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Repeated heating refines the grains and microstructure, and improves fatigue strength [5, 6].
Figure 2 shows the relationship between the TRO crack area and the number of cycles to failure.
Fig. 2 Relationship between TRO crack area and number of cycles to failure (Nf).
There was no pearlite, but clear grains can be seen.
The grains were not clear, but the lamellar structure was much clearer.

In some cases, the rule seems to be adhered to very closely by a good number of independent data-points.
Original papers are also included which discuss the statistical shift model for the rule, and its relationship to the kinetic properties of grain and interphase boundaries.

When the current density is small, with the smaller and uniform particle size of surface, the large nucleation rate of the unit time per unit volume, the more number of nuclei per unit volume and the smaller each grain growth leeway, the crystal grains will grow finer.
As the current density increased, the nucleation rate decreases, the grain growth rate to accelerate, get more coarse grain.
Due to the large current density, the unevenness of the nucleation is prominent, causing the uneven grain of the surface of the grain size distribution and partly grow rapidly, so that the particle size is unequal.
Deposited layer has obvious grain boundaries and the equiaxed grain is main grain particles.
The grain size is gradually increase with the increase of current density of electro deposition and grain uniformity irregularly changes.

Fracture surfaces of the joint under room temperature tension (A. without laser treatment B. with laser treatment) Laser remelting is a rapid melting and solidification process, resulting in a large number of fine equixed grains.
In metals and alloys, the diffusion can happen in grain and the outer surface of the grain boundaries, phase boundaries and dislocation lines.
Therefore, the laser melting layer of the sample with a large number of grain boundaries makes the diffusion velocity faster than the one without laser treatment.
Thirdly, the grain refinement by laser melting produces lots of equiaxed grains, the proportion of exuiaxed grain phase increased and made the heat affected zone change from FL microstructure to NFL microstructure which have poor mechanical properties.
The cracks originated from the grain boundaries, then extended to the matrix.

The adsorption of polyelectrolyte chains on plate are studied using coarse-grained, bead-spring molecular models and Molecular dynamics computer simulation.
Simulation Model and Method We use a coarse-grained model for the system consisting of two solid walls coated with polyelectrolyte chains.
To ensure electric neutrality, NC=NB×CN monovalent counterions are added into the system, where CN=144 is the total number of polymer chains and NC is the number of counterions in the system.
Note the number of counterions is equal to the monomers of B-block in the system.
The density of brush, the length of B-block and the number of counterions become larger with the increase of N.

Therefore, the grain refinement can be realized only by forging to break the coarse grains.
Grain growth dg=[d01.6+18750 t exp (-124360/RT)]11.6 (12) where d0 is the recrystallized grain size after deformation, t is the holding time after recrystallization and dg is the grain size after growth, which is related to d0 and t.
The average grain sizes of test and simulated results are presented in Table 5.
Simulation parameters Value Unit SI Mode deformation/heat transfer Mesh number of workpiece 20000 Size ratio 2 Node number of workpiece 3927 Initial forging temperature 1000℃ Environment temperature 20℃ Convection coefficient 0.02N/sec/mm/℃ Die temperature 20℃ Heat transfer coefficient 11 N/sec/mm/℃ Friction type 0.7（shear） Fig. 2 Distribution of the grain size in numerical simulation.
Fig. 3 The boundary dimension and grain size.

The grain size reaches a relatively small value at strain rate of 1 1 s− , then the grain size increases gradually with the strain rate increasing.
As can be seen from Fig.6, the equiaxial grains are elongated under compression, some irregular serrated grains are appeared on the grain boundary with the increase of deformation.
Then grain boundary is bowed protruding, torn off and formed the small recrystallized grains.
The number of recrystallized grains is increasing, and a complete dynamic recrystallization is occurred.
The deformation condition of point 3 is between point 2 and 4, so the grain size is bigger than point 2 and the grain is elongated to be relatively inferior.

In addition, this model takes into account the statistical distribution of grain/carbide sizes, as well as the distribution of crystallographic orientations of grains.
Its value is pre-determined by the maximum grain / carbide particle size, and depends on presence of a crystallographic texture.
The main physical factor governing this effect is the crack nuclei-number-density .
Generally, the crack nuclei number is a functional of .
Dlouhy, Computer simulation of effect of grain size distribution on Weibull parameters, Theor Appl Fract Mech. 35 (2001) 255-260

A number of cases is described when such alloying was applied and was successful.
As a rule, the covering applied to the form consists of the following components [2, 3]: · The grain basis.
The main substances serving for the grain basis are: graphite, soot, ferrochrome slag, zircon, drill, etc
In the production of the modifying covering the metal powder with a small amount of fire-resistant and slag-forming additives is used as a grain basis or filler.
If SiC powder that was activated this way gets in the casting when molding copper is 0,04% it leads to a considerable crushing of its grain sizes.

On the other hand, at high temperatures the precipitation is often uncontrolled and a recovery of the ultrafine-grained microstructures may occur.
applications to press through a minimum number of passes when using a continuous production facility [18].
Figure 5: A TEM image showing the grain structure in the Al-Zn-Mg-Zr alloy after processing through 4 passes in ECAP.
Furthermore, the application of the ECAP process may increase not only the strength but also the ductility of the age-hardenable samples after a certain number of ECAP passes.
Furthermore, the application of the ECAP process may increase not only the strength but also the ductility of the age-hardenable samples after a certain number of ECAP passes, when a large fraction of high-angle boundaries developed during repeated ECAP processes facilitates grain boundary sliding.