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To have reasonable statistics and accuracy for the grain size distribution the number of grains measured was in the range of 428 to 1700.
From the sets of measured grain diameters, the two dimensional log-normal grain size distribution, f (d) [23] is arrived by using the following relationship: ……(2) where s is the std. deviation, d is the grain diameter and dg is the peak grain diameter.
Peak temperature, °C Heating rate, °C/s Number of grains Mean volumetric grain size (μm) Standard deviations 950 10 1497 6.0 0.52 950 100 1700 4.4 0.47 950 1000 1741 4.2 0.51 1150 10 670 15 0.60 1150 100 839 11 0.54 1150 1000 596 11 0.62 1350 10 763 61 0.53 1350 100 514 33 0.52 1350 1000 428 32 0.42 Fig. 3a: Representative austenite grains for 100oC/s heating rate and 1150oC austenitizing temperature.
Fig.4 represents the precipitate size distribution in terms of number and volume of precipitates in the base metal and depicts that the precipitates can be broadly divided into three families: Ti-rich (TiN), Nb-rich (NbCN) and Mo-rich (Mo-C).
The relatively sluggish grain growth at the lower times appears to be due to the presence of precipitates that pin the grain boundaries and resist grain growth.

In this figure, a grain in the first line is represented by the number 1.1.
The grains in the second and third lines are numbered as 2.1, 2.2, 3.1, 3.2 and 3.3.
Numbering each abrasive grain, displacement of each grain is measured for the reference.
It can be seen that each displacement of abrasive grain around contacting grain is different depending on each position of grain in analysis.
On the other hand, displacements of the abrasive grains around contacted grain were same displacement for each grain.

It is known that curved and poorly defined grain boundaries of the ARB processed alloy become sharp and stable as the number of ARB cycle increases.
As the number of ARB cycle increased, dislocation cells disappeared and equiaxed ultra-fine grains appeared.
The yield stress and tensile strength vary similarly with the number of ARB cycles.
However, the gap increases as the ARB cycle number increases, which points out that grain boundaries become equilibrated and grain boundary strengthening operates with the cycles.
Wear rate vs. number of ARB cycles for commercial purity 1100 Al. 0 1 2 3 4 5 6 7 5 10 15 20 25 30 Wear Rate (1x10 -13 m 3 /m) Number of Cycle Applied Load: 0.5N Applied Load: 1 N

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.

Thus high strain and strain rate are directly related to the large number of turns and high rotation speed, respectively.
The SADP taken with the aperture of 740nm showed wholly completed rings confirming that a fine grain structure with 0 0 40 80 120160 200 240280 320400 Number Grain width , nm 12 8 4 16 360 12 8 4 0 Number 16 0 4080 120 160200 240 280320 400 360 Grain length , nm Grain length Grain width 500nm 500nm bcc α 500nm500nm 40 50 60 70 80 90 100 Intensity, cps 2 theta, deg.
It is generally considered that the α' nucleated at the shear bands intersections, which are in the forms of ε, mechanical twins and stacking-fault bundles, and the number of α' embryo increases with the number of intersections and the number of the intersections increases with imposed strain [13].
On the other hand, a large strain is beneficial to produce high 200nm200nm b cc α 200nm200nm Grain length Grain width 25 20 15 10 5 0 0 20 40 60 80 100120 140 160 180 Number Grain width , nm 25 20 15 10 5 0 0 2040 60 80 100 120 140 160 180 Number Grain length , nm densities of defects like deformation twins and stack faults.
These defects can produce a great number of intersections and hence the effective nucleation site for α' embryo.

The transition probability from one orientation number to another is given by: T (8) where is the energy change.
To test the model, the problem has been simplified by considering Goss grains (G) (gray grains) in an isotropic matrix of (M) grains.
Conclusion The onset of abnormal grain growth of Goss grains can be linked to the preferential interaction between particles and grain boundaries.
AGG occurs only when normal grain growth is pinned for Goss neighboring grains.
The large size grains resist AGG and the Goss grain shape becomes anisotropic.

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.

The development of the microstructure during grain growth is caused both by the change of average grain size and, what is of concern for crystallographic texture evolution, by the change of the grains' orientation and misorientations distribution in the grain structure.
The direction of p remains the same Journal Title and Volume Number (to be inserted by the publisher) 3 when the sense of the field is reversed.
The freedom to change the magnitude of the driving force for boundary migration by exposing the samples to magnetic fields of different strength yields the unique opportunity to change the dri- Journal Title and Volume Number (to be inserted by the publisher) 5 ving force on a specific grain boundary and thus, to obtain the driving force dependence of grain boundary velocity (Fig. 3).
For a comparison, the reduced mobility of the curved 86° 1010< > tilt boundary σ⋅= mA at 673 Journal Title and Volume Number (to be inserted by the publisher) 7 K in a Zn bicrystal was measured to be K673 ZnA =3.2⋅10 -8 m2/s [28] yielding an absolute mobility (assuming σ∼0.46 J/m2) of K673 Znm ≅7.0⋅10-8 m4/J⋅s.
In contrast, the same heat Journal Title and Volume Number (to be inserted by the publisher) 9 treatment in the same magnetic field results in a distinct difference between usually symmetrical texture peaks when the sample is tilted by +30° or -30° to the field direction around the rolling direction leading to a configuration where the c-axis of grains corresponding to one texture component is aligned normal to the field direction.

Grain Size Sensitivity Modeling and Analysis.
Fig.1 Grain contact model of lapping (uneven grain) A contact model of lapping is show in Fig.1.
The number and size of active grains in the work field are created according to Fig.2 by a randomizer.
(b) the number and size of active grain in the work field are generated by a randomizer.
Typical grain size distribution Fig.3.

For higher number of passes the grain size did not change anymore.
However, the misorientation rose constantly with increasing number of passes, as demonstrated by the SAD patterns in Fig. 2 and 3.
Fig. 4: Mean grain size along the longitudinal direction of both alloys as evaluated from the grain size distributions of 700-1000 grains for each sample.
With increasing number of CCDP passes the yield stress and peak stress of both alloys grew due to strain hardening and grain size strengthening (Hall-Petch hardening) caused by severe plastic deformation.
Furthermore, both alloys showed strain softening after reaching a peak stress during compression. 250 300 350 400 450 500 0 2 4 6 8 10 12 14 16 18 Al-1.5Mn (P) Al-1.5Mn (S) CCDP passes Mean grain size d0, nm aa bb c d cc dd The higher the number of CCDP passes the stronger the strain softening (Fig. 5b-c).