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Moreover, the more the number of TiC particles synthesized in the melt, the finer the solidified austenite grains.
In this way, after the alloy melt was isothermally treated to form a great number of TiC particles, some unreacted carbon atoms were transformed into fine D-type graphite and aggregated at austenite grain boundaries during sequent solidification.
Moreover, the more the number of the synthesized TiC particles is, the finer austenite grains become.
A number of models were proposed to predict particle behavior in front of a moving solid/liquidt interface [7].
Moreover, the more the number of TiC particles, the finer the solidified austenite grains became.

Fig. 2 Microhardness as a function of number of CECC pass.
A large number of low angle boundaries (LABs) are also observed in the interiors of grains (Fig. 4 (a)).
Some areas have elongated grains containing large number of LABs.
Fig. 6 Volume fractions of the fiber textures as a function of number of CECC pass.
With the increase in the number of CECC cycle (effective strain), the efficiency of grain refinement will be limited [20].

In low doped BaTiO3 the grain size is around 1-3 µm, while in ceramics with high dopant content (1.0 at%) the grain size distribution was in the range of 3-10 µm.
Introduction Because of intrinsic capability of perovskite structure to host the ions of different radius size, a large number of different dopants can be accommodated into the BaTiO3 lattice.
Manganese as additive segregates at grain boundaries and can prevent grain growth.
A number of studies are confined to the effect of additive and grain size on the ferroelectricparaelectric phase transition [10-12].
For 0.1 at% doped ceramics a small-grained microstructure (1-3 µm) is observed, while for 1.0 at% doped ceramics the grain size is ranged from 3-10 µm.

Introduction Ultrafine grained (UFG) metallic materials having grain size smaller than 1 µm can be realized by various means including severe plastic deformation (SPD) [1].
The mean grain sizes were measured by mean interception method.
In the previously studied ARB materials, the strength became higher with increasing the number of ARB cycles, and the elongation dropped down below 10 % by 1 ARB cycle.
The mean grain thickness is 210 nm.
The mean grain thickness is 170 nm.

D=3ΓgbVm/(C0-Cg) with Cg the carbon concentration in grains, Γgb the grain boundary excess, and Vm the molar volume of iron.
So far the synthesis of NC iron-carbon alloys has been published in a rather small number of studies [14-18].
After the annealing treatment, a pronounced grain growth happens in the powders with low C0, e.g.
Figure 3 Grain size distributions of the ball milled Fe-0.4wt.
When GBs are saturated with defectants GB energy may become zero at high enogh chemical potentials of the defactant and in turn the grain growth will be inhibited, leading to an equilibrium grain size [1].

In general, the dynamic recrystallization causes grain refinement and stress softening, and the strain induced grain growth causes stress hardening.
Let diffusion creep, grain boundary sliding and dislocation creep are numbered by 1, 2, 3, respectively, and subscript k=1, 2, 3 denotes the variables related with the k-th mechanism, such as fk denotes the volume fraction of the k-th mechanism.
D0, D1, D2, Dc, is initial grain size, unrecrystallized grain size, recrystallized grain size and maximum difference of grain size ,respectively. γ0 is grain boundary energy per unit area of grain boundary.
Fig.8 Un-recrystallized grain D1.
Fig.9 Average grain size D.

The five-parameter grain boundary character distribution (GBCD) of a material contains both the grain boundary plane orientation and the lattice misorientation information.
The statistics that are used to quantify the differences between the synthetic and experimentally observed structures are texture or orientation distribution (OD), GBCD, number and area fractions of S3 and coherent S3 boundaries, S3 cluster distribution, and twin density.
The main simulation code used in this study is the grain orientation assignment algorithm.
To demonstrate the capability of the twin insertion algorithm, the twin grains were removed from an experimental structure, Inconel 100, and were then regenerated with the twin insertion algorithm.
The largest S3 cluster measured in the experimental Inconel 100 structure consists of 98 grains, which can only be observed by analyzing the fully-reconstructed 3D structure.

Grain Boundary imaging.
Sample geometry Fig. 2. 3D rendering of the crack shape at different numbers of cycles as seen along the stress direction (z direction).
Crack front - grain boundary interaction.
From Fig. 3a, it can be deduced that the crack front geometry is influenced by the different grains in which it propagates : the front seems to propagate faster in grain Y (between points 2 and 3) than in grain Z (between point 1 and 2).
Nielsen and al. : Three-dimensional maps of grain boundaries and the stress state of individual grains in polycrystals and powders.

Methodology As the first step in MPF method a system with certain number, N, of different PF, f1, f2, f3, …fN, is determined.
By using step function, number of local phase, n, is defined as
PF evolution is explicitly defined as: (4) where i, j and k are number of local grain from 1th to nth at the numerical grid, and subscript x and y refer to derivation on the x and y axis.
It can be seen from the figure that all grains move forward without significant grain growth on the side direction of each grain.
At the end of simulation processes, only several grains with high orientation angle exist and experience grain growth while low orientation angle grains either diminish or exist as small grain (second grain from the right).

A comparative study on the wear behavior of cast and forge aged A356 alloy with addition of grain refiner and/or modifier D.
aemail: drmallapur@yahoo.com Keywords: Forged A356 alloy, Grain refinement, Modification, T6 heat treatment process and Wear.
It could be conceived that forging process creates large number of micro voids, particularly at the interface of brittle silicon phase and ductile aluminium matrix.
In addition the frictional force is always lower in grain-refined and modified alloys and this is due to the fact that, strength and hardness of the alloy improves with the addition of grain refiner and modifier.
Addition of grain refiner leads to decreases in the grain size and results in the formation of more number of grain boundaries.