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Again, when grain growth ceases it is widely assumed that each grain present arose from a single nucleus.
The numbers are staggering, it is simple arithmetic to show that, in Fe-Si, for example, the abnormal Goss oriented grains must have consumed ~100,000 of their neighbors.
The final grain size was ~30µm.
Grain EG1 in Fig. 2b could have arisen from three such grains as shown in Fig. 2a.
The critical length for a process similar to SIBM is observed to be 3-5 subgrian diameters, i.e. 3- 5µm Acknowledgement It is a pleasure to acknowledge financial support for this work for the Research Grants Council of Hong Kong Special Administrative Region of China, numbered RGC 7067/97E.

In this paper, Nc is defined as the number of cycles when a crack or a slip greater than the grain size is observed using a microscope for the first time on the polished surface.
Solid plots show the number of cycles to fracture (Nf), while the open plots show the number of cycles to crack initiation (Nc).
Fig. 4 Relationship between stress amplitude and number of cycles to fracture or crack initiation.
The horizontal axis in these graphs denotes the number of cycles standardized by Nc (N/Nc).
When the horizontal value increases, the number of cycles increases.

Based on the concept, we used CNTs directly as cutting grains for nano machining [4-7].
Grain Spacing L.
Based on VHigh (Eq. (1)), the grain spacing L (Fig. 2) can be obtained as L= (VHigh/ng) 1/3, (2) where ng is the grain number in the CNT wheel (Fig. 2).
In a single layer of a MWCNT, the number of carbon atoms nCi can be obtained as nCi=niCRnCA/nC-C=(AiCNT/ACR)nCA/nC-C=4πdilCNT/(33/2lC-C2), (4) where niCR is the number of carbon rings in a CNT layer, nCA is the number of carbon atoms in a carbon ring, nCA=6, nC-C is the number of C-C bonds for a carbon atom, nC-C=3, AiCNT is the area of the CNT layer i, AiCNT=πdilCNT, di is the diameter of the layer i, lCNT is the mean length of CNT (Table 1), ACR is the area of a carbon ring, ACR=33/2/2lC-C2, lC-C is the C-C bond length (Table 1).
An abrasive grain takes a circular path Ideal Actual Ideal Actual Ideal Actual 500 600 700 800 900 1000 1000 1250 1500 1750 2000 5 6 7 8 9 10 500 600 700 800 900 1000 60 70 80 90 1005 6 7 8 9 10 500 600 700 800 900 1000 80 85 90 95 1005 6 7 8 9 10 Mean length lCNT (nm) Mean outer diameter dCNT (nm) Mean layer number nLayer b - Feed of workpiece per cutting edge s (nm) a - Grain spacing L (nm) a b a b a b through the surface of a workpiece (Fig. 5).

It is generally known that the breakdown electrical field EB can be expressed by the following equation [9,10]: EB = n•Vgb, (1) where n is the average grain number per unit length, Vgb is the breakdown voltage of one grain boundary of SnO2 ceramics.
Whereas, the increase of EB for SCTI is related not only to the grain size, but also to the breakdown voltage of one grain boundary Vgb.
That is, the electric charge states of defects on the grain boundary should be affected greatly by doping In2O3 considering that the grain boundary barrier has great relation with defect states.
In this study, the presence of Schottky barrier is inferred from the good linear agreement of ln(J/AT2)-E1/2 curves (Fig. 3) and the barrier height is obtained from the following relationship: , (2) where A is Richardson constant, kB is Boltzman constant, E is electrical field, and β is a constant in reverse proportional to barrier width ω and grain number per unit length n.
Thus, it is reasonable to suppose that some compoundsubstance including yttrium may locate at grain boundaries to hinder the combination of SnO2 grains.

With increasing number of passes the grains changed from an elongated shape to a more equiaxed structure, which was especially pronounced after 8 and 16 passes (Figs. 1, 2).
The fraction of high angle grain boundaries increased with rising number of passes, and a value of about 40% for the precipitated and about 50% for the supersaturated state was obtained after 16 passes (Fig. 3).
It was noticed that the higher the number of passes the softer the material became after annealing for 1 h.
For both alloy constitutions it was found that the formation of a new equiaxed microstructure progressed with increasing number of passes.
EBSD maps revealed that with increasing number of passes the fraction of the equiaxed grains in the microstructure had increased during annealing for 1 h.

It was found through experiment that, the grain was very coarse in the cast ingot of 5N5 high purity aluminum, and the average grain size is about 60mm.
The grains are very coarse, and the average grain size is about 60 mm.
After eight ECAP passes of Route BC (Fig. 4(b)), the grain was refined furtherly, and the average grain size is less than 50μm.
We can see the presence of a large number of dislocations and the dislocation has occurred tangles, and has formed cellular sub-structures.
A large number of dislocations appear again in the sample after eight passes, maybe because that the dislocation was restarted under the shear deformation.

The occurrence of size effects in cobalt was examined by the analysis of mechanical properties of samples with thickness t, in a large range of grain size d giving a number of grains across the thickness t/d.
The influence of size effects on the mechanical properties of metals can be analyzed through the number of grains (of diameter d) across the thickness (t) parameter t/d.
For smaller grains, the deformation is assisted by dislocation gliding whereas for the biggest grains, twinning is the main straining mechanism.
Geers, Size effects from grain statistics in ultra-thin metal sheets, J.
Hug, Hall–Petch behaviour of Ni polycrystals with a few grains per thickness, Mater.

Introduction As demonstrated in a number of recent publications, grain boundaries in submicro- and nanocrystalline materials obtained by severe plastic deformation (SPD) are non-equilibrium and considerably differ from the grain boundaries of recrystallization origin in conventional polycrystals [1,2].
After the 7000С annealing the abnormal grain growth was observed in some areas and very coarse dislocation free grains surrounded by much smaller crystallites appeared in the structure.
The line with the higher isomer shift (component 1) corresponds to the Mössbauer atoms located in grain boundaries, and it is referred to as the grain-boundary line.
First of all, they could result from migration of grain boundaries.
Grain growth in central areas starts at 10000С, and in the periphery at 7500C.

In work [8] on pure α-Fe (99.95 wt.%), a nanostructured layer with a large number of deformation defects was formed by the surface mechanical attrition treatment (SMAT) as pre-treatment.
CRA-regime resulted to the formation of a coarse-grained structure with an average grain size of d=70±18 μm in size.
Grain-subgrain structure, CR-regime Coarse-grained structure, CRA-regime Fig. 1.
Ion-plasma treatment produces the composite layers on the side surfaces of 316L steel samples with both grain-subgrain and coarse-grained structures.
For both fine grain-subgrain and coarse-grained samples, the composite layers possess high values of nanohardness.

High compressive tensions are generated below the grain.
The secondary chip formation takes place behind the grain.
This experimental set-up allows the analysis of the resulting scratch groove after a defined number of revolutions.
This procedure comprised the recording of SEM-pictures after a certain number of revolutions and at a selected position of the sample.
In Fig. 5 (a) the produced scratch groove on a high-strength concrete sample at three different numbers of revolutions n = 2, 10 and 20 rev is shown.