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The paper presents experimental data demonstrating the super-strength and “positive” slope of the Hall-Petch relation when passing from micro- to nanostructured state in a number of metallic materials subjected to severe plastic deformation.
In recent years our laboratory in close collaboration with colleagues and partners performed a number of investigations of unusual mechanical performance of SPD-processed Al and Ti alloys as well as in several steels [10,16-20].
Although it is possible to achieve the nanocrystalline structure with grain sizes less than 100 nm in a number of metals and alloys by means of HPT [23, 24], for SPD processing by ECAP and HPT it is typical to form ultrafine-grained structures with mean grain sizes within the submicrometer range so that, typically, the grain sizes are ~ 100-300 nm [21,23,24].
Non-equilibrium grain boundaries with dislocation arrays are typical of different materials after SPD processing, and their role in the mechanical behavior of UFG materials has been studied in a number of reports [23,27,28].
Figure 7 shows the data for a number of Al alloys presented in the form of the Hall-Petch relation in which the yield stress (σ0.2) is plotted against the inverse square root of the grain size (d-1/2) for the UFG Al alloy 1100 produced by ARB-rolling and consequent heat treatment [37] as well as for an ECAP-processed alloy Al-3%Mg alloy [38].

For samples sintered at high temperatures, a significant change of grain morphology was observed and a large number of plate-like grains develop, see Figs. 1d, 1e and 1f.
However, in the present work, the plate-like grains are not the minority, and the grain sizes of these grains are not abnormally large.
Grain growth exponent.
Change in grain morphology may certainly result in a change in grain growth exponent.
Therefore, the grain size employed in the present study is underestimated for the plate-like grains and approximately true for the equiaxed grains.

Due to the increase of the number of operating slip systems, the strongest dislocation interactions are realized in the stage.
Stage V: In a number of previous reports, this stage is presented as another large strain stage.
The shift of hardening stage due to grain size reduction A number of previous works have reported that grain size reduction to certain levels tends to result in changes of hardening mode at the onset of plastic deformation.
As can be seen in the figure, given a test line LT, d is defined as the reciprocal of the mean linear intercept of the test line with grain boundaries; and is equal to the length of test line LT, divided by the total number of intersections, N, N L N d T L == 1 , (7) where, LN is the number of interceptions of grain boundaries per unit length of the test line.
(9) Note that, Eq 8, 9 and 10 are valid only when the number of grains in a crystal is so large that these quantitative stereology equations converge to the smooth functions of d.

It is to be noted that columnar grains are still present in the grain refined sample.
The grain size of non-grain refined alloys (Al-0.8% Mg and Al-4% Cu) was calculated to be 800-900 µm (Fig 4 (a and c)), whereas grain refined alloys have grains 300-400 µm in size (Fig 4 (b and d)).
Grain size of reference and grain refined alloys were reduced significantly.
Nucleation efficiency refers to the effectiveness of a given type of inoculant with specific physical characteristics and solidification conditions, such as number density, size distribution and cooling rate.
Similarly for the MgAl2O4 between 200 nm and 2 µm in size, number density was approximated to be between 108 and 1010 particles/cc.

It was found that the grain size reduction of the material, which was processed using a die with an angle of 90°,wassignificantly more than that of a die with angle of 120°for the same numbers of ECAE.
It was also mentioned that the specimens processed with route A had an elongated and banded structure and those with route C had larger number of equiaxed grains.
As received after the 2nd pass after the 4th pass after the 5th pass Fig.6: The microstructures of the extruded specimens at a magnification of 200 Fig.7: Variation in the grain size versus the number of passes Table 1: The Grain size of the material for different passes Sample ASTM micro-grain size number (n ) The number of grains per square inch (N ) Average grain size (µm ) As received 6 32 45 The1st pass 8 128 22 The2nd pass 8.6 369 13 The3rd pass 11 1024 8 The5th pass 13 4096 4 The6th pass 14 8192 2.8 The Fracture Toughness The toughness is a measure of the amount of energy a material can absorb before fracturing.
The impact energy absorption varied cubically with the pass number.
The impact energy absorption varied with respect to the number of passes.

The elements of oxide film consist of α- Fe2O3 with sphere grain of 5-50nm.
This phenomena is demonstrated that the composite abrasive grains in oxide film is a compound structure which is centered by abrasive grains, with α-Fe2O3,Fe(OH)3 surrounded.
Second, research the micro structure of oxide film, element, shape, grains size, and covering parcels situation of oxide film which surround abrasive grains, and the forming mechanism of composite abrasive grains.
Therefore, a layer of circular ring which center on abrasive grains and surrounded by α-Fe2O3 formed around the abrasive grains in cutting, namely composite abrasive grains.
Acknowledgements The research project was supported by the general program of the National Natural Science Foundation of China (Approval number of project: 51475147) and the Science and Technology key Project of the Education Department of Henan (Item Number: 13A460341) References [1] B.

Currently, a number of characterization methods and techniques are applied for better understanding of γ massive (γm) microstructure, in order to tailor-make microstructures related with specific structural applications.
A number of theories based on the results of electron microscopy has been proposed regarding the formation of the massive grains in TiAl-alloys, these studies have all been performed two-dimensionally [6-8].
In practice, when analysing an orientation map obtained from SEM-EBSD, one can very often see that a number of γ variants are missing.
Even though, the maps do not show any drastic changes in γm grain morphology, the number of grains present in the analysed area is different.
(a) (b) Table 1 The frequency of each γm variants formed arising from one of the γ nucleus Grain Name/Depth of investigation γγγγn γγγγn T γγγγnb 1 γγγγnc 1 γγγγnd 1 0 µµµµm (Number of grains/ surface area) 27/1290 µm 2 14.25/2 µm 2 21/1063 µm 2 31/5258 µm 2 0/0 µm 2 13 µµµµm(Number of grains/ surface area) 24/984 µm 2 0/0 µm 2 27/494 µm 2 33/6332 µm 2 3/33 µm 2 The variant γnc1 arising from the nucleus γn is the dominant variant in Fig 3 (a).

The simulated results of the grain growth by the model are very close to the grain growth of Al2O3-based ceramic materials.
The initial size of grain is D0.
It is assumed that the requirement of heat for grain growth in the total heat is R1, heat causes the growth of grain, the conversion factor is r.
(12) The parameters r, R1, R2, R3 are positive number. α is the consumption rate of heat, β is the consumption rate of space.
This model is a new model of grain growth.

Change the state of the cell to grain X with probability proportional to the number of cells of grain X that are located in its neighborhood.
On the left, 2 cells are depicted, each given a certain activity ai = µici = ni/Vi of a solute element (ni is the number of solute atoms, µi the activity coefficient and ci the concentration of solute element i).
Each cell i represents a volume Vi with a concentration of solute atoms ci or a number of solute atoms ni.
This calibration links the value of the surface area A to a value for the neighborhood radius r. r can be chosen arbitrarily within such limits that on average a feasible number of cells is found.
Only boundaries with relatively small unit cells can be treated in such calculations since the number of atoms in the simulation must be no more than a few hundred to make the calculations feasible.

From these images above, it can be seen that in all simulation results, with the lapse of simulation time, the average grain size of the matrix gradually increases, the number of grain decrease, and the grain boundary moves to its curvature center.
Fig. 2 Change curves of average grain size with time Fig. 3 Logarithm analyses curves of grain growth The reason for this is that the number of the second phase particles in the matrix are different because of the different size distributions when the volume fraction and the average size of particles are same.
As shown in Fig. 4, when the size of the second phase particle fits lognormal distribution, the number of the big particle is abundant, the total number of the second phase particles decreases, and then the pinning effect on grain boundary is weakened at the same volume fraction.
Fig. 4 Distributions of second phase particles (a) Distributions of particles’ number; (b) Distributions of particles’ volume fraction Conclusions A modified grain growth CA model is set up, which investigates the pinning effects of the second phase particles with different size distributions on grain growth.
The exponent of grain growth is not a constant number and decreaces gradually with the increasing of pinning force.