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Summary results from field UT in the Río Papaloapan Bridge Structural deficiency Number of anchorage elements Type of element Large Grain Size (ASTM 2) 8 2 High Pore Content 2 1 and 3 Probable large Grain Size 6 2 Once the structural deficient elements were identified, a rehabilitation project was proposed to replace these elements and an integrity analysis was required to evaluate the structural reliability of the remaining elements, considering the statistical characterization of their microstructural, mechanical and chemical properties.
Characteristics of the removed anchorage elements Id number for anchorage element Anchorage element type Semi-Harp Cable Deficiency 1 2 1 13 Large grain size 2 2 2 12 Large grain size 3 2 2 13 Large grain size 4 2 3 10 Probable large grain size 5 2 3 11 Large grain size 6 2 3 12 Probable large grain size 7 2 4 8 Probable large grain size 8 2 5 10 Probable large grain size 9 3 6 3 High pore content 10 2 6 13 Large grain size 11 1 7 1 High pore content 12 2 7 8 Large grain size 13 2 7 9 Probable large grain size 14 2 7 10 Large grain size 15 2 7 12 Large grain size 16 2 7 13 Probable large grain size 17 2 1 6 Good condition 18 3 2 4 Good condition 19 2 5 5 Good condition 20 1 6 1 Good condition Table 4.
No. 5 Large grain size (b) Element Id.
No. 19 Fine grain size Figure 11.
The element that was initially classified as large grain size and resulted with a fine grain size with a large number of pores, was incorrectly classified because of the pore content, where ultrasonic energy dissipation presents almost the same behavior.

The obtained shear strain depends on the geometry of the sample and number of revolutions applied and is calculated according Eq. 1, where r, t and n are the radius, the thickness of the sample and the number of revolutions.
In the present study, the number of revolutions was chosen in such a way that a certain amount of plastic strain is reached at a radius of 3mm.
Nuclei A, C, D and E grow each to a single grain.
In Ultrafine Grained Materials III
In Ultrafine grained materials III, page 629, 2004

The number of layers includes all metal and ceramic layers.
Ni grains form big aggregates and distribute among Al2O3 grains.
The Al2O3 grain size in Al2O3 sample is about 0.4-0.7µm.
The grain size of Al2O3 in the (Al2O3+20wt%Ni) and (Al2O3+50wt%Ni) is about 0.3-0.5µm and 0.4-0.6µm.
According to the Hell-Petch formula, the strength will increase as the grain size decreases.

The mean grain size is about 20 µm.
Moreover, grain fragmentation sets in (continuous dynamic recrystallization [5]) leading to a bimodal grain size distribution.
With increasing number of passes the mean grain size is reduced to the micron range.
The inclination decreases with the number of passes.
The inhomogeneity decreases with the number of passes.

Nanostructured and ultra-fine grained metals have higher strength but extremely limited ductility compared to coarse grained metals.
The final microstructure after rolling had a grain size of 100 to 200 nm and following short annealing at 180 o C for 3 min resulted in a "bi-modal" grain size distribution in the nanocrystalline to ultra-fine grain range.
The volume fraction of coarse grains with a grain size of 1 to 3 µm was about 25%.
Considering a material with i-modal microstructures, the number of the ith-order grains with a grain size of di can be described by a power law as D i i d C N = , (1) where Ni is the number of grains with a grain size of di, C is the constant; D is the fractal dimension.
Three-grain unit cell model of MMC with the periodicity boundary conditions.

So it leads to less hardening and lower resistance against deformation of surface grains and makes the surface grains deform easier than those grains inside because dislocations moving through the grains during deformation pile up at grain boundaries but not at the free surface [2].
With the decreasing specimen size and invariant grain size, the share of surface grains increases, which leads to increasing ratio of free surface grain to all grains (Fig. 1).
The function can be differentiated as (4) The surface layer model has the limitation that the number of grains in the thickness or radial directions must be more than two, i.e..
For easier understanding, we give the definition as follows (5) Here, for micro sheet, N is the number of grains in the thickness direction.
For micro cylinder, N is the number of grains in the radial direction.

In reference[4], factory experiment showed that the ratio of equiaxed grain zone and the equiaxed grain density all decreased with increasing casting speed.
By this way, the propagation of grain occurs.
In this study, casting speed is the only variable, hence we assume that the number of the original separated grain is the same at different casting speeds.
As a result, the value of H (Formula 6.) is chosen as the measurement criterion of the number of the heterogeneous nucleation nucleus.
In this situation, the number of the survival separated grain which can become the heterogeneous nucleation nucleus finally is greater.

With the increasing in environmental management, and people developed a number of non-cyanide silver cyanide-free solution .the cyanide-free silver-plated was tested and research by a large number of Scholars and they got some results[5-9].
Fig.2 XRD pattern at different ultrasonic power The the grain size was caculated by the eq.1.
Tab 1 shows the the relationship between ultrasonic power and the grain size.
With the ultrasonic power increasing, the average grain sizes of the silver coating significantly reduced ,but when the ultrasonic power increasing ,the grain sizes of the silver coating did not have a significantly change.
When the nucleation rate was faster than the grain growth rate, the grain had been refined[12] .

In addition, it is noted that the maximum elongation is displaced from 1.0 × 10 2 s-1 to 3.3 × 10-2 s-1 when the number of ECA pressings increases from 6 to 8.
A similar trend was noted in an Al-Mg-Li-Zr alloy [23] and it was attributed to the increase in the fraction of high-angle boundaries with increasing number of pressings.
There are two trends noted in Fig. 5: Firstly, the flow stress for the material decreases significantly after ECAP and decreases slightly with the increase of the number of passes.
This effect is the direct result of grain size reduction over ECAP.
Processing of ECAP at 473 K using an Al-7034 alloy results in an ultrafine grained microstructure having grain sizes reduced from ~2.1 µm to ~0.3 µm and breakup of precipitates of η-phase (MgZn2) from rod-shaped to smaller spheroid. 2.

The several numbers of methods using external forces have been applied to introduce fluid flow during solidification of molten metal in casting process.
Microstructure of the ingots cast with the conventional Direct-Chill method exhibited relatively fine dendrite grains at the surface area, but coarse dendrite grains at the ½ radius and large equated dendrite grains at the centre.
Globular grains were obtained in AZ91 alloy subject to high intensive ultrasonic vibration.
The grain size was reduced gradually from 202µm to 146µm with increasing ultrasonic power [21].
The result shows that the long dendritic silicon phases are split into number of particles [22].