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Modeling of single grain grinding force The grain shape on the wheel surface is assumed to be a spherical shape.
Modeling of heat flux distribution Number of grains per unit area Ns, probability density functions of grain diameter f(x) and grain protrusion height P(x) were derived in Ref. [5].
They are expressed as: (2) (3) (4) where ω is grain density, dgx is grain diameter, x is given by x= dgx-dmean, dmean is the mean grain diameter, given by dmean=(dmean+dmean)/2, dmin and dmax are the minimum and maximum grain diameters respectively, h is grain protrusion height, hmean is the mean grain protrusion height, given by hmean=(hmean+hmean)/2, hmin and hmax are the minimum and maximum grain protrusion heights respectively.
The number of grains in each segment can be calculated from NΔ=Ns·b·Δl. h0 is defined as the minimum protrusion height of the grain, which is just contact with workpiece at position l, given by h0=hmin+hcul,max.
Statistical Calculations of Grinding Abrasive Number Based on Normal Distribution[J].

It show that the number of crystal planes that satisfied the Bragg law is reduced, and the grain size is smaller, so it can be indicated that the degree of crystallization is worse.
The Si2ON2 grains well combined with SiC grains to form a three dimensional net and protect the SiC grains not oxidation in the air.
Small Si3N4 grains also can be seen adherent on Si2ON2 grains.
It can be infered that most Si3N4 grains are generated from the decomposed Si2ON2 grains.
It can be seen that columnar Si3N4 grains are adherent on SiC grains, and almost no Si2ON2 grains can be seen in the image.

The results showed that the number of pits in 304L was much more than that in 316L.
Some literatures [5] point out that corrosion occurs in grain boundaries in the first place.
Therefore, the number of grain boundaries will affect the material's corrosion. 3.2 Corrosion Morphology The corrosion morphology of 304L and 316L stainless steel in 85% food grade phosphoric acid after 90 days is showed in Fig.2, It is clear from the micrographs that neither of 316L nor 304L stainless steel has larger and deeper pits, indicating the two steels have higher ability against pitting attack.
However, the surface of 316L resulted in a very low number of pits compared to the surface of 314L.
Conclusions (1) The grain size of 316L is greater than that of 304L and the number of grain boundaries in 316L is more than that in 304L

In the course of annealing, these nuclei increase in their sizes, their number increases as well, and gradually they form continuous fine-grained layers.
In the dark-field images taken in the reflections of Nb and Nb3Sn the grains of the superconducting phase (upper right corner) are adjacent to the residual Nb densely populated with a large number of very fine (10-20 nm) nuclei of the Nb3Sn.
Compared to the previous sample, a greater number of second-phase particles are observed (indicated with arrows in Fig. 14c).
The number of these particles is not very great and not enough for the pinning force enhancement, but the Nb3Sn grains in the vicinity of these particles grow coarser.
Here, it is important to remember that wide zones of fine equiaxed grains are of great importance for high performance of the wires not only from the viewpoint of greater number or uniformly distributed pinning centers (grain boundaries).

Oxides materials with perovskite structure are well stabilized by its high dielectric constant (κ) that leads these classes of materials for a large number of technological applications.
On the other hand, the uS samples presents smaller and square grains, without a visible grain boundary phase formation as presented in the cS ceramics.
Figure 4 shows the EDS microanalyses of the a) grain and the b) grain boundary phase of the 1150/24h cS sample.
EDS analyses of a) grain and b) grain boundary of the sample presented in the Fig.3c.
The grain size of the cS samples was higher than those for uS samples, it can be due to the copper-rich phase formation in the grain boundary, which contributes to the grain growth.

The model also explicitly tracks the precipitate populations at grain boundaries and in the grain interior.
There are a number of calibration parameters in the model that have to be found by fitting predictions to experimental measurements.
The calibration procedure is discussed in more detail elsewhere [1, 2].Grain Evolution Model The grain evolution model predicts the dynamically recrystallized (DRX) grain size and subsequent grain growth in the FSW--SZ.
These new grains will then be susceptible to grain growth, giving the final SZ grain size.
This grain growth is modelled using a simple classical grain growth model based on the mean grain size and a single (average) HAGB energy.

At lower deformation, these bands are parallel and start and terminate at the grain boundaries.
As the strain level increases, the number of the twins band increases and they intersect each other.
This figure shows also the presence of annealing twins in some grains, specially in larger grains, which give evidence of a low value of the SFE in the alloy.
At lower deformation (Fig. 3a), it is observed a microstructures of nearly equiaxed grains with straight deformation twins present only in a few grains.
The major gliding activity is located in the not twinned austenite grains.

Lumped capacitance model is valid when the value of the Biot number is smaller than 0,1.
A polycrystalline material contains a large number of grain boundaries, which represent a high-energy area due to inefficient packing of atoms [10].
Lower overall energy is obtained in the material if the amount of grain boundary area is reduced by grain growth.
Grain growth involves the movement of grain boundaries, permitting growth of larger grains at the expense of smaller grains.
We can conclude that the driving force for grain growth is reduction in grain boundary area.

The grain size was measured by the linear intercept method counting 100 grains.
TEM pictures at different magnifications were recorded both with a CCD camera and on film for measuring of particle number density, average needle lengths, average cross section areas, and width of the precipitate free zone (PFZ) at grain boundaries.
The grain structure is recrystallised in all four alloys analyzed in this work.
The results from the linear intercept measurements counting 100 grains were close to 150 µm for all alloys.
Hardness vs. number density of hardening precipitates Figure 5.

It is evident that the stronger ACB synthetic diamonds provide the maximal number of the cutting edges on the working surface of the grinding wheels.
The grain size of the diamond wheels has a significant influence on the forming of the roughness of the surface, since with increase of the dimension of the synthetic diamonds the micro-profile of the cutting surface of the wheel changes because of the reduction of the number of the diamond grains per unit working surface of the wheel.
With increase of the grinding wheel speed from 18 m/sec to 32 m/sec (vw = 25 m/sec; Sах = 10 m/min; Str =1.5 mm/stroke and t = 0.03), the parameter Ra decreases from 0.32 µm to 0.2 µm, which is associated with the increase of the number of the cuts by the diamond grains per unit time, and also with the decrease of the thickness of the cut that is performed by the individual grain, i.e., because of the specimens surface "sparking-out" effect.
The weakening of the bonds between the neighboring surface grains of the nitride ceramic leads to brittle fracture of the surface with the subsequent mechanical action from the active grains.
It was established that the specific number of the craters, the grooves, and the cracks on the surface of the specimens that are ground by the diamond wheel depends on the characteristic of the wheel and the grinding regime -and intensification of the grinding regime leads to increase of the number of these defects.