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Abrasive machining works by forcing the abrasive grains into the surface of the workpiece so that each grain cuts away a small bit of workpiece material and the machined surface topography is produced by the abrasive grains leaving scratch marks on the workpiece surface.
A number of single grain cutting experiments were carried out in the past few years and has significantly improved the understanding of the abrasive machining process [2-4].
The cutting edge of abrasive grain is assumed to be rigid to save computation time since the grain is much harder than the workpiece.
It is because these boundaries were contacted with the abrasive grain.
Acknowledgement This work is supported by National Science Foundation of China (NSFC, Grant number 50975198).

As the number and scope of application in the aerospace industry increases, the titanium alloy has been hailed as the“modern metal” and“strategicmetals”.
Because the resistant of dislocation slip will increase, and the amount of slipping is reduced in the same time, when the number of paramagnetic obstacles increases.
Grain size.
The sub-grains generated will play a role of fine-grain strengthening.
The recrystallization grain size is inversely proportional to the nucleation rate and is proportional to the grain growth rate.

In rapid/warm plasticity, grain boundary sliding (GBS) and dislocation activities predominate the deformation mechanisms, and continuous dynamic recrystallization (CDRX) occurs resulting in grain refinement [3, 4].
The as-annealed microstructure had average grain sizes of 5.0 μm in α phase and 3.6 μm in β phase.
The average grain sizes, which were defined as the sizes of grains surrounded by HABs, were measured along the cylindrical axis by the intercept method.
Figures 3 (c) and (d) show the number fractions of sub-boundaries (2°–15°) on some low-index planes among randomly-selected sub-boundaries of about 10 at different strain levels.
CDRX was observed, resulting in monotonic grain refinement both in α and β phases.

Introduction Following the demonstration of superplasticity in a 3 mol% yttria stabilized tetragonal zirconia (3YTZ) by Wakai [1], there have been large number of studies on that material [2,3].
In fine grained ceramics, diffusion creep is likely to occur by matter transport along grain boundaries, as proposed by Coble [5], and this process involves n=1, p=3 and Q=Qgb, where Qgb is the activation energy for grain boundary diffusion.
A value of n~2 was attributed to grain boundary sliding, and higher values of n were related to a grain size and temperature dependent threshold stress.
Measurements after creep testing indicated that there was no significant change in either the grain size or the aspect ratio of the grains.
A very limited number of dislocations could be identified and they are shown by arrow marks.

Change in BPR affects the total number of collisions, the motion pattern and the types of collision.
The number of collision per unit time could increase and produce more energy transferred to the powder particles and results in faster MA [3].
All of these changes were caused by the size of grain [4].
The powder mixture then became more refine and as a result, the grain size became smaller.
The increase of BPR from 5:1 to 10:1 resulted in an increase of number of hit between powder-ball-wall.

Based on these facts, a number of attempts have been made to develop Cu coating over FeCo nanoparticles [7, 10].
Grain size and lattice strain of FeCo/Cu samples.
Here, it is to be noted that the grain boundaries act as a barrier and restricts domain wall movement.
The above expression indicates that as grain size increases, coercivity of the material decreases.
The grain size and lattice strain determined for FeCo/Cu nanocrystalline core/shell powders by SLPA technique have shown that heat treatment causes grain growth and reduction of lattice strain.

This is mainly because in the composite electrodeposition process, the addition of SiC nanoparticles can increase the cathode polarization and reduce the overpotential of the metal nucleation and promote the formation of new crystal nucleus; Meanwhile the adjunction of nanoparticles inhibit the grain’s aggregation and grew up, played the role of refine the grain of matrix metal.
(a) Pure nickel coating (b) Composite coating Fig.1 SEM images of the pure nickel coating and composite coating Compared two TEM images（gauge 100nm）of coatings illustrated in Fig.2, the average grain size of the pure nickel coating is about 90nm, while the composite coating’s grain size is about 25nm, the grain size of which a quarter of the pure nickel coating’s .
It also proved that the addition of nano-SiC particles can indeed refine the grain coatings, the presence of nano-SiC metal matrix deposition increases the nucleation probability, prevented the growth of grains.
Coating porosity is the number of pores in per unit area.
Analyse through the SEM and TEM examine, the surface of Ni-SiC composite coating is more smooth, organizations are also more uniform and compact for the grain are refined by the adding of nano-SiC particles; 2.

Results and discussion Morphology and grain size.
On the other hand, when the nucleation dominates the deposition process with a large number of nuclei generated on the substrate, the growth of nuclei and crystallites is strongly impeded.
Determination of grain size.
In this way the grain size was calculated to be about 27nm.
EDX analysis showed that CuO forms inside the grains, while Cu2O grows along the grain boundaries.

The level of the effective (accumulated) strain can be controlled by number of cycles of shear-compression.
The maximum number of cycles (four) is constrained by decreasing of height of the specimen after each cycle.
The level of effective strain up to e ~ 4 can be controlled through adjustment of the height reduction of the specimen and number of cycles of shear-compression.
Significant grain refinement was observed in low-carbon steel AISI 1010 after 4 cycles of shear-compression testing.
Ohori, Grain refinement of high purity aluminum by asymmetric rolling, Materials Science and Technology. 16 (2000) 1095-1101

With increase of nitrogen flow, the morphology of the TiN thin films films changed from characteristic pyramidal shaped grains to columnar-shaped grains.
The increase of hardness with increasing nitrogen flow rate is attributed to the decrease in grain size.
As the number of gas molecules increased with the increasing nitrogen flow rate the average energy of the bombarding particle decreased.
For 1sccm nitrogen flow rate, it shows the pyramidal shape grains.
By increasing the nitrogen flow rate, pyramidal grain shape disappeared and columnar structures were observed.