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The relationship between the number of trials and microstructures are shown.
The studies have shown that the multi-run FSP process causes decrease of the grain size and increase of the homogeneity of the microstructure.
First, FSP has been used to generate fine-grained microstructures amenable to high strain rate superplasticity.
The white particles are intermetallic since they are composed of heavy elements with large atomic number Z.
Simultaneously, a large number of dislocations and the presence of sub-boundaries in the stir zone indicate that the material is not fully recrystallized.

The fatigue life Nf was defined as the number of cycles up to a drop of 25% of the stress amplitude in relation with stabilised stress amplitude.
These diagrams give the evolution of the stress amplitude versus the number of cycles in a logarithmic scale for the tests conducted at different strain ranges.
The higher the strain variation, the longer the hardening period as indicated by the number of cycles for reaching the maximum 400 500 600 700 800 1 10 100 1000 10 4 10 5 2% 1.6% 1.3% 1% 0.9% 0.8% Stress amplitude (MPa) Number of cycles (N) UR52N+ 400 500 600 700 800 1 10 100 1000 10 4 10 5 2% 1.6% 1% 0.8% 0.6% Stress amplitude (MPa) Number of cycles (N) BöA911 400 500 600 700 800 1 10 100 1000 104 10 5 BöA920 2.5% 2% 1.6% 1.3% 1% 0.8% 0.6% Stress amplitude (MPa) Number of cycles (N) stress amplitude.
In both phases, the dislocation arrangement in a single grain was representative for all grains.
The dislocation arrangement in a single austenite grain was characteristic for all grains (Fig.5b).

For example, Deff of a polycrystalline materials is a weighted average of the lattice and grain boundary diffusivities [7].
A suitably fine-grained simple cubic lattice is simply overlaid on the phenomenological problem.
The number of jump attempts per particle is the discrete quantity that is used that is proportional to real time.
The profiles corresponding to this for various grain models have then been analysed to determine the transition points between the various kinetics regimes identified in grain boundary concentration profiles.
Gust: Fundamentals of Grain and Interphase Boundary Diffusion, Wiley, Chichester (1995)

The grain size increases with increasing deposition temperature.
The grain size increases with increasing deposition temperature.
However, when FACET analyzed the multi-grain growth, grains with the {110} planes outgrew adjacent grains because the {110} planes could obtain a continuous supply of atoms from adjacent planes and from direct deposition flux [8].
Then, when the films have just become continuous, the grain size is very small and the [111] preferred orientation of the grains is not fully completed yet, i.e., the grain orientations in the film growth direction are [111], [100] and [110] directions.
The grain size increases with increasing deposition temperature.

The recrystallization grains appear when the cold steels annealed at 655oC and then the grains grow up with the annealing temperature increased to 840 oC.
The dislocation density decreased and new grains formed when the cold rolled steel annealing at 655 oC and the dislocation disappeared and the equiaxed grains formed.
The grains grow when the annealing temperature increases to 810 oC.
There are large numbers of deformation bands in the deformed microstructure which can increase the nucleation rate when the cold rolled steel is subjected annealing treatment at high temperature[8].
Fine recrystallization grains were seen after annealing for 100sec at 655oC.

Once a certain number of grains is selected, the above procedure is applied to a certain number of microstructures, so to average the fields of interest over different realizations, in a framework of statistical homogenization.
A sample polycrystalline microstructure, generated by Voronoi tessellation, after initially selecting the number of grains , is shown in Fig.1a.
Morphologies with = 10, 20, 50, 100, 200 grains have been considered and, for each selected number of grains, 50 different morphologies have been considered.
It is noted how the scatter of the effective properties decreases as the number of grains within the considered realizations increase.
A grain boundary formulation for crystal plasticity.

It reveals that the surfaces of all as fabricated products possess a plain texture with the expected clear grain boundary for ceramic materials and that the grain structure is very homogeneous.
When the sintering temperature reaches 1300 °C, the structure is very dense and the grain boundary is also very clear, implying that the SnO2 grains are well crystallized with good integrality.
(1) Where n is the average grain number per unit length, Vgb (~ 2.2–3 V [11]) the breakdown voltage of a grain boundary.
According to the previous work [12], the decreasing nonlinear coefficient might be associated to the reduction of the effective grain boundary, and the phase of CoSnO4 and CoCr2O4 has an important influence on the grain boundary.
At the lower sintering temperature there is not enough effective grain boundary to form, however, some effective grain boundary would be destroyed at the higher sintering temperature.

The columnar grains grow parallel to the heat transfer gradient which is perpendicular to the ingot axis.
The closer to the extrusion zone the more grains “bend” towards the growth axis (Fig. 4c,d).
For the G1 much less cracks were observed whereas for alloy I1 large number of cracks was present even in the not extruded upper part of the sample.
In this way the grains along the extrusion axis obtain the [001] orientation.
The rotation of the grains is easily visible in the pole figure (Fig. 5c) that shows that the grains in the transient zone are tilted (in this very region of about 45o).

The transfer of externally applied loads is in most cases not homogeneous, but takes place mostly in a limited number of particles creating so-called force chains.
This paper provides a numerical approach for determining the PF of a given grain size distribution by number of particles and mass fraction.
Fig. 3 Grain size distribution of soils used for the study Regarding the first part, a list of particles are generated before the sequential packing process according to the grain size distribution (GSD), the predefined volume of specimen and its porosity.
The number of particles must be an integer number.
Fig. 7 Proportion by number of primary fabric particles Fig. 8 Proportion by mass of primary fabrics The quantitative results show that the PF of the wide-graded soils may take only just over 2% by number of particles (Fig. 7), but it contributes just under 40% by mass (Fig. 8).

There are typically as cast, abimodal grain size and fine recrystallized grain structure.
The abimodal grain size structure consists of coarse deformed grains and fine recrystallized grains.
It can also be seen from Fig. 3 that there are a large number of fine grains along the twinning boundaries.
It is likely that the small grains are merged to the big grains by grain boundary sliding and grain rotation.
Bradai, Grain growth in AZ31 alloy after uniaxial compression, Trans.