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In other words: cyclic stress and number of cycles together determine whether a PSB is formed or not
The resulting grain size was approx. 60 ± 10 mm.
The resulting grain size was indeed 60 ± 10 mm.
The number of cycles was 1.59 x 1010 (same specimen as used in [4]).
For stress/plastic strain amplitudes far below the conventional PSB threshold of 63.0 MPa and 6.2 x 10-6, such as Ds/2 = 36 MPa and Depl/2 ≈ 3.0 x 10-6, only few grains exhibit a changed dislocation structure, i.e. small loosely connected dislocation patches (not shown in this paper), whereby the number of grains decreases the lower the amplitudes are.

(1) In this numerical model, nucleation site i for one kind of precipitate was assumed in the matrix (i=1), dislocations (i=2), grain face (i=3), grain edge (i=4) or grain corner (i=5) as illustrated in Fig.3.
Dislocations and grain boundaries (grain face, grain edge and grain corner) serve hetero- geneous nucleation sites, whereas homogeneous nucleation is assumed in the matrix [1].
Here, ni, Ci and Vi are the number, solute concentration and volume fraction of vacant i sites, whereas those with overline refer to the equivalents of occupied i sites by precipitates.
Results of numerical modeling Fig.4 shows the changes of number density N(__)i and volume fraction V(__)i of precipitates nucleated at site i as a function of aging time t at 443K.
(a) (b) (c) 1 3 4 5 1 3 2 1 3 1 3 2 4 5 2 3 4 5 3 4 5 2 1 Fig.4 Aging time dependence of number density and volume fraction of precipitates nucleated at different sites at 443K.

However, rough rice grain is different from other grains because it has an outer cover shell (palea and lemma) and a bran layer.
In this sense, the current study aims to analyze the moisture removal and its effects on the stress cracking and the number of brown rice grains (BRSMG CONAI variety) at the temperatures of 60 and 80oC.
Air Rough rice grain T (oC) RH v(m/s) Mo(d.b.)
The increased number of cracked kernels probably occurred due to stress induced by moisture gradients during drying [9,10].
This process strongly influences the current number of cracked or broken grains.

Multiscale Modeling of SPD Processes for Grain Refinement I.V.
Second, the meso-level, the level of grain groups and single grains.
It is devoted to finding out the reasons of the deformation straining, the evolution of the grain size, dislocation density (total, in cell-grain interior, in cell-grain boundaries) and vacancy concentration depending on the SPD conditions.
In connection with this, the ingot material starts failing after a certain number of ECAP passes, when it has exhausted its strain capacity.
It's considered that the reason, why the grains of greater diameter split into a number of substructure elements, is the decrease of the total latent energy stored in the material due to the plastic deformation inhomogeneities.

The Ms temperature is increased with increasing the AGS and can be represented as follows: G0.303.542)C(M os ×−= (1) where G is the number of ASTM grain size. 50 100 150 200 250 300 350 400 450 : Ms Strain Temperature ( o C) 850 o C-10min 900 o C-10min 950 o C-10min 950 o C-120min Fig. 1 Dilatational curves measured during quenching from different austenitization Fig. 3 Relation between the austenite grain size and the Ms temperature 6.75 7.00 7.25 7.50 7.75 8.00 8.25 8.50 8.75 280 290 300 310 320 330 340 350 Ms temperature ( o C) ASTM grain size number Fig. 2 Optical microstructures of the specimens quenched from different austenitization conditions: (a) 850℃-10min, (b) 950℃-10min, and (c) 950℃-120min The reason why the Ms temperature increases with increasing the
Thus, the fine austenite grains have more grain boundaries which play a role as obstacles to the growth of the martensite, finally reducing the Ms temperature.
At stage I, where the martensite volume is less 30 percent, the specimens with fine austenite grain sizes (ASTM grain size number: 8.44 and 8.68) reveal faster transformation kinetics probably because the fine grains provide more nucleation sites for the martensite transformation at the grain boundaries.
The transformation rates of the coarse grained (ASTM grain size number: 7.01 and 7.69) specimens at stage II, where the martensite volume is 30 to 80 percent, are faster than those of the fine grained specimens, because the grain boundaries obstacle the growth of martensite once nucleation is almost done.
(2) where VM is the martensite volume fraction, T is cooling temperature, G is the number of ASTM grain size, a0, a1, b0, b1, α, and β are the optimized parameters determined base on experimental kinetic data.

The critical grain holding power of diamond sticks can be calculated by dividing the critical grain holding　pressure by the number of grain based on the specification of the diamond wheel.
As another reported, The number of grains which acts on grinding was calculated by modeling a grain on a cube.[4] It is confirmed that the critical grain holding power of resinoid bond diamond wheel which makes copper the filler is about 0.1N.
(2) 　fc：Critical grain holding power of one grain（N/piece），Fc：The grinding force just before the grain on a wheel work surface is dropping out（N），n：The number of grains which acts on grinding（piece）．
In addition, the number of grains which acts on grinding is calculated by Eq.3
(3) λ：The number of the grains per 1 square mm（piece／mm2），ℓ：The length of the arc which the wheel and the workpiece contacts on the surface grinding（mm），B：Width of a wheel（mm） 　 And, the length of the arc which the wheel and the workpiece contacts on the surface grinding can be calculated by Eq.4

The number of passes can attain 40, and only a low alloy Mg as an AZ31 (Mg-3%Al-0.8%Zn in wt.pct.) with moderate strength is a suitable candidate for sheet fabrication.
In addition, fine-grained Mg alloys tend to significant grain coarsening due to rapid grain growth at elevated temperature.
Journal Title and Volume Number (to be inserted by the publisher) 3 Fig. 1.
Grain size distribution charts for specimens after rolling and static annealing at (a) 250°C and (b) 275°C. 0 10 20 30 Rolling at 300°C (a) Percentage, % Grain size [µµµµm] 1 10 Rolling at 275°C 0 10 20 30 40 50 Rolling at 300°C (b) Percentage, % Grain size [µµµµm] 1 10 Rolling at 275°C Journal Title and Volume Number (to be inserted by the publisher) 5 Fig. 4.
It is seen from a comparison of Figs 1a and 5 that static annealing after IR at 275°C converts the structure of the rolled specimens into the less constrained state: the grain boundaries are more regular after annealing, the dislocations are less visible within the grains, the number of fine particles is reduced within the coarsened grains.

The number N of the straight cut grains was counted.
If the distribution of the grains were uniform and isotropous, N grains were cut in the line segment of the length L, which was perpendicular to the direction of AB.
Therefore, there were N2 grains in the area of L2.
So, the mean length of the grain was: a=
Table 2 The grain size measured results Number Measured value a1 (mm) Measured value a2 (mm) Measured value a3 (mm) average value a (mm) no nano-oxides addition 0.875 0.583 0.583 0.644 0.01 wt% MgO 0.438 0.875 0.583 0.632 0.02 wt% MgO 0.583 0.438 0.292 0.438 0.05 wt% MgO 0.875 0.583 0.875 0.778 0.01 wt% CaO 0.438 0.583 0.350 0.457 0.02 wt% CaO 0.292 0.583 0.292 0.389 0.05 wt% CaO 0.583 0.583 0.292 0.486 Conclusions Nanometer calcium and magnesium oxides were added into molten steel by the carrier method in the experiment.

A small number of samples were also tested under strain rates of 0.1 s-1 and 4 s-1.
Journal Title and Volume Number (to be inserted by the publisher) 3 20µm 20µm a) b) Figure 2.
Journal Title and Volume Number (to be inserted by the publisher) 5 Once a necklace has formed, the same assumptions can be used to generate an expression for the fraction DRX by estimating the volume unfilled by the necklace.
Influence of initial grain size on a) εp and σp and, b) the DRX grain size and fraction. 4.
The regions shown in this plot are numbered to be consistent with previous work; the missing Region II is the dynamic recovery steady state region.

Ultrafine-grained steel with ferrite grain size less than 4μm, has attracted more and more attention in recent years, for grain refinement is the only way to improve strength and toughness simultaneously [5].
Sampling point and serial number of samples are shown in Fig.1.Hot strip thickness is 2mm, and reduction of each pass from F1 to F6 is 55, 54, 46, 34, 32, 20 %, respectively.
Grain size of the ultrafine-grained steel has been measured and the average grain size is around 3μm.
Large strain accumulation in austenite comes from the large plastic deformation of the stock in the unrecrystallized region, which increases the effective austenite grain boundary area per unit volume and the number of nuclei per unit area of effective austenite grain boundary.
That not only accelerates the nucleation of ferrite grains, but also postpones the growth of ferrite grains, which lead to ferrite grain refinement.