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The production of fine grained materials by SPD, led to a large number of investigations focusing on the microstructure development and related to mechanical properties.
Compared to other SPD processes the HPT technique offers a large number of advantages, as stated in [4].
Transmission electron microscopy (TEM) was used to evaluate the ultrafine grain microstructure evolution with respect to site on deformed disc and the number of turns at corresponding εeq.
The ufg grain substructural features in disc edge support this selective growth of fine grains, as e seen Fig. 4.
Specific behaviour resulted as strain was increasing with number of turn.

The number steps of one sign is determined by a misorientation of crystals and the number of pairs steps of various signs depends on the temperature according to the exponential law.
Consequently the number of the excited atomic configurations in the grain boundary arises.
Figure 12 represents the examples of such dependencies at some values of parameter κ ( )25,13,12 −−−=κ signed accordingly by numbers {2, 3, and 5}.
At low temperatures the number of such excitations is not enough and their sizes are rather small against distance between them.
With growth of temperature the number of clusters as well as the number of atoms included in them grows.

Development of models to predict drying process has assisted in understanding the factors affecting drying process such as temperature, relative humidity and velocity of drying air and optimizes them for reducing drying time and saving energy without performing a large number of experiments [8].
Applications in grains.
The equation used to obtain the heat and mass transfer coefficients are given by [13]: (8) (9) where DAB is the vapor diffusivity in the air, hm is the mass transfer coefficient, hc is the heat transfer coefficient, dp = 2.50 mm is the particle diameter, J/kg K is universal constant for air, Re is the Reynolds number, Pr is the Prandtl number, and Sc is the Schmidt number, obtained by the following expressions: (10) (11) (12) being m the fluid viscosity that past over the grain The value of temperature, relative humidity and velocity of the drying air, and convective mass transfer coefficient, convective heat transfer coefficient, initial and equilibrium moisture content, initial temperature and dimensions of the rough rice used in the simulations are shown Table 1.
Bean grain drying analysis.
Hall, Thermal properties of grain, Trans.

The number, shape and size of austenite decomposition and transformation product has important indirect effects．For micro-alloying steel contained micro-alloying elements such as Nb, involving dissolution and precipitation of carbon and nitrogen compounds, it is even more necessary to study The rule of austenite grain growth.
Austenite grain growth law analysis Option 7 different temperature in 900 ~ 1250 ℃ range, and heat the Nb Micro-alloyed Steel for 10 minutes, then measured average austenite grain size and the level of grain.
Higher than 1150 ℃, the grain growth process grow unevenly.
When Heating temperature (Th) is low, such as Th = 900 ℃ or 930 ℃, the number of the undissolved second phase particles is larger.
The observation to several different samples precipitates in the field shows that as the temperature increased, the number of undissolved second phase particles gradually reduced, the observed proportion of fine particlesdecreased, the average particle size increases.

In this way, the number of nuclei per unit area on the grain surfaces can be approximated to the number of nuclei per unit area in the planes.
An estimated grain size of 50 μm should result.
It is clear that a larger number of nuclei, i. e. a larger number of nuclei per unit of grain boundary area produced results in agreement with Cahn’s theory [7].
Fig. 6c, which has fewer nuclei has coarser grains.
Conversely, when the number of nuclei increases the nuclei become close to each other, clustering on the grain faces.

In order to investigate the influence of grain size on notch sensitivities in fatigue of a fine-grained carbon steel, rotating bending fatigue tests were carried out using specimens with a V-grooved circumferential notch of commercial fine-grained carbon steel with grain size of 6.5µm.
Recently, ultra-fine-grained steels with grain size smaller than a few µm have been developed and the mechanical properties were investigated.
These results suggest that fatigue properties of notched member with a fine grain are different from the ones in conventional grain sized steel.
In the following, these materials were called as a fine-grained steel and a coarse-grained steel, respectively.
Both of fatigue limits σwl and σw2 are increased by refining grain size, though 10 4 10 5 106 10 7 200 240 280 320 360 400 N0.05 Nf Stress amplitude , σa ( MPa ) Number of cycles , Nf , N0.05 ( cycle ) Fine-grained steel Coarse-grained steel Fine-grained steel Coarse-grained steel 104 105 10 6 280 320 360 400 Stress amplitude , σa ( MPa ) Number of cycles , (Nf-N0.05) ( cycle ) Fine-grained steel Coarse-grained steelthe increase is small in σw2.

Greer, Grain refinement of Al alloys: Mechanisms determining as-cast grain size in directional solidification Acta Mater. 53 (2005) 4643-4653
They proposed that the final grain size, d, is linearly related to the reciprocal of growth restriction factor for a number of alloy systems, i.e.: d=a+bQ Eq.(2) They stated that a is related to the number density of active nucleating particles while b to the diffusivity of the alloying component under consideration.
Men et al have to assume grains are mono-sized.
The number of growing grains is determined by a free-growth condition.
Fig. 2a shows predicted grain size and 1/Q relations.

In the bicrystals, the observed independence of the peak strain can be ascribed to the limited number of nucleation sites along the grain boundaries, so that this feature of the flow curve is largely determined by the orientations of the component grains of the bicrystals.
DRX nucleation took place at the grain boundary at a strain as low as 0.05, although the number of new grains was quite limited.
Only the number of primary slip traces was counted.
Concurrently, the number of new grains at grain boundary increases.
The new grains appeared behind migrating grain boundaries and were all first-order twins of the parent grains.

Shape of Moving Grain Boundary and its Influence on Grain Boundary Motion in Zinc Vera Sursaevaa and Boris Straumal b Institute of Solid State Physics, Russian Academy of Sciences Chernogolovka, Moscow District, RU-142432, Russia a sursaeva@issp.ac.ru, bstraumal@issp.ac.ru Keywords: grain boundary migration, grain boundary shape, grain boundary faceting, zinc Abstract.
Introduction The classical concepts of grain growth in polycrystal are based on a dominant role of grain boundaries.
The classical von Neumann-Mullins relation of two-dimensional grain growth kinetics [1, 2], determines the change rate of the grain area ()()263 3 b b n A SA n π π π=− − = − & , (1) where bbb Amγ≡ is the reduced GB mobility, mb is GB mobility, γb is GB surface tension, n is the number of triple junctions for the respective grain, i.e. the topological class of the grain.
This means that the equilibrium shape of GB consists of a small number of flat sections with a low energy, which are connected by curved parts, where all crystallographic planes are represented.
Shvindlerman: Grain Boundary Migration in Metals.

This means that we are particularly interested in the number of grains that nucleated and grew independently.
The third issue is whether the average grain sizes should be calculated with respect to the grain area (or grain volume) or to the grain number.
In this case the average of the grain number is the most appropriate quantity.
The area size of a grain was obtained from the number of data points in the grain multiplied by their pixel size.
Table 1: Average grain size as a function of the number of grains considering all grain boundaries with a misorientation larger than 3° (small angle and large angle grain boundaries).