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The statistical model of grain growth and the onset of the abnormal grain growth It has been well established that a necessary condition required to allow homogeneous abnormal grain growth in polycrystalline materials is the presence of unstable grain growth inhibitors (second phase particles, atom drag..); its effects on the evolution of Grain Size Distribution (GSD) and some of the conditions for the onset of abnormal grain growth has been already clarified by different papers [1,2].
By analyzing the GSD we can divide it into three zones, as pictured in Fig. 2: one containing the grains which tend to shrink, one containing the grains which tend to stagnate and the last one containing the bigger grains which are allowed to grow when in contact with the grain Ri.
Fig. 2: Statistical distribution of the grains and relative behavior in correspondence to grain Ri
An analysis of the statistical significance by the numerosity of each grain classes, in relation with the total number of the grain population, led to choose the class width of the histogram as equal to 2 micron.
The build up of a microstructure with very few grains of relatively large size (3 times the smallest grains in the system) embedded in a large population of small grains (coincident with a high peak in GSD) produces an acceleration process for the grain growth kinetics with features of a discontinuous process.

The experimental results show that the copper billets with refined grains have higher strength than those with coarse grains prepared by annealing treatments.
Experimental Setup Grain Refinement.
Without the reduction of the initial billet cross-section, the process can be repeated a number of times and the billet is rotated by different routs between consecutive passes in order to obtain uniform strain.
This phenomenon is particularly clear in the case with the coarse grains (annealed copper) at 25 ºC.
An inhomogeneous deformation occurs in the case with coarse grains as illustrated in Fig. 5(a).

On the other hand, it is reported that grain refinements cause improvement of ductility and appearance of super plasticity.
However, the tensile strength of AC4CH declined along with the increase in the number of passes.
During the pressing, the billet undergoes severe shear deformation but retains the same cross-sectional geometry so that it is possible to repeat the pressings for a number of passes, each one refining grain size.
Moreover, ECAP-Back Pressure (ECAP-BP) method was reported to be more effective for grain refinements than ECAP method [9].
Fig.4 shows the relationship between number of passes and Charpy impact strength.

The more the bend numbers in the channel are, the better the slurry is, i.e. the primary a-Al grains are more spherical and finer.
The subsequently turbulent melt continuously washes against the primary α-Al grains on the channel inner surface, so this phenomenon impels a great number of the primary α-Al grains to gradually separate away from the inner surface.
This condition means that a great number of the separated primary α-Al grains can be survived and the spheroidization of the primary α-Al grains can be more perfect.
This condition means that a great number of the separated primary α-Al grains can be difficult to be survived and the spheroidization of the primary α-Al grains can be not perfect or not possible. 3.2 Effect of bend number on the slurry microstructure The bend number in the channel has also an important effect on the slurry microstructure.
(2)The more the bend numbers in the channel are, the better the slurry microstructure is, i.e. the primary a-Al grains are more spherical and finer

The {110} texture with the peak at {110}<110> and {110}<221> was observed in this work, however, a large number of experimental of XRD revealed the {110} texture distributed disperse and vary weak Goss texture was formed, which is totally different from the conventional process.
The growth of Goss grains has an significantly incubation period as the increase of grain size is more than double at 975˚C and the grain size of Goss grains is less than the average grain size of matrix after the abnormal growth.
This phenomenon is related to the disappearance of exact primary Goss grains that are swallowed by the abnormal grains.
The dispersed AlN, MnS precipitated at in grains and grain boundaries will naturally inhibit the growth of primary recrystallized grains in grain oriented 4.5% silicon steels, and it will be beneficial for the abnormal growth of Goss grain.  
With the increase of annealing temperture, the size and number of Goss primary recrystallized grains devoloped obvious, which due to the high mobility of the special grain boundaries between Goss grains and γ-fiber grain, as shown in Fig. 5c (Indicated by D and E).

The fracture of studying materials were characterized as the ductile fracture due to the existence of a large number of dimples.
The grains of the material before ECAP were heterogeneous and had grain size from 50 to 200 μm.
Simultaneously elongation decreases with higher number of ECAP passes at RT and 200°C.
The number of dimples increased with the increasing testing temperature.
The fracture of ECAP-ed AZ61 alloys were characterized as the ductile fracture due to the existence of a large number of dimples.

Such effects can be eliminated by means of a grain size distribution including two distinguished peaks at the coarse-grain and Nano/ultra-fine grain regions.
In order to obtain the minimum number of regions containing all potential cracks, the number of regions was increased.
The modeling process was initiated with four sections and their number was increased till no more new cracks could be observed in each section.
As it is observed in Fig. 4 and Fig. 5, the obtained results from the elastic-plastic-fracture analysis using XFEM contains a number of dents that could be due to the occurrence of main cracks.
Generally, one can conclude that in fixed volume fractions, the more the number of coarse grains, the more appropriate results may be obtained.

Application of electron backscatter diffraction to grain boundaries V.
This mapping of grain boundary positions is in itself a powerful application of EBSD, because it allows the grain structure to be quantified.
Grain boundary plane determination The macroscopic grain boundary crystallography comprises five independent parameters.
For this reason, nowadays a greater emphasis is placed on the grain boundary plane, and a stereological method for determining boundary plane density distributions, called the 'five parameter analysis', has been developed and used successfully on a number of materials.
(a) Schematic shape of a single grain (b) Representation of a three grain junction.

It is normally found that an unfavorable grain was eliminated by a favorable grain.
These small grains are usually called chill grains.
Finally this grain disappears during growth.
This means that the number of grains decreased with growth because of grain selection.
This is regarded as the “gradation grain”.

And finer grains with the high angle grain boundaries (HAGBs) and disperse second-phase particles could be obtained in AZ61 and AZ91 after 8 passes of ECAE. 1.
The figure shows that there are low angle grain boundaries (LAGBs) with misorientaion<15r and high angle grain boundaries (HAGBs) with misorientation>15 rin the two alloys.
Fig. 3 TEM morphology and misorientation angles of AZ61 (a, b) and AZ91 (b, c) Mg alloy after ECAE 8 passes at 225°C 3.2 The effects of second phase on grain refinement The microstructure evolution of AZ61 and AZ91 Mg alloy during ECAE showed that the grain size decreased with the pass number increasing.
In the AZ61 and AZ91 Mg alloy, Mg17Al12 particles would precipitate during ECAE deformation as pass number increasing.
During ECAE, dislocations are arranged into dislocation boundaries and sub-grain boundaries and then these sub-boundaries evolve to high angle grain boundaries (LAGBs) and high angle grain boundaries (HAGBs).