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Grain refinements to the ultra-fine grained and even the nanocrystalline size regime have been achieved without formation of significant volume fractions of strain-induced martensite.
The mechanical strength enhancements in the linear plane-strain machined 316L have been attributed to grain refinement and stored strain.
Grain size refinement is an alternative strategy for strengthening.
This SAD pattern is consistent with a very large number of small grains, the majority of which is separated by high-angle grain boundaries (HAGB), being present in the associated microstructure imaged in Fig. 4b.
Fig. 5) confirmed a significant difference in grain size and grain size distribution for the 0˚-angle and 20˚-angle tool processing conditions at the tool velocities of 12.5cms-1 and 25cms-1, confirming prior reports [6].

The grain structure of the alloy is anisotropic grains, the average transverse size of which is 2.3 μm.
The average grain size of the formed phases was 25 nm.
In the fine-grained VT6 alloy, the density of boundaries is determined mainly by the transverse grain size.
Fig. 2 For a more thorough analysis of the effect of corrosion processes, a number of studies of the corrosion resistance of titanium alloy VT6 in a microcrystalline state have been carried out before and after ion implantation with aluminum ions in an acidic medium.
For a more thorough analysis of the effect of corrosion processes, a number of studies of the corrosion resistance of titanium alloy VT6 in a microcrystalline state have been carried out before and after ion implantation with aluminum ions in an acidic medium.

Due to the incremental character of the process, it consists of a large number of deformation and dwell steps.
Due to the incremental character of the process every point in the ring undergoes a large number of deformation and dwell steps.
Due to the incremental character of the process it consists of a large number of deformation and dwell steps leading to long simulation times.
The number of simulations necessary for the simulation study was nFCCD = 25.
For a full factorial design the number is much higher nFFD = 81 (4 parameters, 3 levels).

With increase in Cr content, good grain refinement and less hardness have been observed.
Albuquerque et al. [7] carried out a non-destructive evaluation of grain size influence on the mechanical properties of a Cu-Al-Be shape memory alloy with and without grain refiners and shown that the addition of grain refiners increases the stress and strain of the alloy.
The microstructural change with the formation of small grains was observed under OM.
· The microstructure analysis shows the grain refinement in the alloy with considerable reduction in grain size, otherwise the grain size of ternary alloy was around 20 times larger
· The reduction in the grain size shows the improvement in the hardness

There are a number of factors to be allowed for in order to improve the predictions: (a) a realistic polyhedral shape of interacting grains and their respective spatial coordination; (b) relative rotation of neighboring differently oriented crystals due to their difference in strain rate; (c) dependence of each crystal slip pattern on the plastic strain distribution among its immediate neghbors.
On the polycrystal surface, where constitutive grains have a less number of neighbors, a kind of periodical conditions is employed: a lacking number of neighbors (with their crystal orientations) are reproduced by appropriate grains from an opposite side of the aggregate.
Here, the strain rate imposed on the grain interface by its neighborhood is expressed as ∑= − Σ − = 14 1i i 1ki Cn 1k S S 1 D D , ∑ = Σ = 14 1i iSS , (3) where Si is the area of grain face number i.
Iterations can be interrupted at any number of active slip systems, in particular k<5, and at respective residual ||∆||.
Some inaccuracy of the prediction may also be ascribed to idealization of such factors as actual shapes of considered grains and the numbers of their next neighbors.

The amount of unidentified compound was much smaller than Al6Mn.Change in the number of DRX grains at the center of the extrudates under-extrusion with distance from the die mouth is shown in Fig3.
During hot-extrusion, the number of DRX grains in Meso10 alloy didn't change.
In Meso10-1.3Zr alloy, the increase in the number of DRX grains stopped 8mm rear from the die mouth, and DRX have stopped there.
Near the die mouth, the number of DRX grains hardly increased and it shows DRX didn't occur in each sample.
Fig.3 Change in the number of DRX grains at the center of the extrudates under-extrusion with distance from the die mouth.

The thickness of each layer was almost 10% of the average grain size and the number of sections varied from 8 to 12 depending on the steel.
In order to calculate the grain boundary pole, an algorithm was used to connect the related grain boundaries of two adjacent sections.
This method was used to connect the grain boundaries of two adjacent sections and to calculate the average grain boundary pole throughout a grain boundary.
For each pair of orientations, it is assumed that a spherical grain with cube orientation is inside a grain with different orientation, so that there is a uniform distribution of grain boundary poles.
Depending on the neighboring grain, magnetic free poles with different magnitude of density will appear at grain boundaries.

Hence, the region near grain boundary flows plastically prior to the matrix.
Therefore, the dislocations concentrated near the grain boundary.
The propagation of dislocations to the matrix is easiest when the maximum shear stress in grain is parallel to longitudinal grain boundaries by applying the external stress in the 45° direction of elongated grain structure.
The diminishing of yield strength anisotropy in peak-aging condition could come from increased number of operating slip system near the grain boundary regions with PFZ.
Acknowledgements It is a project supported by natural science foundation of shanxi province China (project number: 2009011028-1; 2011011021-1).

Grain boundary velocities are calculated from the fluxes of vacancies to grain boundaries.
Atomistic models can account for fine details in systems, but these methods are not yet feasible for simulating many industrially relevant interconnect structures due to the vast number of atoms involved, e.g., on the spatial and temporal scales needed to interpret reliability studies on test structures.
The model accounts for grain structure, including the orientations of the individual grains, their mechanical anisotropy and the effect of grain boundaries on the redistribution of vacancies with the grains.
Here the <100> grain is growing at the expense of the <111> grains.
The fastest-moving grain boundaries in the system are those along the <100> grain.

Unlike isothermal annealing, wherein grain growth increased with time, increasing number of repetitive annealing cycles showed formation of ultrafine grained recrystallised microstructure.
On the other hand, the subsequent process of grain growth mainly relies on the grain boundary energy because it occurs by grain boundary migration.
The grain size distribution analysis is shown in Fig. 4.
Nearly 50% of grains were of very fine size (< 2mm) when numbers of annealing repetitions, as shown by black and red data points in Fig.4, were less.
Figure 4: The plot shows the variation of grain size distribution with increase in repetitive annealing numbers.