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Meanwhile, as the cooling rate falls, nucleation rate decreases, resulting in size enlargement and number reduction of primary silicon [5, 6], that is, the number of primary silicon particles changes from 10~20 in an area of 1000×1000µm cast by water-cooled copper mold to 0~5 in an area of 1000×1000µm cast by the refractory mold.
For the formation of grain, there are mainly two ways: homogeneous and heterogeneous nucleation, either of which should meet the needs of supercooling degree [7].
There are 0-5 primary silicon particles in an area of 1000×1000µm; in other cases, the number of primary silicon is obviously more than that of the former.
By comparing, it is found that with the addition of Al-3Ti-1B modifier, the shape of eutectic change from small point to thick lamellar, and both the number and the size of primary silicon increase.
(2) With slower cooling rate of the sample, the modification effect of Na salt modifier is weak; increasing the cooling rate of the sample can effectively improve the effect of grain refinement of the Na salt modifier on 4Y32 A-alloy

The initial grain diameter was 13.6 mm.
The various grain diameters were also measured, and the number of different sizes were presented in Fig. 6(b).
Almost 18% of grains kept the original size, and 17% of the grains had the approximate diameter of 7 mm.
As can be seen from Fig. 7, there are quite a few equiaxed grains which is indicative of recrystallized grains formation.
Many of the small recrystallized grains had high-angle grain boundaries showing that they are not sub-grains.

Specifically, the improvement of compressive strength is due to the fine grain strengthening and second phase strengthening.
In the early stage of immersion, large numbers of hydrogen bubbles which arise from the surface of the aged specimens were evidently observed.
In the process of aging treatment, Mg-Zn phases will precipitate from Mg matrix along grain boundaries and grow rapidly, which extends to the interior of the grain and restricts the grain growth, making the grain size decrease (Fig. 3(b)).
Form Fig. 3(c), the grain boundaries become wider and further extend to the grain.
Because the SiC located at the grain boundaries can restrict the grain growth or cause more precipitation of Mg-Zn phases, and further restrict the grain growth.

There is a number of disadvantages typical for all the existing multilevel constitutive models of polycrystalline metals.
Taking into account and the relation (4.1) the grain spin lattice tensor can be expressed as follows:
These models have a serious deficiency: lack of taking into account the interaction of neighboring grains in a polycrystalline sample; in fact, grains in these models are considered separately.
Therefore, we will consider the model of the lattice rotation of grains based on taking an explicit account of the latter.
The first component describes the lattice rotation together with the material in the grain during the imposed kinematic effect.

Phase composition of EH36 is given priority to with ferrite, in addition to a large number of TiC precipitations [4].
From the thermodynamics, the introduction of the deformation stored energy can lead to elevate Ae3, the number of balanced transformation increase with a certain temperature, which should be a universal rule of all steels.
Grain size of Volume 3 is finer than others.
The nascent ferrite cores diffuse and grow up rapidly under stress at the high temperature, then become the ferrite grains with different orientation located on the original austenite grain boundaries as zonal or chain.
TiC mainly precipitates in the process of hot-rolled deformation, the greater the deformation, the lower the deformation temperature, and the more the number of precipitated phases, the smaller the size of them.

From Fig. 7, the number/size of cavity was analyzed by an Image Analyzer with its results presented in Fig. 8.
Both number and size increased with increased hold time.
Under the same hold time, the number/size of cavity of HAZ is greater than that of base metal.
Relationship between the number and size of cavity with various hold times.
Crack growth path and cavity at prior austenite grain boundary (ht:1000s).

The average grain size decreased with increasing the YM content.
This decrease probably can be attributed to segregation of Y3+ and Mn3+ ions at the grain boundary, led to the decrease in the mobility of grain boundary.
According to the above results, it is believed that YMnO3 inhibited the grain growth and thereby reduced the grain size.
This is due to the reduction in grain size [9].
Acknowledgements This research is financially supported by Faculty of Science, Prince of Songkla University under contract number 154003.

The transition between both stages happens when the number of particles disappearing due to coarsening is greater than the number of particles forming due to nucleation [9].
M(t) represents the mobility of grain boundaries and Nrex the number of recrystallization nuclei per unit volume.
The effect of Nb solute drag in reducing mobility has been included following Canh´s solution [13]: 1 1 )( −         += Nb pure C M tM α ,         −      = T E T E DE TN bb bb b bV κκ κδ α sinh )( 2 Eq. 7 where Mpure is the mobility in a pure material, δ the width of the segregation profile, Nv the number of atoms per unit volume, Eb the binding energy of solute atoms to grain boundaries and D the cross-boundary diffusion coefficient.
Finally, the number of recrystallization nuclei per unit volume is proportional to SV, the grain boundary area per unit volume, Nrex = kSV/AC, with k a geometric factor and Ac, the area of the nucleus, that depends on the driving force. k is an adjustable parameter whose value is directly related to the recrystallized austenite grain size.
These calculations have been performed using the same value for the fitting parameter k = 0.06. 1.E+18 5.E+20 1.E+21 2.E+21 2.E+21 3.E+21 0.001 0.1 10 1000 100000 Time (s) N (Number density)m -3 0 20 40 60 80 100 Precipitate Volume Fraction (%) Number density Precipitate Fraction 875ºC 1015ºC Ps a) 0 10 20 30 400.1 10 1000 100000 Time (s) Precipitate diameter (nm) MODEL 1015ºC 875ºC ε= 0.4, ε = 1s -1. b) Fig. 2 Evolution of the particle (a) number density and volume fraction, (b) size at 875 and 1015ºC From Fig. 3 it results that the mechanical softening is, in both cases, larger than the recrystallized fraction.

It’s also an important method to obtain the bulk ultrafine-grained materials of pure metals, alloys and powder materials, etc. [1.2].
Therefore, it is possible to obtain a large accumulated strain by re-pressing, and then achieve the effect of refining the size of the grains substantially.
Therefore, the large-sized extrusions must go through a multi-pass ECAP to achieve the effect of uniform grain refinement.
Therefore, the large-sized extrusions must go through a multi-pass ECAP to achieve the effect of uniform grain refinement
Acknowledgements This work was financially supported by the Guangxi Natural Science Foundation (Gui Ke Qing: 0832006) and the open foundation of the key laboratory of new processing technology for nonferrous metals and materials, Ministry of Education, Guangxi University (Contract Number: GXKFJ-17).

Localized transformed bands consisted of fine equiaxed dynamic recrystallized grains with its band width 50µm approximately can be observed for 90° specimen (Fig.2(c)), while coalescent of micro-voids or micro-cracks at localized transformed bands consisted of fine recrystallized grains could also be found at the same fracture cross section (Fig.2 (d)).
Therefore, the formation of localized deformed bands consisted of fine equiaxed dynamic recrystallized grains should be the reason leading to fracture.
The number of the integral for 90° specimen, which equals to the area under the 90° specimen curve, is bigger than that of 0° specimen obviously, as showed in Fig.1.
The higher temperature rise is also conducive for dynamic recrystallization of AZ31magnesium, and contributed to the formation of localized transformed bands consisted of fine equiaxed dynamic recrystallized grains, crack initiation and propagation.
Cracks initiated and propagated along localized deformed bands consisted of twin intersection for 0° specimen, and that cracks initiated and propagated along localized transformed bands consisted of fine equiaxed dynamic recrystallized grains for 90° specimen.