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Based on the results of cellular automaton, the transformation fraction of α phase is calculated with the number of lattice and isothermal phase transformation kinetic equation is also calculated with data of transformation fraction, and the effect of hot compression deformation parameters on phase transformation is also discussed.
For simplicity, the phase transformation process is divided into two stages, i.e., formation of initial microstructure and phase transformation process.The initial microstructure is created via a normal grain growth algorithm and dislocation density is uniform and identical for all primary grains.It is considered that the driving force for nucleation is provided by the variation of disloation density.The dislocation densityof a deforming matrix at every time step increases based on the dislocation density .If the dislocation density of a chosen cell exceeds the critical dislocation density,the cell becomes a nucleus for phase transformation.For a newly formed grain,the initial dislocation density is set to zero inside the grain,and increases as the grain grows with hot compressing deformation of the matrix.If impinge each other,the growing grains cease to grow in the impinging direction, but continue to grow in another direction with the increase of strain.When the dislocation density of
a phase transformation grain reaches the saturation value,the grain ceases to grow.And if all the phase transformation grains cease to grow,the phase transformation process terminates[7].
It is proposed in the present study that nucleation of phase transformation occurs only at grain boundaries.Nucleation of phase transformation is related to the accumulation of dislocation,and when dislocation densityexceeds the critical dislocation density,nucleation occurs at grain boundaries at a nucleation rate.For the hot compression deformation the critical dislocation densitycan be experssed as[9]: (4) Where M is the total number of CA cells,is the deformation temperature,and N is the number of phase transformation cells which varies as the function as well as m,where m is the strain rate sensitibity.
For a newly formed grain,the initial dislocation density is set to zero inside the grain and increases when the grain grows with continued deformation of the matrix.When the dislocation density of the phase transformation grain reaches the saturation value,the grain ceases to grow.The value ofcan be calculated by[9]: (5) Results and Discussion Microstrutural evolution of phase transformation.

TEM results have also been used in order to evaluate grain size evolution.
It is reasonable to conclude that there is not a continue evolution of the material with increasing number of passes through ECAP processing.
Highly deformed grains some of them with large number of interior dislocations are present in the sample.
However dislocations seem to be localized within the grains.
Some new boundaries begin to appear changing the appearance of the grains.

It seems that a crack in the range of low growth rate prefers to propagate along the grain boundaries under hydrogen environment while in the range of high growth across the grains accompanied by brittle striation patterns or river patterns.
In the low fatigue crack growth rate, hydrogen enhances the crack path near the grain boundary.
Although the fatigue crack propagates along the grain boundary, it does not occur at one cycle.
Moreover as we can observe the slip behavior near the grain boundary, even the intergranular crack may be influenced through the slip behavior by hydrogen.
( Δεt =0.80 % , 0.1 Hz) 0.1 1 10 10-10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 Crack growth rate dl/dN [m/cycle] Crack length l [mm] In H2 0.8% 0.1Hz In H2 0.8% 6Hz In N2 0.8% 6Hz In H2 0.37% 6Hz In N2 0.37% 6Hz In H2 0.8% 0.1Hz In H2 0.8% 6Hz In N2 0.8% 6Hz In H2 0.37% 6Hz In N2 0.37% 6Hz Fig.5 Fatigue crack growth rates h l=1.13 mm dl/dN=2.8×10 -5 m/c l=0.95 mm dl/dN=1.63×10 -7 m/c l=1.06 mm dl/dN=1.48×10 -6 m/c l=1.18 mm dl/dN=1.86×10 -9 m/c l=1.23 mm dl/dN=4.39×10 -8 m/c Crack length l [mm] Number of cycles N 012 3 1 2 3 In H2 0.1Hz In H2 6Hz In N2 6Hz ×104 l Crack length Crack length l [mm] Number of cycles N 012 3 1 2 3 In H2 0.1Hz In H2 6Hz In N2 6Hz In H2 0.1Hz In H2 6Hz In N2 6Hz ×104 l Crack length l Crack length Fig.3 Fatigue crack growth plots (Δεt =0.80 %) Crack length l [mm] Number of cycles N 0123 1 2 3 ×105 l Crack length ( In N2 6Hz ) In H2 6Hz

The number of cycles was 36. [4] Cross-sectional TEM specimens were fabricated using a focused ion beam (FIB) mill with a microsampling unit.
The lower is composed of isotropic Nd2Fe14B grains, the middle one has a columnar structure of rectangular Nd2Fe14B grains about 2-3 µm in height and 1 µm in diameter, and the upper one is again composed of small isotropic grains.
However, the size of the Nd2Fe14B grains in each layer differs largely from that of the IDM films, respectively: Isotropic Nd2Fe14B grains in the lower layer are of 50-300nm in diameter, columnar grains in the middle layer are of about 1µm in height and 300nm in diameter, and isotropic fine grains in the lower layer are of several ten nm in diameter.
Micro-crystalline Nd2Fe14B grains are formed randomly on the layer of the columnar grains. 4.
At the first, isotropic grains are formed, but only the recrystallized grains suitable for the growth direction can keep growing up, and then an aggregate of columnar grains are formed to be the middle layer.

The microstructure evolution during HPT was investigated as a function of processing parameters: hydrostatic pressure [6], number of revolutions [5], strain rate and temperature for a number of different materials such as Cu [3], Ni [2] and Al [4].
Similarly, homogenisation of microstructure with the number of turns has been observed for copper, nickel, aluminium and Armco iron [1-4].
The predictions of the model with respect to the ultrafine grain size produced by HPT will also be shown to agree with experiment. 2.
The calculated cell size is in good agreement with experimentally observed grain refinement, cf. [3] where the grain sizes of 140 nm in the rim regions was reported.
For hydrostatic pressure of 8 GPa the grain size of 120 nm is predicted which is comparable with the result from [6] reporting a grain size of 100 nm for hydrostatic pressure equal to 10 GPa.

The grain became more minute quasi-equiaxed as 15㎛ when 1Mo and 0.5Hf were added to Fe20Al6Cr (fig, 2(c)), the grain became the most minute quasi-equiaxed as 116㎛ when 1Mo and 1Hf were added(fig, 2(d)).
Therefore, the effect of adding Mo and Hf for being minute of grain refining was shown 0.1 Hf 〈0.5〈1.0.
In the case of superlattic peak, plane index is an even number and is showed in an odd number (example (200)s, (222)s) which was resulted when the sum total of plan index was divided by two.
The basic peak is shown in an even number, (example, (220)F, (400)F) which was resulted when the sum total of plan index was divided by two.
This increase of the rate of yield strength can also raise the precipitation hardening when the precipitated material of the second phrase is precipitated not only in grain but also grain boundary.

In order to simulate the polyhedral grain nucleation in alloys, 3-D cell population growth processes are studied in space-filling periodic cellular systems.
This is due to the fact that materials characterized by cellular structures (froths, foams, tissues, grain aggregates in polycrystals, glasses) occur frequently in nature and in practice.
For this FTC system consisting of a finite set of cells the Euler-equation is valid in the following form : 0NFEV =−+− (1) where N is the number of cells (combinatorial polyhedra), F is the number of faces (interfaces), E is the number of edges, and V is the number of vertices, respectively.
The total number N of cells is N=∑ fN where Nf is the number of f-sided cells (f=4,5,... fmax).
The cell population growth algorithm based on inserted tetrahedra may be applied to simulate grain nucleation and growth processes occurring during solid state transformations in alloys with polyhedral microstructure (for example, abnormal grain growth and recrystallization processes).

The non-ohmic properties of ZnO varistors originate from the grain boundaries and highly depend on the grain size [4].
There are connected pores around the grains.
Some grains are about 1µm in size, which means that the grains begin to nucleate and grow.
Thus, there are shortcuts for currents which contain only a small number of insulating intergranular layers.
The ZnO grains as well as the spinel phase are obvious in the image, and the average grain size is 3 to 4 µm.

It is also well known that in most of the ultrafine-grained metals and alloys decreasing the grain size below 1 mm leads to significantly reduced ductility due to a decrease in the work hardening capability [3,4].
This way, additional work hardening effect i.e. improved ductility can be produced due to increase number of geometrically necessary dislocations on the boundaries between fine and coarse grains.
Hodgson, Study of the grain size effect on the deformation behavior of microalloyed Steels, Proc.
Minamino, Strength and ductility of ultrafine grained aluminum and iron produced by ARB and annealing, Scr.
Majta, Study of the effect of grain size on the dynamic mechanical properties of microalloyed steels, Mater.

A digital image is composed of a finite number of elements, each of which has a particular location and value.
The alignment of the grain formation confirms the directional component of the grain growth for the sub merged arc welding process.
Total Grains in the Image Area of the Grains Area of the Total Image % Area of Grains 195 1.0167e+004 1.3873e+005 6.8281% No. of Grains Area of Grains (in terms of pixels) Figure 7 - Bar Chart representing distribution of size and area of Grains.
The grains are predominantly of smaller variety and the counts for larger grain are almost negligible as it is reveled in the bar chart (see Figure 7).
The grains are predominantly of smaller variety and the counts for larger grain are almost negligible.