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A grain growth simulation based on the concept of grain boundary migration driven by the radius curvature has been tested to study the abnormal grain growth (AGG) of the Goss grains in silicon steels in presence of particles.
The grains with a radius jR greater than nR ( nRjR > ) resist to the normal (abnormal) grain growth.
The transition probability from one orientation number to another is given by: T         > > ≤ < = 0)ΔEornRij(R 0 0)ΔEandnRij(R 1 p (11) Where E∆ is the energy variation.
The black grains correspond to the Goss grains.
The large size grains resist AGG and the Goss grain shape becomes anisotropic.

l Grain samples.
Each grain type contained 360 kernels.
The aim to the analysis was to classify the objects derived by image processing into a defined number of the classes according to their specific features.
Classification of cereal grains using machine vision: I.
Shape analysis of grains of Indian wheat varieties.

The specimen and grain size dimensions (in experiments and simulations) were chosen such that, first, the number of grains in thickness was decreased from approximately three to one, i.e. columnar grains.
Thereafter, the number of grains in the specimen width was also decreased towards one, i.e. a single grain in a cross-section.
The extended model of Evers et al. proved suitable for the investigation of grain statistics effects in specimens with a limited number of grains [10].
Schematic illustration of the dependence of the tensile strength on the grain size for tensile sheets with a limited number of grains across the thickness.
• For components with a single grain across the thickness and a considerable number of grains in the other dimensions, the stress level depends primarily on the ratio of the thickness and grain size.

Mean grain size.
For very large grains only the center of individual grains was indented.
With decreasing grain size five different segments for nanohardness (labeled as number 1, 2, 3, 4, 5) and two segments for modulus (labeled as number I and II) can be observed. 3.3.
It has been revealed by simulations[17, 18] that the strength of NC Cu decreases with decreasing grain size in the grain size range of 3.28 to 6.56 nm, where the NC Cu deforms via a large number of small “sliding” events of atomic planes at grain boundaries, with only a minor part being caused by dislocation activity in grains.
It is has been reported that the diffusivity of impurity elements (like sulfur) in Ni is several orders higher than the self-diffusivity of Ni at high temperature [28], therefore impurities such as sulfur are expected to segregate to the much smaller number of grain boundaries of larger grains at these annealing temperatures.

The dependence on the grain orientation of the alignment of planar dislocation boundaries in plastically deformed metals has been investigated by examining grains of S orientation ({123}<63-4>) in cold-rolled polycrystalline aluminum.
One concern with TEM investigations however is that the number of grains that can be analysed is somewhat limited.
In this way we are able to show a clear correspondence between the boundary alignment and the grain orientation.
This high volume fraction of rolling texture orientations allows a large number of grains with S orientations to be examined in the samples.
At this moderate reduction the EPBs can be easily recognized while the grain rotations are sufficiently small to allow identification of the original grain boundaries from the ECC and EBSD images.

Microstructures formed by the hot-rolling were confused to be observed by an optical microscope and SEM, awing to a number of fine precipitates.
Solid lines show large angle grain boundaries, in which the difference in orientation between the neighboring grains is larger than 15 degree, while fine lines show small angle grain boundaries.
many small angle grain boundaries are observed in larger grains, while they are less observable in smaller grain.
The smaller grains were formed by dynamic recrystallization during hot-rolling remaining strained large grains.
Averaged grain size in (a) was about 10 µm, but the microstructure was composed of extremely fine grains and coarse grains.

Different methods are available for grain refinement of metals and alloys e.g. grain refinement by rare earth elements and severe plastic deformation, SPD, methods.
To determine the grain size and the general microstructure of ZA22 and its microalloys, cylindrical specimens of 10 mm diameter and 10 mm height were machined from each, mounted on araldite, then ground using successive grit numbers of silicon carbide paper, followed by polishing with one micron diamond paste, and finally etched using (5% HNO3 + 3% HCl+4% HF+88% H2O) solution for 20 seconds and the Metallurgical examination was carried out using the optical microscope type (NIKON108).
Hence it improves its formability and reduces the number of stages required for forming the alloy at large process strain in excess of the plastic instability strain.
Birch: The Effect of the titanium Boron Concentrations on Aluminum Grain Refining Alloy.
Zaid: Poisoning of Grain Refinement of Some Aluminum Alloys (Seventh, Cairo Intern.

It was found that the more plastic deformation imposed in a single pass, the more ultrafine grains with high angle grain boundaries are achieved.
Two routes A and BC were adopted up to a total number of 4 passes in the present work.
The number of cycles at failure was recorded at the applied stress amplitude.
Fig.9 Dependence of the stress amplitude on the number of cycles to failure for ECAPed samples (2A and 2BC; present) and coarse grained(CG Al and 8BC; Ref. [8]).
Concluding Remarks The microstructure and Mechanical characteristics of the ECAPed 1050 Al alloy using two routes A and BC was examined in the present investigation and the following conclusion can be drawn: 1- The ECAP process via route BC to two passes resulted in fine cell size and relatively higher angle of misorientation. 2- The compressive strength is usually higher than that of tensile strength for same number of passes for both routes. 3- The tensile and compressive strength is usually higher for route BC compared to route A for same number of passes. 4- The value of uniform elongation is low, though the total elongation is as high as 18%. 5- The number of dimples on the fracture surface decrease with the refinement of grain size. 6- Route Bc exhibited higher fatigue strength under HCF condition compared to route A, for the same number of passes.

It has been postulated that the HPR expression which is valid for coarser grains is not valid for finer grains because the constant of proportionality in the HPR that depends on the resistance of the grain boundary to dislocation movement is no longer a constant as continuing refinement of the grain size occurs [4].
During experiments, the mechanisms of deformations in materials are analysed by monitoring the behaviour along grain boundaries and in the interior of grains.
It was found that nanostructured materials have larger "grain boundary layers"-to-"grain sizes" ratio compared to bulk materials.
Working with a 3-D sample composed of large, possibly infinite, number of grains, is a time consuming and tedious task to gather accurate information about every grain.
Conclusions This paper shows that both average grain size and grain size dispersion play vital roles in the design of specific mechanical properties.

Such grains were called "parent"-grains because they are formed during primary recrystallization.
The average number of the special boundaries per one "parent"-grain decreases with increasing complex stacking fault energy, the energy of the antiphase boundaries and the ordering energy [2].
The grain boundary ensemble parameters, namely, the proportion of the "parent"-grains without special grain boundaries, the average number of the special boundaries per one "parent"-grain, the fraction of the twins S3 in the spectrum of the special boundaries and the average relative energy of the special boundaries depend on the long-range order degree (Fig. 2).
An increase in the "parent"-grain fraction without special grain boundaries with increasing long range order degree leads to a decrease in the average number of special boundaries per one "parent"-grain (Fig. 2b).
The dependences of the "parent"-grain proportion not containing a special boundary (a), the average number of special boundaries per one "parent"-grain (b), the twin boundary S3 proportion in the special boundary spectrum (c), the mean relative energy of the special boundaries (d) on the long-range atomic order degree degree (Fig. 2c) cannot to be explained by the influence of the stacking fault energy on the special boundary spectrum.