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Nomenclature rKth threshold stress intensity factor rKth(0) threshold stress intensity range at load ratio of zero rK0 hypothetical threshold stress intensity range at zero grain size kf fatigue notch factor ky material constant: hardening contribution from grain boundaries d grain diameter s0 yield strength with no grain boundaries sy yield stress L total test line length Va volume fraction of ferrite Na number of ferrite grains intercepted by the last line M magnification of the print W width of specimen a crack length a a/W rP applied load range (Pmax – Pmin) B thickness of specimen R stress ratio Introduction In order to accurately predict the fatigue lives of components, it is essential to consider the growth behavior of fatigue cracks at near threshold levels.
Left hand numbers represent the amount of rolling deformation, the center letters indicate the cooling medium applied (BQ=iced-brine quenched, HWQ=hot water quenched and OQ=oil quenched) and right hand numbers represent the intercritical annealing temperature.
Grain Size Measurement: Average grain size was measured from photomicrographs using mean linear intercept method.
Effect of ferrite grain size on ΔKth Table 1.
They showed that, although the yield stress became relatively insensitive to grain size, for coarse grain rKth increased as the grain size was increased.

In this simulation, a series long-range orientation field variables η are chosen to describe the microstructure and spatial orientation of grains: η1(r, t), η2(r, t), η3(r, t)...ηp(r, t), p is the possible number of the grain orientations in the system, and it is taken as 32 as suggested in ref. [16].
When the grain is marked as η1, η1=1 in the grain, and ηi(i≠1)=0; η1 is continuously changed from 1 to 0, when it passes through the grain boundaries between η1 grain and the adjacent grain.
It is shown from Fig. 3 that the grains grow up from 20min to 80 min, and the number of grain boundaries is decreased.
The grain size is largest when there is no particles when the annealing time is the same, which means the particles will hinder the grain growth, because they have the pinning effect on the grain boundary moving.
Particles (small dark spots) are located at grain boundaries in the grains.

Methodology of High-Carbon Wire Rod Perlite Grain Grade Identification I.G.
When viewing each view field, the 1st grade grains are counted and the grains of another dispersion are counted (2-10 grades).
Afterwards, the percentage of 1st grade grains is determined in relation to the total quantity of grains.
According to the scheme (Fig. 1), in the cross-sectional area of the samples, the pearlite dispersion was measured in each view field (Table 1), with the percentage of the 1st grade grains defined relatively to the total number of grains.
To the determination of the zones boundaries with the different 1st grain grade pearlite percent values (1 is the zone with a large pearlite percentage; 2 is the zone with a lower pearlite percentage) To improve the methodology for the perlite grain grade determination, it is necessary to define the number of the counted view fields.

The experimental results show that the ferrite fine grain around 5μm supports the properties of both high strength and plasticity, while the ferrite with percentage more than 90% leads to high elongation, and the large number second precipitation phase NbC with uniform fine size around 10nm is helpful to fine ferrite grain and form strong(111)textile fiber.
The test micrograph displays that the large number fine second phase particles are founded, as shown in Figure 2 (a)～(b).
It is well known that the small large numbers of NbC particles are blocking (100) textile grain growth because it has weak deformation store energy during cold-rolling procedure.
(2) The optical micrograph shows that the uniform fine ferrite with grain size less than 5μm is gained, and the large numbers of ferrite with the percentage more than 90% is obtained for the experimental steel sheet, while the fine grain ferrite leads to high strength and the large percentage ferrite results in high plasticity
(3) The TEM analysis and X-ray diffraction measurement results show that there is large numbers of small precipitation particles, which leads to fine grain and form strong beneficial (111) textile in the experimental steel sheet.

Particularly in presence of complex geometry shapes, rare grains nucleating apart from the primary grain, become a serious problem in directional solidification, when characterized by high-angle boundaries with the primary grain, extremely brittle due the elevated amount of highly segregating elements and the absence of grain boundary strengthening elements.
In this paper, constrained dendrite growth and heterogeneous grain nucleation theories have been used to model the formation of stray grains in directional solidification of Ni-base superalloys.
It is obtained [6]: Rg=A3T∆Tcol3-∆Tn3 (1) from eq. 1 the condition for the existence of the equiaxed grain is derived: ∆Tcol3=∆Tn3 (2) It is here assumed that the critical grain radius for the successive development of a stray grain is of the order of the primary dendrite arm spacing.
For β below this limit equiaxed grains can form.
The mathematical description of the growth of constrained dendrites and of the nucleation on foreign substrates allows to evaluate the influence of a number of parameters, inherent to both the physical properties of the alloy and the way the temperature field in the liquid metal varies during the process.

Introduction The fine-grained structure (typically ≤ 10µm) is in general known to be an important factor for a number of superplastic alloys.
In the condition of coarse grained material (16.2 µm), a number of dislocations are observed both near the phase/grain boundaries and inside the α grains, which indicates a transition from boundary sliding to matrix deformation and deformation occurs in β phase as well as α phase with the coarsening of grains.
Many researchers [5-9] have studied the grain growth in fine grained materials (≤10 µm) during SPD.
And the grain growth model during superplastic deformation has been utilized to analyze the grain growth.
(2) For coarse grained material (16.2 µm), dislocations are not only observed in the vicinity of the phase boundaries but also inside α grains and near the α/α grain boundaries, and subgrain boundaries are observed in α grains.

A statistical model of grain growth [8,9] is modified to incorporate the described alterations in grain shape.
Grain growth is assumed to evolve because of reduction in the total grain boundary area.
Both the grain boundary energy γb and the boundary mobility are taken the same for all the grains.
Microstructure evolution was traced by changes with time in the grain size distribution as well as in the mean grain diameter 〉〈D (it is calculated as the number averaged value, diameter of barrel-like grains being supposed D'), in the average diameters of spherical and columnar grains, 〉〈D s and 〉〈D c, respectively, and in the volume fraction of columnar grains, Vc.
The parabolic law Eq. 3 describes the growth and consumption of grains on condition that the grain size distribution remains self-similar.

In one time step Δt, with decreasing casting temperature, overcooling is increased δT, new nucleating number in unit volume can be calculated: (9) Nucleating ratio is given: (10) Vc is whole simulation volume.
For clearly observing evolution of grain growing, only four grains are limited to survey.
Simulation result of grain growing at solidified time 9.0s is shown in Fig. 2(b), grains begin to grow, although dendrite envelop is limited, the arm of four grains are still continuous grow.
During to short solidified time, arms of dendrite of four grains are small, around four grains, heat transfer condition almost has no difference, so grain appearance is an equiaxed grain.
Simulation result of grain growing at solidified time 15s is shown in Fig. 2(c), four grains is grew up, with increasing solidified time, solidification circumstance for four grains are not identical, therefore grain growing velocity appear deviation, as shown in Fig. 2(c), grain with marking ‘a’ has fast growing velocity, and its dendrite arm size is more big.

The discussion leads to the following guide: simultaneously controlling the initial grain size, diffusivity, dynamic grain growth, homogeneity of microstructure and the number of residual defects is essential to attain high-strain-rate superplasticity.
For suppressing damage accumulation by the void growth, it is necessary to reduce the number of residual defects in the sintered body and to suppress cavity nucleation during deformation.
Such a microstructure should appear when a small number of residual defects grew with plastic flow under strongly suppressed cavity nucleation.
If cavity nucleation is active as observed in conventional materials (Fig. 2), a large number of micrometer-sized voids must grow from cavity nuclei during superplastic deformation.
For this attainment, the knowledge about superplastic deformation, cavitation and dynamic grain growth emphasizes the importance of simultaneously controlling the following factors: the initial grain size, the number of residual defects, diffusivity, dynamic grain growth and the homogeneity of microstructure.

The rest of the lattice represents the grains.
For the segregation effect to be simulated we introduce w3 – a jump frequency for a particle to jump from the grain boundary plane to a grain site.
To simulate a thin-film (instantaneous) tracer source, 106-108 particles are created and released from the surface (according to the segregation effect for the purposes of avoiding the possible time-dependent segregation) and allowed to diffuse for a time t (proportional to the number of jump attempts per particle).
These concentration profiles are built up simply by determining the number of particles that have reached a given distance from the tracer source plane after the diffusion time t [16].
Contributions to the concentration depth profile from inside of the grains and from the inside of the grain boundaries separately.