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The relation between the grain size of 16MnR steel and the fractal dimension of fatigue fracture, and the relation between the grain size of 16MnR steel and the fatigue mechanical properties were discussed.
The grain sizes of material were also measured with the comparison method.
There were also the relation between fracture fractal dimension and grain size, The fracture fractal dimension Dm can be estimated according to the grain size G.
There were also the relation between fatigue mechanical properties and grain size, The fatigue mechanical properties Ji can be estimated according to the grain size G.
Acknowledgement The research work is supported by Nature Science Foundation of Anhui Province Education Department (Grant Number:KJ2009A126).

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.

The microstructure was effectively refined and the mean grain size was decreased from 800 μm to 3–15 μm.
The number of extrusion passes was defined as the number of the specimen passed through the die.
Results and Discussion The mean grain size of the as-received Mg-3Y alloy was estimated to be around 800 μm.
New recrystallized fine grains with new misorientations could easily form at prior grain boundaries during CEC.
Compared with the conventional extrusion, the maximum texture intensity Mg alloys diclined with the increasing number of passes [6,8].

Cu-0.3Cr alloy: The microstructure of Cu0.3%Cr in the starting condition consisted of equiaxed grains with grain size 8-10 µm.
Fig. 3 (a) shows the GBCD as a function of the number of passes.
The components BE /BE got strengthened with number of passes.
The grain size was quite uniform with a fine distribution of equiaxed grains.
Texture weakened after ECAE in the α- phase with number of passes.

The size of the ferrite grains is by an order of magnitude less than the original grains size.
Closer to the disk axis the number of defects increases sharply.
The maximum number of twins in large ferrite grains which includes the twins belonging to different systems is more than one hundred.
The number of twins grows on getting close to the centre of the plate under examination.
A great number of cracks is seen along the localized plastic flow bands (Fig. 8 a).

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.

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.

Equal channel angular pressing (ECAP) is useful method to obtain the ultra-fine grained and the high hardened metal.
The as-deformed metals retained high dislocation densities, a large number of low angle sub-grain boundaries, and showed being in non-equilibrium configurations [7].
The grain of as-heat treated Al exhibited an equi-axial, uniform, and coarse structure.
The grains were elongated, having an angle of 15 - 30 degrees to the ECAPed out direction.
Rotated Goss component, {110}<110>, increases with the number of passes ECAP, decreases with annealing.

Journal Title and Volume Number (to be inserted by the publisher) Fig 2.
Each lattice site is assigned a number, Si, which corresponds to the orientation of the subgrain in which it is embedded.
The number of distinct subgrain orientations is dependent on the measuring step size and area.
A grain boundary energy Ji is attached to the grain boundary sites and zero energy for sites in the grain interior, according to ( )∑δ−⋅= nn j SS i I i ji1JE
(3) Journal Title and Volume Number (to be inserted by the publisher) where ijδ is the Kronecker delta, the sum is taken over nearest neighboring(nn) sites and Ji is a positive grain boundary energy.

A small number of crystal plasticity simulations and tensile tests are carried out with the aim of demonstrating that control of twinning can improve the uniform elongation of magnesium based alloys.
A number of authors have recently drawn attention to this fact in their analysis of Mg-3Al-1Zn subjected to Equal Channel Angular Pressing [2,3].
Fraction of Grains Undergoing Twinning - Sachs Analysis The fraction of grains undergoing twinning, XT, is determined, in part, by the texture.
Assuming that only one deformation mode is active in each grain, the grains expected to twin can be estimated by combining a Schmid factor (SF) analysis with the fact that twinning only works in one direction.
That is, more grains should undergo twinning under uniaxial compression, compared with tension, for a random aggregate.