abrasive grain or a resultant trajectory of a set of grains unless the grinding conditions are considered.
,n) exhibits a certain degree of stochasticity, where n is the actual number of abrasive grains in l.
Let m be the expected number of abrasive grains in l.
(1) Equation (1) simply means that one can continue to do i = i +1, if Lgi £ l is true; the final value of i is the number of grains n.
This yields drgi = d - dgi (error in the depth of cut), rgi = rG - drgi (grain radius), Dgi = 2rgi (grain diameter), Vgi = wGrgi (grain velocity).

Voro++ provides a radical Voronoi tessellation starting from a randomly generated set of seed points whose number corresponds to the number of cells obtained.
The number of iterations is referred to as the Lloyd factor in the following.
Another 2D VE has been generated separately with the same number of grains per 3D VE length in each direction, Fig. 1(c).
Afterward, the number of grains that possess a specific volume fraction is depicted in histogram bins in Fig. 2.
(a) (b) (c) Fig. 2: Statistical overview of the number of grains versus their volume fraction for 3D sections and 2D volume elements (for 2D with a unit out-of-plane dimension assumption) generated separately and by means of sectioning 3D volume elements.

It was shown [4] that an increase in the number of ECAP passes led to a considerable increase in the static strength properties of the AA5056 in comparison with its initial state.
(ii) The ECAP results in deformed microstructure consisting of UFG grains alternating with unrecrystallized regions of coarse initial grains (Figs. 1(b) and 1(c)).
The average size of the ultrafine grains was ~1.2μm, the volume fractions of the coarse- and UFG grains were ~0.3 and ~0.7, respectively.
The room temperature mechanical properties of similar Al–6Mg–Sc(–Zr) alloys with the grain size of about 10mm (the microcrystalline (MC) state) and with the grain size of the order of 100mm (the coarse grained (CG) state) [11,12] are also given in Table 1 for comparison.
Also a large number of secondary cracks are often observed in these local regions.