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As the time change from t to t + δt, grains position will also change to , where it holds in general that
Function sign() in Eq. (5) is defined as (6) and the overlap between grains ξij is defined as in [11] , (7) where Di is diameter of grains i.
Experiment Two dimension grains are represented by small and thin disks, which are distributed artificially.
Each configuration is recorded and then analyzed using tailored software to get particles position and number of contacts on each particle.
Each particle position and contacts are obtained from tailored software, where illustration of the observed contacts between grains is given in Fig. 2.

Because of these special performances, engineering ceramics are expected to be used increasingly in a number of high-performance applications ranging from electronic and optical devices to heat- and wear-resistant parts [1-2].
Then, the material removal rate by one grain is given by: r 4 V CCM hL o �����= . (5) where, � is the rotation speed of the tool; r is the radius of the grain’s track.
Assuming that the density of effective cutting grains is � in terminal face of drilling tool, the number of effective grains in area dA (see Fig.5) is: drr2dAn ���� �=� = . (6) Then, the material removal rate of the tool is: ( )RRCC rCC 3 1 3 2 hL 2 2 hL 2 v 3 8 dr R R 8M 2 1 
����� ��=������ ��= � � � . (7) 1 2 3 4 1.
Fig.3 Schematic of diamond tool drilling process Journal Title and Volume Number (to be inserted by the publisher) 409 The number of effective grains in the terminal face of the tool is [10]: ( )RR d K 2 1 2 2 3 2 g 2 0 1 6 AN
��� � � 
 � � � � � � �=� = � . (8) where, ( )RRA 2 1 2 2
=� , R2 is the external radius of the diamond wheel; R1 is the internal radius of the diamond wheel; K1 is a proportional constant; � g is the concentration of abrasive grains; do is the mean diameter of the abrasive grains.
Acknowledgement The work described in this paper is supported by National Nature Science Foundation of China(Subject number: 50275087).

There are two well-known variables of SiAlON called α and β, which are derived from α and β-Si3N4 respectivley. It is generally accepted that β-SiAlON tends to develop into elongated grains, while α-SiAlON usually occurs in equiaxed grains.
However, some recent experimental results show that α-SiAlON ceramics with elongated grains can also be obtained by controlling the nucleation and grain growth process properly [3-7].
In the samples sintered at 1500 and 1600 ºC, a large number of submicron grains existing dispersedly were found, together with some large pores.
While in the samples sintered at 1700 and 1800 ºC, the grain size increased obviously and some little pores were visible near the grain boundaries.
Therefore, the fracture toughness of the samples with elongated grains was improved, as shown in Table 2.

However, a number of studies have found recrystallization nuclei in orientations that were not expected from measurements on deformed structures.
Electronmicroscopy Observations Within recent years there have been a number of investigations into the local orientation is deformed metals and the development of recrystallization nuclei [4-22].
A smart way to avoid the uncertainty discussed above concerning "below-surface grains" possibly leading to nucleation of grains with orientations not seen at the surface is to work with columnar grained sample - i.e. samples where the surface grains extend through the entire sample thickness.
Recrystallization and Grain Growth.
Rex and Grain Growth 2 nd, eds.

Microstructure of wires fabricated usin 800 rpm consists finer equiaxed mg grains with finer precipitates homogeneously distributed along the grain boundaries.
To fabricate the magnesium based components, machining is main process and as the number of applications increasing with the use of magnesiumm, the scrap volume is also increasing.
It consists of approximately equiaxed grains of 100 µm with the grain boundaries discontinuously covered by the precipitates.
The microstructure consists of larger grains surrounded by finer grains with precipitates at their grain boundaries.
The average grain size at higher rotational speeds is 180 µm which is much higher than the as cast base metal grain size.

Most of the available publications are devoted to ECAP, in particular to the dependence of the material properties on the number of the ECAP passes applied [15,16,17].
The average grain size was deq=300nm (Fig.2b).
The HE+ECAP combination gave a structure with the average grain size deq=327nm (Fig.2d) which was highly homogeneous with well-shaped equiaxed grains.
After subjecting it to HE, its structure became appreciably refined and contained well-shaped equiaxial grains and a small number of defects The average grain size was 200nm (Fig.3b).
The average grain size was 190nm (Fig.3c).

Microstructures of CGP processed Al experienced diffe- rent number of pressings (εef) at room temperature: a) top groove ε ~ 0; b) top groove ε ~ 0; c) sheared area ε ~ 0.58; d) 1 pass ε ~ 1.16.
The interior of these new grains is free of disloca- tions; grain boundaries are straight and they have a similar morphology of polygonized subgrains.
TEM microstructure analysis results also indicates a very low fraction of submicron grains with high angle grain boundaries even in case the strain applied is the highest.
Considering fact, as to the subgrains and grains size, the CGP method for grain refinement in pure Al appeared to be not so effective.
A distinction between the values for the initial state and the deformed plates subjected to CGP straining due to different number of pressings is evident.

It is possible to calculate the number of atoms associated with interfaces (grain boundaries and triple junctions) in the material, regardless of grain size, when the structure is simplified as follows: i) all crystals have the same average size; ii) all crystals have the same shape and iii) all grain boundaries have the same thickness.
For a grain shape of a 14-sided tetrakaidecahedron (Fig. 2) and a grain boundary thickness of =1D nm, the volume fractions, Vic, of atoms associated with interfaces varies with grain size according to [7]: (1) Similarly, for the same assumptions, the total grain boundary area, S, per unit volume, V, of material with the same grain shape varies with grain size as follows [8]: (2) TJ GB Fig. 2: Grain boundary (GB) and triple junction (TJ) defects in a crystal aggregate [3].
It can be seen that both values are rather small at large grain sizes, but increase rapidly with decreasing grain size down to 10 nm.
Table 2 also shows a significant increase in grain boundary area with decreasing grain size which has a considerable effect on properties that depend on interfacial area, such as the driving force for grain growth.
Table 2: Volume fractions of atoms associated with grain boundaries (Vic) and total grain boundary area per cm3 (S) of a 3-D nanomaterial as a function of grain size for a grain boundary thickness of 1 nm.

The grains decreased -gradually with the increase of the fire time [5].
Comparison and Analysis of Measured Grain Size with Calculated Results.
The final grain size of end face is 4 grades approximately.
(2) With the increase of fire time and the reduction, the domain of uniform and fine grains enlarges and the grain size could be fined in the multi-fire forging process
(Item number: 50675146).

AZ grain is produced by mixing alumina grains with zirconia grains of 30%wt., which is about 1300 in knoop hardness [4].
And the stock removal with AZ grain is larger than that with WA grain that is similar to that with GC grain.
That is, the interference intensity of GC grain is larger than of WA grain because of higher hardness of GC grain.
AZ grain acts on the workpiece surface stronger than WA grain, as the result that AZ grain including zirconia abrasive is softer than WA grain but its specific gravity is larger than that of WA grain.
The number of acting abrasive grain on the workpiece surface is estimated to be proportional to the abrasive concentration, but stock removal at 30%wt. is remarkably larger than those at other concentrations.