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The dynamic recrystallization coefficient can be defined as the capacity to decrease the dislocation density via the growth of fresh grains; this coefficient equals the difference between the number of subgrains with sufficient energy for grain nucleation Nnucl (from whom grain growth occurs) and the number of growing grains Ngrowth, divided by Ngrowth [5].
Grain growth is a thermally activated process, thus Ngrowth follows an Arrhenius form, where the energy barrier for grain growth QDRX is composed by the difference between the energy induced by the boundaries motion when grains are growing (Edisp) and the strain energy to drive grain growth once high-angle grain boundaries form (EHAGB).
(3) The onset for dynamic recrystallization occurs when high-angle grain boundaries (HAGBs) form via the accumulation of dislocations leading to grain nucleation [6].
In analogy to a previous analysis for cell formation [3], dynamic recrystallization can be considered to start when the stored energy at the boundaries (Esub) equals to (i) the necessary energy to nucleate dislocation-free grains (Egrain); (ii) the displacement energy for boundary-dislocations to onset grain growth Edisp and (iii) the equivalent slip energy of dislocations migrating from the grain interior to the boundaries (Eint) [5].
The model results show good agreement in the dynamic recrystallization onset range, number of oscillations before undergoing steady state and the steady state stress for strain rates below 2.7 × 10−1 s−1.

A large number of dimples are observed on the fracture surface, implying as ductile fracture.
It can also be seen that from the weld zone to the base metal, the number of LAGBs decreased gradually.
A large number of shear dimples were observed.
From the weld zone to the base metal, the number of low angle grain boundaries is gradually reduced.
In the 35J / mm sample, the number of low angle grain boundaries was about 0.29, and a large number of deformation twins can be formed during the deformation process, which has a great contribution to the strength of the weld.

The dynamically recrystallized grains were mainly at prior grain boundaries, and had a grain size of about 2mm.
Figure 2) Misorientation profile across the dotted line shown in the EBSD map at slice number 38.
Relationship of dynamically recrystallized grains to the old grains.
The recrystallized grains formed a necklace at the prior grain boundaries.
An example is shown in figure 3, where at slice number 8 the grains A and B at first seem to be unrelated, however at slices 9 and 10 it can be clearly seen that grain B has a very close orientation and is linked to the old grain A.

With the improvement of laboratory equipment and development of computer technology, a large number of experiments and numerical simulations have been made since 1970s..
Zhang Gang of Tongji University for the first time established the numerical model based on the grain size curve to simulate the pipe process [3].
We can obtain the porosity in two-dimensional after the three-dimensional model is built according to the grain size curve and porosity in the software CAD. 2.1 porosity change and particle number calculate The porosity transitional equation between two-dimensional and three-dimensional space is got by Hoomans(1996), and Dr.
Fig.2 Grain sizes diagram of different gravel Tab.1 Number of particle under different diameters Cu 10~7number of particles 7~5 number of particles 5~2 number of particles 2~1 number of particles 1~0.1 number of particles 2.5 66 133 2650 849 12627 14.5 0 0 2241 2228 50509 30.5 264 159 565 1910 38671 * This is the ideal value, in order to reduce the computing time, according to the recommendations of literature [5] value and the present calculation conditions, the model was further simplified. 2.2 Mechanical model and Micro Calibration The soft-sphere model, which was proposed by Cundal and Strack in 1979 was adopted in Granule in the Numerical model.
When convergence had happened, both force chain map and flow chart show that grain structure of the sample was stable.

With increasing number of ECAP passes this difference decreased.
Fig. 2 The fraction of high-angle grain boundaries (HAGBs) in the crept samples as a function of the number of ECAP passes.
It is important to note that there is a difference in the appearance of the creep curves between the unpressed and the pressed materials and there is a difference in the fracture strain levels for the pressed material with different numbers of ECAP passes: pressed samples are denoted by the numbers B1-B12 where the numeral denotes the number of ECAP passes.
This softening may be related to the increase in the spacing of HAGBs at approximately constant subgrain size with increasing number of ECAP passes, resulting in the fraction of low-angle grain boundaries decreasing considerably (Fig. 2).
Fig. 5 Standard creep curves for unpressed (coarse-grained) state and states after various number of ECAP passes for: (a) Al, (b) Cu, (c) Al-0.2wt.

The equiaxed grains have been elongated, and a large number of grains crashed under huge shearing force, even these small grains created by grains’ crashing were also elongated.
With the increasing of number passes, the amount of fine grains is increased greatly.
These grains appeared to be separated by high-angle boundaries in some areas because the diffraction rings are more obvious and the numbers of the rings are increased.
Fig. 6 Average micro-hardness of alloy each surface of copper alloy on different passes With the increasing of number passes, the micro-hardness values increased and the trend is obvious (as shown in Fig.6).
With the increasing of number passes, micro-hardness values increased gradually.

(b) surface foil, grains larger than 100µm; (c) subsurface foil, grains larger than 600µm; (d) mid-thickness foil, grains larger than 100µm; (e) mid thickness foil, grains larger than 600µm.
This is direct evidence that Goss grains can grow by consuming grains belonging to the η fibre.
General grain growth was all that was found.
Quite clearly there is still something special about precisely oriented Goss grains, which makes them different from grains in the Goss spread.
Research Grants Council for the grant numbered CERG7515/03E.

%Ni alloy with the average grain size of about 30 nm.
For cubic grains 
 = 2�/d.
However, the number of relevant experimental points is too small to extract reliably the inter-agglomerate boundary diffusivity.
The GB diffusion measurements in a coarse-grained material in the C regime are accompanied with serious experimental limitations and high requirements to the sensitivity of the radionuclide detection equipment, since the fast tracer flux proceeds only in a relatively small number of GBs.
The counting statistics is decisively improved since the small atomic fluxes occur in a huge number of short-circuit diffusion paths.

Many oblique strip grains appeared between equiaxed grains and fibrous tissue.
(a) Small grains, (b) Fibrous tissue during recrystallization process, (c) Fibrous tissue, (d) Long strip grains, (e) Coexistent structure of long strip grains and large equiaxed grains, (f) Large equiaxed grains.
Figure 4(a) shows that a large number of equiaxed grains have formed in outermost layer of specimen, and their sizes are very uniform.
Figure (f), only a large number of etching pits can be observed which distribute in surface of sample uniformly, and in fact the organization in this region should be larger equiaxed grains.
In the macro scale, plastic deformation is usually reflected as increasing of hardness, while in the micro scale there are a large number of dislocation and dislocation tangles.

However, stray grain formation and solidification cracking contribute to microstructure degradation.
(2) where Γ is the Gibbs-Thomson coefficient, R is the dendrite tip radius, Pei is the Peclet number for i, mi is the liquidus slope, C0,i is the initial concentration for i, ki is the partition coefficient for i, ζc(Pei) is a function of the Peclet number, Iv(Pei) is the Ivantsov solution and Ghkl is the average temperature gradient near dendrite tip.
Stray grain formation is infelicitously restricted in crack-unresistant region of [100] dendrite growth.
Inconsequential stray grain nucleation, small morphology transition between columnar and equiaxed dendrites and predominant columnar dendrite growth happen.
Numerical analysis of stray grain formation during laser welding nickel-based single-crystal superalloy part I: columnar/equiaxed morphology transition.