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Equation (7) and Fig. 4 also show that, for a given annular flaw size, a solid containing large a number of small pores will have the Young's modulus less affected by the presence of pores than a solid containing a small number of large pores.
Clearly, in this range of grain sizes, the strength of the polycrystalline alumina is controlled entirely by the flaw size rather than the grain size.
In fact in small grain size ceramics, where the flaw size is much larger than the grain size, the inherent flaw size may control the strength rather than the grain size.
It is shown that a solid containing larger number of small pores will have higher strength than a solid containing smaller number of larger pores.
At sufficiently small grain sizes, the strength becomes independent on grain size and the major factor that controls the strength is the flaw size which for nanocrystalline ceramics such as alumina (Fig. 5) can be much bigger than the grain size.

However, at 200 �exposure, a great number of θ' precipitates at the expense of T1 may be responsible for higher tensile strength in the Ag-free alloy than that of the independent addition of Ag and combined additions of Ag and Ce alloys. 1.
It can be clearly seen from Fig.1(d) and Fig.3(c) that there are similar features in grain boundaries between unexposed and exposure alloys.
Grain boundary after exposures 1000h at 107 is� still clear and there is no extensive development of PFZ near grain boundaries and no presence of equilibrium phases at grain boundaries.
Therefore, the main reason that tensile strength of the Ag-free alloy 1 at 200 exposure is greater than � that of the other two Ag-containing alloys results from presence of a great number of ��� phases in the Ag-free alloy 1.
When thermal exposure at 200� ,a number of θ' precipitates at the expense of T1 phases in Ag-free alloy make the tensile strength higher than that of the independent additions Ag and combined additions of Ag and Ce alloys .

The stored energy and the grain boundary energy are assigned to each cell.
During a time increment inct the grain boundary moves along a distance d.
This condition determines the number of CA steps and the value of the time increment.
Because of the mobility law (equation 9), preferentially in the neighboring grains rather than in the parent grain After one recrystallization step, the material is partially recrystallized.
In the recrystallized grains, the dislocation density increased 0 500 1000 1500 2000 2500 3000 3500 0,00E+00 5,00E+13 1,00E+14 Number of cells Dislocation density (m 1st Deformation step 2nd Deformation step xperimental curve temperature and for the two phases, the interaction matrix is assumed weak, which means that dislocations can easily pass through the obstacles corresponding to the latent dislocations.

Increasing the solid-solution temperature to 1060°C would cause parts of the NbC to dissolve, thus a large number of the thin sheet-shaped NbC would appear in the solid-solution and aging specimen.
Fig. 1(a) shows that massive precipitations are distributed within the grain boundary, and they display irregular shapes with the average size of 20 ± 1 μm.
Fig. 1(a) also shows a large number of needle precipitations (δ phases (Ni3Nb)) around the irregular Laves phase.
The irregular Laves and needle of δ phases obviously appeared within the grain boundary, as shown in Figs. 2(a) and 2(b).
It is reasonable to suggest that the main controlling factor of yield stress is precipitations rather than the grain size for alloy 718.

Similarly average grain size of Ni become about 8 nm after the aging at 473 K.
After the aging at 573 K, average grain size of Ni became about 6 nm, indicating that grain size did not grow.
Both of them were comparable in grain size and consituted two-phase structure.
Grain size distribution of Ni3P cannot be evaluated because of limited number of grains in the micrograph.
There is a grain with strong intensity of P, but solute P is not segregated at the grain boundary.

These forces make zirconia grains aggregate together and coalesce to form bigger grains.
Because of the larger pinning effect of the dispersed grains, the grain Fig. 3.
Thus, large zirconia grains mainly remain at the grain boundaries without being captured into the matrix grains.
With the grain boundaries diffusion and grains combining, few single zirconia grains or small aggregate of zirconia grains are embedded in alumina matrix grains before they can coalesce with others.
Acknowledgement This research is financially supported by the Promotional Foundation for the Excellent Middle-aged or Young Scientists of Shandong Province under grant number 02BS049.

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).

After the test, the number of load cycles were recorded and plotted on a graph as a dependence of frequency change from number of cycles (Fig. 2).
Thereby plastic deformation originated preferentially in grains that had appropriate crystallographic orientation, deformation evoked deformation strengthening in some grains resulting in higher values of microhardness in those grains in comparison with those grains where plastic deformation did not occur.
Cyclic loading generated plastic deformation in the grains close to the main crack but also in those grains that were further from the crack.
On the other hand there were also grains where plastic deformation did not occur.
This was given by the inappropriate orientation of grains against the applying stress.

In conclude, with the increase of filament number, the uniformity of temperature field improved a lot.
Fig.2 Influence of filament number on the temperature field of the substrate Fig.3 Influence of filament diameter on the temperature field of the substrate The influence of the distance between the hot-filament and the substrate hf on the temperature field of the substrate surface is shown as Fig.4, presumed that the hot-filament Tf＝2400℃, filament number n=12 hot-filament diameter df =0.06cm.
It can be seen from Fig8 that the grains of diamond film were arranged densely; the grain boundary was very clear, and the grain size was uniform.
The grain size at the center of the film was basically same as the grain size at the edge of the film.
(1) The substrate temperature increase along with the increase of filament number, hot-filament diameter, and with the decrease of the distance between the hot-filament and the substrate.

Background Severe plastic deformation (SPD) has emerged as a promising technique for creating ultra fine grained (UFG) metals and alloys, with grain sizes of a micrometer or less.
There has been a tremendous interest in developing severe plastic deformation processes, as well as in the study of mechanisms that cause grain refinement during SPD, as evidenced by the large number of publications and topical symposia [1,2,3,4].
Figure 4 shows the change in hardness on the cross section of the billets of different sizes with increasing number of passes.
In addition to conventional forging stock and the ECAP material, this part was also made with a cast fine grain AA-6061 with a starting grain size of ~100 µm.
Ferguson, "Multi-axis Deformation Methods to Achieve Extremely Large Strain and Ultrafine Grains," in Ultrafine Grained Materials, Ed. by R.S.