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Under these circumstances, there exists a competition between the decrease in grain size (grain refinement) due to the imposed plastic strain and an increase in grain size (grain coarsening) due to the increased temperature of the specimen subjected to deformation.
Since the evolution of ultrafine grains takes place by thermally activated processes, the role played by the interfaces such as grain boundaries in controlling the grain size is significant.
This assumes further significance due to the presence of large number of grain boundaries in ultrafine grained materials.
During large strain deformation, as the imposed strain increases, original grain boundaries are compressed and are elongated in the direction of grain flow resulting in high aspect ratio grains, with the thickness of grains decreasing with increasing strain.
Based on Fig.3(a), it may be noted that when the thickness of the deformed grain (grain size) is smaller than the grain boundary diffusion distance, atoms diffuse and ferrite structure is fully recrystallized consisting of new equiaxed ultrafine grains; On the other hand, when the thickness of deformed grain is larger than the grain boundary diffusion distance, atoms diffuse to a short distance leaving a mixture of elongated and newly generated grains.

Kinetic strength in grain growth is evaluated for HAZ of welded pipes.
The grain growth is assumed diffusion controlled and Arrhenius temperature dependency is applied for the rate of growth in grains.
Thermal cycle induces the number of diffusive jumps and exploring the grains, and in a non isotherm cycle the intensity of the diffusive jumps can be evaluated by the term of kinetic strength as it is suggested by Ion et al. [1].
The grain growth is obtained from the computation of equation 3, where go is the grain size in parent metal.
Mohanty: A modified analytical approach for modeling grain growth in the coarse grain HAZ of HSLA steels, Scripta Materialia, Vol. 50 (2004), p. 1007-1010

The results show that the grain size decreases with strain.
The ultra-fine grained structure formation process was discussed in detail.
It was interesting that, for such a level of strain, the structure was characterized by sharp grain boundaries and there were few dislocation tangles in the grain interiors.
The main idea is the breaking-up of the original grains into cellular substructures and then the cellular substructures transform into equiaxed grains.
Acknowledgements The author would like to acknowledge the financial support of National Natural Science Foundation of China under granted number 50471017.

There are a number of instances of ductile ultra fine-grained materials.
However, most of the limited number of studies of tensile ductility in nc elemental metals have revealed poor ductility.
Distributions of both number and volume fractions of grain sizes were presented.
The mode of the volume distribution was found to be much larger than that for the number distribution.
Ma, Ultrafine Grained Materials, ed.

The higher the prior strain level, the higher the velocity of grain boundary migration and the higher the annealing twin density in the recrystallized grains.
A "twin" refers to a grain that has one or two twin boundaries with a larger grain in which it is embedded.
Annealing twins are quantified by their density, which is defined as the number of intercepts of annealing twin boundaries per unit length [7].
The average grain boundary migration velocity is estimated as the change of average grain size of recrystallized grains per unit time.
(a) All grains (b) Recrystallized grains 3.

Modeling of Kinetics and Grain Density Evolution during Isothermal Phase Transformation W.
Introduction The well-known Kolmogorov–Johnson–Mehl–Avrami (KJMA) model considers the relation of transformation fraction and experimental variables, such as time t, temperature T or heating rate Φ, rather than the actual grain number [1].
However, grain density is important for mechanical properties and solute segregation.
KJMA model uses the extended fraction due to extended grain to express actual fraction, while in fact the formation of new grain is determined by the untransformed volume [2-4].
Theory and calculation During isothermal phase transformation, the number of supercritical nuclei in a unit volume, at time during a time lapse, is given by, with as nucleation rate.

Fine grain size and uniform distribution of nanocrystalline in nanostructured coating improve the wear resistance of coatings due to fine-grained strengthening and dispersion strengthening effects.
Because the average diameter of nanostructured coating is small, so the distance between grain boundary and dislocation source is small and the number of pileup dislocation is few.
Fine-grain strengthening effect restricts crack initiation and propagation.
And more grain sector and more uniform distribution of the grains improve the mechanical properties of the coating.
Summary (1) The abrasive wear resistance increases with the decrease of WC grain size

As the K2O was added to 0.5 mol%, the number and the size of abnormal grains were increased by much.
It can be seen that the number of abnormal grains increases with K2O addition.
Therefore, the number of grains that show abnormal growth is increased.
An increase in the sintering temperature also lowers the critical driving force, resulting in an increase in the number of abnormal grains.
Further reduction in the critical driving force, the number of abnormal grains increases more with increasing sintering temperature.

One of the challenges to achieving a fine grain size in Mg-Al alloys has been to develop an effective and efficient grain refiner [2].
Whilst it is clear that UT can be effectively used to reduce the grain size in castings, there are a number of issues that need to be addressed before transferring the technology to gravity fed or low pressure die castings.
Fig. 3 shows two casting sections with an extremely fine grain structure at the bottom where UT was applied and a region of relatively coarser grain size in the bulk of the casting.
However, it is clear that there are a number of issues that need to be considered when applying UT to commercial castings.
UT was able to decrease the grain size further than SiC additions alone, whilst the SiC addition leads to a more extensive region of fine grains than UT alone.

AFS Grain Fineness Number: From the sieve analysis the AFS grain fineness number (GFN) of the base sand was determined.
This parameter is the number which corresponds to the sieve number, in the set of sieves used in the test, through which all the grains would just pass if they were of the same size.
The dredged sand had rounded grains.
Rounded grains produce densities about 8-11% higher than angular grains [8].
The grain fineness number (GFN) of mould sands ranges from 40 to 220, the higher numbers representing fine sands [13].