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Parameters such as GOS (Grain Orientation Spread) or GOS/D (D the diameter of the grain) or GND (Geometrically Necessary Dislocation) densities have been determined for the whole set of grains as well as for subpopulations (smallest grains, largest grains for example).
Thanks to the high indexing speed of the EBSD systems together with the good spatial resolution of the FEG-SEM, it is possible to obtain good statistics in terms of the number of grains and in terms of the number of pixels inside the grains [8].
j For a grain i, the Grain Orientation Spread reads GOS(i) = [ 1/J(i) ] wij (1) where J(i) is the number of pixels in the grain i and wij is the misorientation between the orientation of pixel j and the mean orientation of grain i i Then, for a set of I grains, GOS reads GOS = (1/I) GOS(i) (2) k For a pixel j, the Kernel Average Misorientation reads KAM(j) = [ 1/K ] wjk (3) where K is the number of pixels around pixel number j j For a grain i, the Grain Average Misorientation is GAM (i) =[ 1/J(i)] KAM(j) (4) where J(i) is the number of pixels of grain i i And, for a set of I grains, GAM reads GAM = (1/I) GAM(i) (5) Similar to the KAM(j) values, the misorientations around each pixel over a given step size can be used to determine the density of GNDs (Geometrically Necessary Dislocations) [10,11,12].
Fig. 2: GOS values (in °) versus the % of elongation (for all the grains, for the largest grains and for the smallest grains).
This could be understood on the basis of the high number of available slip systems.

The results show that the microstructure which contains a number of cake shaped grain can be refined and homogenized by the feasible annealing holding time.
The most of these grains are irregular in nature.
But some recrystallized grains and caked grains can be easily observed in these micrographs in Fig.1(b).
A bimodal grain size distribution consisting of larger and finer grains has been observed after full recrystallization in Fig.1(d).
Conclusions 4.1 It is found that the ferrite grain size is grown up with longer annealing holding time at 850 ℃.The ferrite grains are fully recrystallized with 150s annealing holding time, the microstructure which contains a number of cake shaped grain can be refined and homogenized by the feasible annealing holding time. 4.2 It is known that the recrystallization can largely be effect by the annealing time .The change of strength for test steel is small when the annealing time is up to 150s.

Characterization of Grains Size by Ultrasounds Ali Badidi Bouda1, a, Mohammed S.
Grain size is an indicator of material fatigue.
The different grain sizes are obtained by rolling.
Frequency spectrum Dictionary - View detailed dictionary 1. noun 1. quantity 2. amount 3. number 4. deal 5. measure 6. batch 7. increment 8. gob 9. grist Fig.3.
The grain refinement was obtained by rolling.

Grain boundary engineering has been well established.
Keywords: Grain boundary engineering, Fracture control, Grain boundary brittleness, GBCD, Triple junction, Magnetic field application.
One of the authors first introduced new grain boundary-related factors, so called "the grain boundary character distribution (GBCD)" and "the grain boundary connectivity" when he proposed the concept of grain boundary design and control [4], now widely termed "Grain Boundary Engineering"[6-10].
Now, we can determine the orientation and distribution of a huge numbers of grains and the characterization of grain boundaries in a polycrystal without much difficulty by using computer-aided and fully automated OIM, even for ceramics such as polycrystalline SiC with the average grain size of 2 µm, as shown in Fig. 1.
(a) SEM (b) OIM microstructure, not only the grain size ( i.e. the density of grain boundaries ) widely used in the past, and also the connectivity of grain boundaries with different characters.

According to the empirical Eq.7, the initial node number of the hidden layer is 6.
Then make use of the successive steps of growth to determine the node number of optimum implication layer as eleven.
Eq.6 ； Eq.7 ; In Eq.7, l refers to the number of hidden nodes; m refers to the number of input nodes; n refers to the number of output nodes; a refers to constant between 1 to 10.
Research on Coarse Grain Soil Maximum Dry Density Test[J].
Fractal Graphic of Coarse-Grained Soil Category[J] .

The UFG structure contains a significant volume fraction of grain boundaries and exhibits a high number of lattice defects (mainly dislocations) introduced by severe plastic deformation during the HPT processing.
The largest grain refinement was achieved by high pressure torsion (HPT) [5].
Small grain size (in the nanocrystalline range) leads to a significant volume fraction of grain boundaries which represent obstacles for movement of dislocations.
A high number of defects is created in the UFG specimens in the course of HPT processing.
It has two reasons: (i) The extremely small grain size leads to a significant volume fraction of grain boundaries which provide nucleation sites for the second phase particles.

The numbers indicate the boundary misorientations in degrees.
The number and size of deformation micro shear bands increase with straining.
This annealed microstructure consists of layers of equiaxed and elongated grains with transverse grain sizes of 2.1 and 1.1 mm, respectively.
The former ones are free of substructure, while the latter ones involve a number of low-angle subboundaries (Fig. 5d).
Acknowledgements The financial support received from the Ministry of Education and Science, Russia, under Grant No. 14.575.21.0092 (ID number RFMEFI57514X0092) is gratefully acknowledged.

It was found that the crystallinity of grain boundaries degraded much faster than that of grains as shown in Fig. 2.
In Fig. 2, the change of IQ values of grains and uncracked grain boundaries and cracked grain boundaries are summarized as a function of test time.
The IQ values of both grains and grain boundaries decreased monotonically with the test time.
It was found that the accumulation of dislocations deteriorated the crystallinity around grain boundaries drastically and decreased the strength of grains and grain boundaries.
Acknowledgement This research has been supported partially by Japanese special coordination funds for promoting science and technology, Japanese Grants-in-aid for Scientific Research, and JSPS KAKENHI Grant Number JP16H06357.

Also characteristic was increasing of the number of bands with increasing of deformation and mutually crossing of the bands.
Increasing of the number of passes through the angular channel favor homogenization of the materials.
Intersections of the bands and shear bands leads to material divide to parallelograms, which at the later stage, with the increase of number of intersecting bands leads to a microstructure homogenization.
The measurements of the grain size reveal that the sample having an initial in annealed-state grain size of about 250 µm reduced to the grain size below 0.25 – 0.32 µm when it was deformed by ECAP process.
The financial support of the State Committee for Scientific Research of Poland under the grant number 11.11.180.653 is kindly acknowledged.

Regarding the microstructure in the longitudinal section of formed specimens, elongation of grains in the central part and grain size reduction in the boundary area are observed.
He also described [2] how a variation of the swaging parameters such as the feed velocity and the number of forming increments influences properties and microstructure of copper wires.
Grain size evolution.
Fig. 8 Grain size (a) before forming, grain size modification after (b) conventional rotary swaging, (c) after the new method.
Bomas, Influence of the number of impacts during incremental forming on the mechanical properties of copper wires, 8th International Conference of Micromanufacturing (2013)