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In the current model, the dynamically recrystallized microstructure will be represented by certain number of representative grain aggregate with different component and different cycle of DRX.
Each grain aggregate has state variables of the component number, dislocation densities, surface boundary area, sum of grain diameter in the grain aggregate, number of grains in the aggregate and volume fraction of grain aggregate.
Where, i represent DRX cycle and j represent component number.
Then, number of nuclei for grain aggregate [j,i] can be defined as follows. . (5) where n, m, Qnucl are constants, f is the volume fraction and Δt is a time increment.
The final tube has an outer diameter of 48.8 mm with thickness of 4mm.The total number of triangular elements used was 4471.

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.

Abrasive grain shape is difficult to define.
Obtained an irregular geometry of abrasive grains.
The next step was to designate the top of abrasive grain, and then the actual interpolation curves radially from the top of the grain using the user-selected number of lines (Fig. 3).
In addition, one can observe that the most cutting surface has a grain ZA, and the smallest grain ZE.
Steel Research International Special Edition, Volume 81, Number 9, Publishing Company Verlag Stahleisen GmbH ISBN 978 – 3 –514 – 00774 –1, 2010, pp. 1482 –1485.

In wheat grains, the levels of Pb and Cd were 50 times and 8 times of the limited values of hygienic standard for grain respectively, while Cu and Zn concentrations did not surpass the standard value.
It suggested that Cu and Zn concentrations in wheat grains were in the safe interval.
To be concerned that the average concentrations of Pb and Cd in wheat grains were 50 and 8 times of permissible limits (GB 2715-2005) respectively, signifying the severe pollution of Pb and Cd in wheat grains.
There was no significant correlation between Cu concentration in wheat grains with that of the other metals, thus, the source of Cu in wheat grains needed further investigation.
Heavy metals in wheat grain: assessment of potential health risk for inhabitants in Kunshan, China.

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.

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 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.

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.

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.

Table 3: Number of grains observed and traces with their inclination relative to RD.
Indeed, a large number of well defined bands are seen inside γ grains.
The Taylor factor does not take into account the number of slip systems which are actually activated to accommodate the local deformation.
If the local misorientation is correlated with the degree of fragmentation (as it seems to be from the EBSD images where crossed slip traces are more numerous in highly misoriented grains), then it should be correlated with the number of slip systems activated in each grain.
The number of bands which can correspond to a <110> pole increases with strain, so does the number of γ grains.