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About five hundred grains were measured for each grain size distribution.
The number averaged SDAS and ferrite grain size values measured at several through-thickness locations for all the slabs, Table 3, indicate that the finest SDAS and ferrite grain sizes are near the top-surface, which experienced the highest cooling rates.
Al- and Nb-rich precipitates were often clustered together in regions of high precipitate number densities, whilst, Tirich precipitates, of size 50-200 nm, were generally found associated with Nb-rich particles.
However, the precipitate distribution was found to be more homogeneous on slab 3 (ratio between maximum and minimum precipitate number density values approximately 1.8 : 1 at quarter thickness position).
The number of these actually present for reheating to 1225°C is very low, which is consistent with the large grain growth that occurs as almost full dissolution of pinning particles takes place.

Coarse grains broke into fine grains, and grew into medium grains.
During rolling of the alloy, the time and number of slippages occurred are different for the difference of grain orientation, and the distribution of grain orientation as well [9-11].
In Table 2, the grain with the size less than 10 mm was defined as the fine grain, the grain with the size between 10 mm and 35 mm was defined as the medium grain, and the grain with the size more than 35 mm was defined as the coarse grain.
Grain size percentages of rolled 1235 aluminum alloy (%) Grain Grain size /mm 50 % hot rolling 90 % hot rolling Fine grain <10 30.03 92.16 Medium grain 10~35 28.53 7.84 Coarse grain >35 41.44 0 The percentages of fine grains, medium grains, and coarse grains were close in 50 % hot-rolled 1235 aluminum alloy, and the percentage of coarse grains was the largest by 41.44%.
Due to the different orientation of crushed grain blocks, there were a large number of dislocation tangles along the boundaries, which prevented the dislocation from further slipping and resulted in strengthened work hardening.

It can be seen that for both applied deformation routes the microhardness increases along with the increasing number of passes.
It should be noted that the first pass causes the strongest anisotropy, which becomes reduced along with the increasing number of incremental ECAP passes.
With the increasing number of passes, primary grains become elongated with the deformation direction on the Y and Z planes and gain a low angle grain boundary substructure.
The grains are equiaxial and the significant amount of high angle grain boundaries creates many obstacles to mobile dislocations.
Langdon, The evolution of homogeneity and grain refinement during equal-channel angular pressing: A model for grain refinement in ECAP, Mater.

The grain size is related to the number of grains in a unit area.
According to the close feature of the binary steel microscopic image, we introduced a filling-and-elimination method to count the number of grains [4].
Counting the number of grains in Fig. 4 by filling-and-elimination counting algorithm, the result is N=46.
Here, the direction number indicates the average value in whole boundary.
The filling-and-elimination counting algorithm can count the number of grains in the image accurately.

Previous research on developing the Interdependence Model assumed that the number density of nucleant particles was constant for the range of alloy compositions considered.
The second term xSd describes the contribution the TiB2 particle number density makes to grain size
Hence, it appears that the main reason for the increase in grain size is not due to changes in xSd due to a change in the number of nuclei that are present, but rather an increase in the value of xnfz.
An analytical model for constitutional supercooling-driven grain formation and grain size prediction.
The Effect of Grain Refinement and Silicon Content on Grain Formation in Hypoeutectic Al-Si Alloys.

Modeling Ostwald ripening remains inexact because of the large number of thermodynamic, kinetic and spatial variables which must be simultaneously considered and the former coresponding models make assumptions about the grain shape, diffusion field around the grains or concentration of the matrix phase to make the problem tractable.
The number of iterations is given in units of Monte Carlo step, MCS.
The total number of states that A-sites could assume was Q = 32, the mole fraction of A was 0.80, and simulation temperature was kBT = 0.7.
Under these conditions, it is not possible for a grain boundary atom from the first grain to jump across several atoms of the liquid phase to the next grain.
Without liquid phase, some grains became larger at the expense of other smaller grains and grain growth occurred almost entirely by the direct exchange mechanism.

Evolution of the ferrite mean grain size as a function of the transformed fraction The number density of ferrite grains was determined for all the steels and treatments.
However, in order to compare the different results and taking into account the fact that ferrite grain size changes during transformation, the number of grains per unit volume, Nv, had to be determined.
Taking into account the fact that the austenite grain size is similar for all the steels, an increase in the number grain density means a major refinement in the final ferrite microstructure, as is observed in Figure 1.
In the case of V-1 steel, it was observed that the number of grains is higher than in the C-Mn steel at all transformation stages, though the difference becomes very important at the later stages when a significant increase in the number of grains, particularly after treatment B, occurs.
In all cases intragranular nucleation takes place at relatively late stages during transformation and contributes to the refinement of the final microstructure by increasing the number of grains.

The measurements were carried out at the acceleration voltage of 20 kV with the step size varying from 50 to 500 nm, depending on grain size (i.e. number of ECAP cycles).
It shows an almost homogeneous microstructure with equiaxed grains separated mostly by high angle grain boundaries.
The grain boundaries are obviously closer to the equilibrium state than grain boundaries in the specimens that underwent a smaller number of ECAP passes.
The ratio KD/Kv is plotted in Fig. 7A as a function of the number of passes.
number of ECAP passes.

Introduction The growing interest in the low energy Σ3n (n=1, 2, 3) CSL grain boundaries (GBs) is indicated by the increasing number of studies on the formation of these microstructural elements.
The numbers of cycles were 1, 2, 4 and 8.
The number of mapped points was 30537 at a step size of 2 μm.
Grain size is increasing significantly with the number of iterations as the strain values are decreasing in a manner of ε/m, where m is the number of iterative steps.
For the same reason grain size in specimens with the lower total strain (ε: 1) is growing faster compared to specimens that suffered higher strain as the number of cycles grows.

Specimen number Yield trength/MPa Tensile strength/MPa Yield-strength ratio 1 600 665 0.90 2 530 670 0.79 Grain boundaries misorientation distribution.
Pipeline steel is a polycrystalline material system, composed by a large number of grains with different orientations and boundaries with different types and structures.
But after yield and in the process of growing up of the grain boundaries, the strain energy will concentrate in the small number of large-angle grain boundaries edge, the capacity of coordination to resist deformation will be weakened, resulting in the quick rupture after yield in the macro-performance.
Fig. 3 Interaction modes of PSBs with large- and low-angle GBs The PSBs through the low-angle grain boundaries does not mean it disappears, instead, it passes to the adjacent grain boundaries, and if there were still low-angle grain boundaries, it will continue to migrate until meet large-angle grain boundaries and pinned up in it.
Therefore, if the specimen has a larger percentage of low-angle grain boundaries, due to the difficulty for defects and stress to concentrate on the low-angle grain boundaries, the defects and stress will be pinned up in a small number of large-angle grain boundaries after reaching the yield stress.