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For AISI 52100 steel in hot working process, it is apt to form a number of second-phase precipitation particles due to the higher content alloying elements.
The DRX grain is much smaller than the original one and the mean grain size of DRX is about 23.5 µm under these deformation conditions.
Only a few small DRX grains were developed along the initial grain boundaries, especially at the triangle grain boundaries.
Furthermore, the DRX grain size is about 22.6µm, while the unrecrystallized grain size is about 92.3µm, which is smaller than that of original grain (108 µm).
Obviously, the DRX grain size is slightly increased with the temperature.

We assume that RSE contains statistically sufficient number of hexagonal grains of diameter D, randomly distributed.
(2) where β is the slip line inclination angle to the axis 1x , 1( )p β is the distribution function of slip line inclination angle, 2( )p D is the distribution function of grain diameter, 0G is the Kirchhoff modulus of the virgin material, 1b is the coefficient connected with the shape of grains. 12β β β≤ ≤ denotes the fan of (sb) ω number of grains with activated slip systems inside RSE.
The initial porosity (Fig. 1a) of the material is assumed to be closed and distributed in grains (pg) and along grain boundaries (pgb).
One can split number of (cr) ω to these two types of cracks into: (cr) (mc) (wc) ω ω ω= + , (6) where (mc) ω corresponds to number mesocracks and (wc) ω denotes the number of wing cracks.
The initiated cracks can develop along grain facets changing their direction.

Salomãoa et al. [1] prepared lightweight Al2O3-MgAl2O4 castable with a large number of pores by adding Mg6Al2(CO3)(OH)16·4H2O, which will form spinel in situ with volume expansion and hinder the densification; T.
It can be seen that, grain sizes of sample 0# are relatively small, most of them are less than 10μm and distribute on the grain boundaries, and there is no pores inside of grains basically.
That is grain boundary can move freely from the control of pores, then the pores are stranded between the grain boundaries.
This may lead to the existence of closed pores inside of grains or the rapidly growth up of partly grains [14].
The result is shown in Fig.5, it can be seen that, higher relative density can be obtained when the relative grain size (which is the ratio of maximal grain size to the average grain size) is smaller.

That is, dispersed graphite particles hinder grain-growth of copper matrix, which results in refined recrystallized copper grains.
When these tiny graphite particles disperse in the Cu grain boundary, pinning effect on the grain boundary is stronger, limits grain boundary migration and velocity, inhibits grain growth.
Meanwhile, in the initial stage of recrystallization of Cu, small graphite particles can act as nucleation, increase the number of nucleation and help for grain refinement.
Larger copper grain can be seen compared with Fig.6.
Under the same conditions, raising extrusion temperature results in sufficient recovery, recrystallization and grain-growth of copper grain.

The damage was largely caused by the nucleation, extension of a large number of micro-cracks inside the workpiece induced by grinding force.
As shown in Fig.2 (a), plastic deformation generated within local areas contacting with the grain after the grains pushed onto the workpiece surface.
Actually the grains will be peeled off from the grinding wheel, that is, self-sharpening of grains.
When the abrasive grain unloading, the first item of each components of stress field is stress caused by elastic deformation, which was reduced with grain unloading until reduced to zero after grains and workpiece completely detaching.
In ultrasonic grinding, the grains impact the workpiece surface actuated by the ultrasonic vibration system with extremely high frequency, so that the grains periodically suppress workpiece and afterwards separate.

Figure 1(b) shows crystallinity along (002) plane is enhanced by increase in number of laser pulse.
With increasing shots, the film becomes uniform as crystals are well aligned and grain boundary is reduced.
Typical GIXRD spectra: (a) Varying doping percentage, (b) Varying number of pulse at vacuum.
Inset is the zoomed view of the grains which shows the hexagonal nature of the grains.
As the films become well crystalline with more number of shots, resistivity decreases hence both carrier concentration and mobility increase as scattering at grain boundary reduces.

S wt% ↑ S>0.01 wt.% is increasing the precipitation of sulphides at γ grain boundaries.
↑αp 9. γ grain size ↑ Intragranular nucleation on inclusions dominates.
Heat input ↑ γ grain size get larger.
Acicular ferrite is directly related to the number density of intragranular nucleation sites in the prior γ grains.
In this work, we have considered the influence of a larger number of parameters over hardness in HAZ, like the dilution factor, number of runs, filler material composition and the results obtained shows that using 5PL function could be an valuable alternative for estimating microstructure and hardness in HAZ.

Both titanium alloys have fine secondary α-phase which appeared granular or acicular near the β-grain boundaries or within the β-grain after hot deformation.
DR is one of the mechanisms of grain refinement in most alloys [5, 6].
There are large number of primary lath α phases in β phase (Figs. 2(a)).
It is clearly observable that fine acicular secondary α phase precipitated at β grain boundaries or within the grain (Figs. 2(b)).
The grain boundary regions are softer than the precipitation hardened matrix and the grain boundary α (GBα) has an effect on the mechanical properties of β-titanium alloys [14].

A new approach to manufacturing preforms and sheets with SMC structure of titanium Ti-6Al-4V alloy is considered in a number works [3-6].
One can also observe separate grains with a size of about 0.8 µm.
The average grain size of the commercial size sheet, 500×1000×2 mm3 was 0.65 µm and the fraction of coarse grains of 1.2-1.8 µm in size was about 10% (Fig. 2,3).
The sheet with the grain size 0.3 µm showed higher yield strength (YS) and ultimate tensile strength (UTS) but lower elongation than the one with the grain size of 0.65 µm.
A higher rate strengthening in the sheet specimen with grain size of 0.65 µm can be accounted for inhomogeneous distribution of β phase in comparison with the state with the grain size of 0.3 µm.

The results indicate that electromagnetic vibration would refine grains and the reduce macrosegregation effectively.
In addition, researches have also shown that physical vibration during solidification could not only reduce hot tearing but also refine the grains markedly.
No large dendrites present any more in the case of 25Hz and the more equiaxed grains would be obtained in the case of 30Hz.
However, it seems that increasing AC intensity would refine grains more markedly than increasing DC intensity.
Therefore, microstructure refinement at the edge of the billet would be resulted owing to a large number of nuclei present near the wall.