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From the photos it is clear that, (a) Capital letters in Fig. 3a are the serial numbers of ferrite grains in the viewing field.
While the specimen has not been fatigued yet, the cyclic number is zero.
(b) While the cyclic number, N, is up to 5040, two ESFCs (C1 and C2) have nucleated on the top of ferrite grain A (Fig. 3b).
The left crack tip of C1 and the right crack tip of C2 are restrained in ferrite grain A by strong restrict of grain boundary.
The new C1 propagates along the boundary of ferrite grain D leftward, and has also penetrated the grain boundary rightward.

The magnesium alloy with the initial microstructure of fine grains (about 3mm) together with little dislocations inside deformed by dislocation and grain boundary sliding mechanisms, accompanied with little change of crystal orientation, but a large increase of hardness.
It is known that due to the lack of sufficient number of slip systems associated with hexagonal close-packed crystal structure, magnesium alloys with coarse grain deforms by twinning and dislocation slipping mechanisms where twinning lead to orientation change and may activate other slip systems [5].
On the other hand, the annealed magnesium alloys with fine grain of 1 μm deform by grain boundary sliding at room temperature [6].
The AZ31 magnesium alloy lying in solid solution-SPD state showed the initial microstructures of fine grains/twins with the grain/twin size of about 3mm.
The AZ31 magnesium alloy lying in solid solution-SPD-annealing (433K) had the initial microstructures of fine recrystallization grains with the grain size of about 3mm.

This glassy phase also wetted the zirconia grains and prevented the grain growth and the formation of facetted grains.
An average grain size was obtained by multiplying 1.78 to average intercept lengths over 1000 grains.
This glassy phase wetted the zirconia grains and formed rounded grains.
When a crack propagates it follows either the grain boundaries or around grains.
Acknowledgements This work has been supported by DPT (the State Planning Organization of Turkey) under project numbers 2003K120470 and 2001K120590.

While the mean grain size reduces to ultrafine-grain regime (257 nm), dislocation motion is still involved to carry the plastic deformation.
Secondly, due to large strain gradients in the inhomogeneous microstructure during tensile deformation, a large number of geometrically necessary dislocation that are forced to be present to accommodate the large strain gradient will induce an additional strain hardening.
In this grain size regime, the NS Ni exhibits narrow grain size distribution (Fig. 2 (e) and (f)) with most of grains locating in "small nano" regime (less than 30 nm) where the normal dislocation activity is already suppressed.
As the mean grain size reduce down into the nano-scale regime, the dislocation accumulation is hard to take place in grain interior.
Dislocations are emitted from GBs and glide through the grain then are absorbed at the opposite side of the grain.

In specimens were examined the sizes and number density of carbides, the prior austenite grain size and the fineness of the resulting hardening-type microstructure.
Size and Number Density of Carbides.
The smaller was the size of carbides in the microstructure, the greater was their number density.
The prior austenite grain size is related to the number density of carbides in the matrix.
Prior austenite grains were polyhedral in all specimens.

The number of the cycle times was pre-set according to the conditions in experiments, the experiment would be interrupted if it reached the number, and then the middle surface short fatigue crack on notches would be observed and recorded, after that the experiment continued.
At the early stage of short cracks’ fatigue life, initiation is the main forms of fatigue damage (Figs.3 (b)-(d)), and the increasing in numbers of short crack instead of in length by the influence of the grain or phase boundary barrier.
The crack growth data are showed in Fig.5 and Fig.6, where x-axis is presented in two different life forms, one is the numbers of cycles; the other is the percentage of life.
The fatigue crack length at the plateau regions was 20~100mm, which equaled 1~5 grain boundary length.
The influence of barriers will not disappear until the crack length increases to 1~5 grain boundary length

A lot of grains are equiaxed grains, and their organization is ferrite, pearlite, and cementite.
A lot of cementite is at the grain boundaries, a small amount of pearlite distributes at the grain boundaries.
Grain sizes of annealed samples are shown in Table 1.
With the temperature increasing, grains turn into equiaxed ones.
（a）850℃{TTP}8451 （b）875℃ （c）925℃ Fig.4 Results of morphology and composition of edult by TEM When the annealing temperature is over 850℃{TTP}8451 , educts increase significantly, the educts are distributing in grain and grain boundary, and a large number of educts are AlN.

The top layer composed of columnar grains and a transition layer with equiaxed grains was close to the substrate.
The top layer composed of columnar grains and a transition layer with equiaxed grains was close to the substrate.
It was also observed that the average size of the equiaxed grain was very small and the thickness of the equiaxed grain layer was very thin.
As a result, columnar crystals normally grew to the surface from a relatively small number of crystallization centers.
The top layer composed of columnar grains and a transition layer with equiaxed grains was close to the substrate.

The initial grains are created using Voronoi tessellation method, and the grain orientations are obtained from the electron back-scatter diffraction test.
The temperature continuity can be found across some grain boundaries while there is a temperature gap at other grain boundaries.
Moreover, the effects of grain properties, such as grain orientation and grain size, on the grain-level deformation heterogeneity are significant.
The plastic velocity gradient is expressed as: , (2) where N is the total number of slip system, is the shear strain rate on the -slip system, is the slip direction and is the orthogonal plane of , and is the dyadic product.
The simulated temperature distribution shows that the temperature concentration appears at some grain boundaries due to the grain-level heterogeneity induced by the difference of grain orientations.

The equiaxed grain shape is expected in route C since the grain restores equiaxed shape at every other passes.
The grain structure in route C also appeared to be rather close to a high angle grain boundary network.
In route Bc, the grains are small in size and the yield stress is high because of small grain size.
The uniform elongation regime is comparatively large considering small grain size and this was because the grain structure is composed of high angle grain boundaries.
Acknowledgement Authors are grateful to the Korea Science and Engineering Foundation for their financial support of this research through the grant number R01-2005-000-11247-0.