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Grain refinement at the central zone is faster due to the strain inhomogeneity.
But the peripheral zone is also refined with the number of CCDC.
The number of initial tetrahedral elements was 30000.
Moreover, the strain gradient increases with the number of CCDC.
While at the peripheral zone, original grain boundaries still can be seen though there are lots of deformation bands in some grains (Fig. 5(b)).

From these results, it was known that contact stiffness depended on the number of abrasive grains existing on wheel surface occurred by the difference of dressing lead.
It is considered that this different tendency of contact stiffness depends on the number of contacting abrasive grain acting to the workpiece.
On the other hand, in measurement for the stationary state shown Figure 7, since the number of contacting abrasive grains to workpiece increases with the increase of the contact force as shown Figure 9, the number of the linear spring as the stiffness of one abrasive grain and/or bond increases.
From this calculated result, it can be regarded that the number of contacting abrasive grain existing on the grinding wheel surface is constant irrespective of the increase and/or the decrease of the table feed rate.
That is, since the stiffness of one abrasive grains is constant to against the different grinding force as shown Figure 8, and the number of contacting abrasive grain under the grinding operation for same wheel depth of cut doesn't vary as shown Figure 9, it is regarded that the stiffness of grinding wheel itself under the grinding operation also is constant for the different grinding force.

Complete suppression of typical columnar grain growth and significant equiaxed grain refinement is observed.
Achieving a fine and equiaxed grain structure, whilst preventing cracks and hot tearing, is typically achieved by chemical grain refinement.
Casting Shearing speed (rpm) Avg. primary α–Al grain size (µm) Avg.
Such oxides may act as substrates for nucleation but are not effective for grain refinement due to their poor wettability and low number density.
· Formation of coarse dendritic α–Al grains is completely suppressed and significantly refined grains are promoted under intensive melt shearing

The addition of these refiners introduces a large number of particles like Al3Ti and TiB2 or TiC into Al melts.
The particles acted as nuclei of α-Al grains in Al melts promote equiaxed and fine grain structures during solidification.
In previous study [2], the role of Al3Ti and TiB2 in Al-Ti-B alloy refiner on grain refining efficiency of α-Al grain in pure Al cast has been reported.
Commercial Al-5mass%Ti alloy ingot was used as grain refiner.
Grain refinement of pure Al cast using Al-Ti alloy refiner.

Each cell has six state variables: orientation, grain boundary, grain number, the number of recrystallization and color display.
Firstly a random number rand is introduced, then the rand and are compared at each time step. lf rand≤, the cellular becomes DRX nuclei, and cellular state variables are updated accordingly.
Recrystallized Grain Growth.
If, the phagocytosis probability is calculated, where i is the number of recrystallizated cellular at neighbor of current cellular.
Then a random number rand is introduced, and the rand and P are compared at each time step.

RE content affects grain size by influencing number and size of fine inclusions in the finished steel sheets.
It can be understood the number density descreases.
AlN and MnS which size is smaller than 1μm can be inhabitors to prevent from grain growth.
RE addition in the steel can refine grains.
The number density of fine inclusions with size less than 1μm in the samples decreases, and the grain of the finished steel grows up homogeneously which is benefit for its magnetic properties.

Table 2 Rolling processes of testing steel plate Rolling process Ⅰ stage rolling Ⅱ stage rolling Pass number Total rolling reduction/mm Average reduction ratio of pass /% Pass number Total rolling reduction/mm Average reduction ratio of pass /% Total reduction ratio of last three passes Ⅰ 6 135.716 12.42 6 69.25 15.24 36.01 Ⅱ 5 132.74 14.58 6 69.252 15.25 40.44 The effect of rolling process on microstructure.The picture of metallographic structure at the place where is 1/4 steel plate thickness is shown in figure 1 (a, b).
Research shows [3] that the way to refine crystal grain includes: the elements (such as Nb, V, Ti ) of grain refinement is formed into stable carbonitride to inhibit the growth of crystal grain, control rolling process (rolling temperature, rolling reduction), refine austenite grain, strengthen cooling rate and refine ferritic structure.
The increase of austenite grain boundary area provides more position for ferrite deformed nucleus of austenite, which refines the rolled ferrite grain.
This explains the phenomenon that yield ratio of steel is increased by refined grain, namely, the thinner ferrite grain, the bigger yield ratio.
Research of Steels Grain Refinement [J].

A polycrystalline microstructure made of grains and sub-grains can be obtained in a random or deterministic way.
In the examples shown in this work, the initial mesh was non uniform and anisotropic, taking into account the presence of interfaces between grains and sub-grains.
A convenient way of constructing a large number of grains is given by the Voronoï tesselation.
Probing algorithms can measure particular instantiations of a microstructure, e.g. grain size, grain shape distribution, or crystallographic texture.
The geometry of the boundary can be derived from the distance function φ with: φφ ∇∇= rrr n (5) n rr ⋅∇−=κ (6) If Ng is the number of grains in the considered aggregate, then Eq. 4 can be generalized using Ng level set functions : ( ) ( ) ( ) ( ) ( ) ( ) ∑= +∆ = gN i i i i i xtnxttxETMtxxtV 1 ,,,)(, , r r γκ χ (7) where the function ( )txi,χ is a presence function within the grain i.

The mean misorientation of individual grains is defined as the average misorientation between randomly selected pairs of measurements within a grain, where n misorientation pairs are considered for a grain in which n measurements were obtained.
Figure 1 CL image with outline of core of grain in white.
Figure 2 (A) CL image with outline of core of grain in white.
pinning) to within grains that grew (Fig. 7).
Numbers give mean misorientation of grains; grains with low numbers are interpreted to have grown during GBM.

The microstructure was dominated by nearly equiaxed grains with mean grain size of ~0.9 mm and HAB fraction of 78%.
Importantly, the grains in the tensioned specimens had nearly equiaxed morphology and grain-size distribution was relatively narrow (Fig. 6a).
In contrast to stir zone material, the base material exhibited a duplex microstructure with a small number of large grains being surrounded by arrays of fine grains (Fig. 6c).
This perhaps means a small population of grains grew at a significantly faster rate than the other, “matrix” grains and thus the observed process seems to fit the definition of abnormal grain growth.
Acknowlegement The financial support received from the Ministry of Education and Science, Russia, under Grant No. 14.578.21.0097 (ID number RFMEFI57814X0097) is gratefully acknowledged.