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Synopsis of the literature on fatigue of nanostructured and ultrafine grain materials An analysis of journal articles and conference proceedings listed in ISI SciSearch®, ISI Proceedings®, and the Engineering Index® since 1990 shows that there has been a steady increase in the number of publications on fatigue in nanocrystalline or ultrafine grain materials.
Fig. 1 shows the increasing rate of growth in the cumulative number of publications on fatigue of this class of materials from zero in 1990 to 498 today.
Having a combination of large and small grains presumably offers both the effects of higher strength associated with the smaller grains and the enhanced ductility associated with larger grains.
The total number of fatigue cycles to failure at a constant applied cyclic stress during totalN can be partitioned into three stages: growth link incub total NNNN --?
where incubN is the number of loading cycles to incubate an initial crack, linkN is the number of additional cycles extend this crack through the short crack behavior stage via additional nanovoid nucleation and linkage, and growthN is the number of cycles to propagate the crack to failure.

Lead has high atomic mass number Z and high density.
Tungsten, which has better shielding properties than lead because of its high Z (atomic mass number), is a material that is difficult to machine or cast, the melting point being as high as 3387°C[4].
Smaller mfp values is an indication of higher number of interaction of the incident radiation beam with the atoms of the sample(s) being tested.
The high number of interaction as the distance between successive collisions reduces resulted in large attenuation values.
Grain size and grain size distribution of the hard component in the tested sample has great impact on the overall microhardness value, small grain size creates more regions of stress concentrations around the hard component and increases the probability of hit of the indenter to the W particles within the brass matrix and consequently gives higher microhardness value.

Martensite cracks constitute 52 out of a total number of 103 damage features analyzed for all strain levels (i.e. 50%).
Table 1 summarizes results from the four different strain levels analyzed in this study, indicating the number of DM cracks formed along PAGbs.
This number is relatively low at the highest strain level (εavg.= 16%) as prior austenite grain reconstruction was not possible for many cases at this strain level, mainly due to high deformation gradients in the martensite.
The increased number of martensite cracks is mainly attributed to the high mechanical contrast between both phases.
In an assumed parallel loading setup of soft ferrite and hard martensite grains, the ferrite grains sustain higher local strains during deformation, while the stresses are mainly carried by the martensite islands.

This goal is still a pending task in spite of the great number of studies that have been carried out since this property was discovered in YTZP materials, and a good example can be found in the following reference [11].
To determine the optimum sintering conditions, a large number of tests were carried out in the SPS, changing either temperature, heating rate, pressure or sintering time.
Density and grain size of the ceramic materials samples.
Grain size of the materials.
In Table 1, average grain size values are included.

Reported in the literature[8], with the increase of the content of Ca, Mg17Al12 reduced gradually, the number of Al2Ca increase gradually in Mg-Al-Zn alloy.
In the solidification process, because of its solution capability in magnesium alloy is quite poor(maximum 1.6%), Ca easy to be pushed into the forefront of α crystal grains, formed a layer of Ca-rich metal film in alpha grain interface, which hinder grains growth.
When Ca reaches a certain level in the alloy, it will form high-melting-point Al2Ca phase with Al, the phase precipitate on grain boundary also to the benefit of inhibit the growth of grains.
Moreover, the supersaturated alloying elements in the matrix precipitate and form new second-phase particles, large number of tiny Al2Ca and MgZn2 dispersed evenly in the alloy, they are mainly located in dislocation, grain boundary or uniform distribute in the tiny equiaxed grains[10].
The smaller size, the greater the number, the more uniform distribution of these second-phase particles, the more contribution to the intensity.

The effect of the loading conditions on the number of cycles to crack initiation is evidenced using a ∆εt-Ni plot.
The majority of the cracks are smaller the average grain size.
In "small SCV slip systems", the effective grain size is much smaller than the actual grain size.
Since the number of PSB remained exactly the same in all the simulated cases, this means that slip irreversibility increase takes place at the scale of individual PSBs.
CONCLUSIONS The number of cycle to initiation of large cracks (50-150µm) in thermal fatigue is 4-5 times faster than in conventional fatigue, for a fixed ∆εt,eq.

It is believed that the increase of the transmittance after HIPing was attributed to the growth of the grain size and the reduction of the number of grain boundaries and pores.
As figure 2 shows, after hot pressing, the grain size is small and not uniform, mainly ranging from 2 to 5µm or from 10 to 20µm, and there are many grain boundaries.
After HIPing, the grain size increased obviously and became uniform, ranging from 50 to 100µm, the grain boundary area decreased, and no pores can be observed.
Therefore, the scatter due to grain boundaries and pores decreased.
Both before and after HIPing, the fracture occurred mainly along the grain boundaries, HIPing treatment increased the grain size and decreased the number of grain boundaries but did not change the fracture mechanism.

The grain size is refined from the initial ~75 µm grain size down to ~1.5 µm.
The initial grain size is ~75 µm.
Though the extrusion ratio was only 15.4, the resulting grain structures are mostly recrystallized and equiaxed fine grains.
The finest grain size achieved is 0.7 µm.
Acknowledgement The authors gratefully acknowledge the sponsorship from National Science Council of Taiwan, ROC, under the project number NSC 91-2216-E-110-006.

The value of ky increases with increasing Taylor factor [5] which generally depends on the number of slip systems.
Because the number of slip systems of hexagonal closed packed (hcp) metals are much fewer than those of face centered cubic (fcc) and body centered cubic (bcc) metals, larger Taylor factor could be obtained for hcp metals than for fcc and bcc metals.
Grain structure is illustrated in Fig.2b and average grain size is about 500 μm.
It is noted that twins appear in grains.
Dynamic recrystallization takes place and the microstructure is composed of large size grains and fine recrystallized grains.

In part B near depositing layer (is termed as the new β zone), the original β grains grow up as the columnar grains along build height direction.
But actually, growth height of the columnar grains want to be small comparing to that of as-deposited stainless steel,13 and the columnar grains are already unobvious when depositing to definite layer number, so its temperature gradient is less than that of as-deposited stainless steel.
This is because of more overlapping tracks, the number of the heat cycle that each depositing layer experience is much more too, thus causing the β columnar grains refine.
But for depositing the triangle entity, according to the characteristics of its depositing path, in one side of longer depositing path β columnar grains are bulky columnar grains, at anther side of shorter depositing path the β columnar grains is thin columnar grains.
The number of overlap track is more, the columnar grain is smaller. 4.