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The starting sheet had equiaxed grains with the mean grain size of 120 µm.
After annealing at 450 ºC, the number of recrystallized grains increased and the area fraction recrystallized was 59%, which was smaller than the 8cycles specimen.
Figure 3 shows a dependence of the area fraction recrystallized on the number of the ARB cycle.
In case of annealing at 400 ºC, the recrystallized fraction hardly changed even when the number of the ARB cycle increased.
Number of the ARB cycle Area fraction of the recrystallized grain /% Fig. 3 Dependence of area fraction of recrystallized on the number of the ARB cycles.

The inset shows the HEA exhibited significant increase in hardness after HPT and with increasing numbers of HPT turns.
A reasonably equiaxed grain structure was observed with an average grain size of d ≈ 60 nm in the HPT-processed Al-Mg system and after PDA the material demonstrated a homogeneous equiaxed microstructure with an average grain size of d ≈ 380 nm.
It should be noted that the error bar on each datum point represents the standard deviation of the total numbers of measurements of 20 tests but the error ranges are too small to recognize in the plot.
Specifically, PDA enables the production of an ordering of the defect structures within the grain boundaries leading to an equilibrium state without any significant grain growth [18].
Langdon, Twenty-five years of ultrafine-grained materials: Achieving exceptional properties through grain refinement, Acta Mater. 61 (2013) 7035-7059

The reduction of the grain size leads to an increased plasticity and higher grades of deformability.
However, the effect on the size of grains of the multi-factor impact was not described in literature.
The fine-grained uniform over the cross-section structure was achieved in the AD0 alloy ingots.
This raises a number of the essentially new tasks before the specialists involved in the development of new technologies and their implementations in production.
The method allows obtaining uniform structure with reduced up to several times size of the grains.

Route A has no rotation of the sample, route BA is rotated counter clockwise 90° on even number of passes and clockwise 90° on odd number of passes, route BC is rotated counter clockwise 90° after every pass (see Fig. 1b.), and route C is rotated 180° after every pass [9].
Increasing the number of passes (the accumulated equivalent strain), secondary phase particle size decreases, its distribution becomes more uniform, and also the grain size of 6063-T1 alloy is more refined.
It was determined that for the unprocessed aluminum alloy, the microstructure shows coarse dendritic grains, with a secondary phase at grain boundaries (specific continuous casting structure).
Increasing the number of passes, secondary phase particle size decreases and its distribution becomes more uniform and also the material grain size is more refined.
Butu, Mechanical behavior and microstructural development of 6063-T1 aluminum alloy processed by equal-channel angular pressing (ECAP): pass number influence, JOM, 64 (2012) 607-614

The effect of thickness and grain size on the scattering was discussed.
thickness in the case of specimen with different grain size.
Many grains exist in the through-the-thickness direction when grain size is very small, so the variation in crack growth resistance becomes small.
Thus, it is demonstrated that the error of estimated cyclic number is small and the measurement accuracy is improved using specimen with small grain size such as ED Cu for smart patch.
(3) The error of estimated cyclic number was reduced using specimen with small grain size such as ED Cu for smart patch.

On the grain scale, the Schmid coupling between the stress tensor and the distribution of crystallographic orientations provides a grain-by-grain distribution in strain.
The number of nuclei per element is computed via Eq. (3) using the local strain at that element, and nuclei are placed in the element.
Journal Title and Volume Number (to be inserted by the publisher) 5 Figure 3.
For e = 0.3, the distribution are similar; however, the nonuniform system has a larger number of very small grains, due to the clustering of nuclei and their subsequent growth impingement in high strain regions.
While both uniform and nonuniform microstructures are quite fine-grained, the nonuniform system contains a significant number of larger grains, which result from nuclei growing in to the low-strain, low-nuclei regions of the microstructure.

Zhan[7] studied high-angle symmetric tilt Σ5 (310) Ag nanowires with varied amount of grain boundaries and the influence of grains sizes.
His work mainly discussed the quantitative relationship between natural frequency and number of grain boundaries.
Our study will highlight the importance of grain boundary misorientation angles and the associated grain boundary energy as the generated grain boundaries is likely to be of metastable structures instead of the stable ones.
Firstly, (310) is chosen as the grain boundary orientation of interest, and the tilt axis is set as x axis and the grain boundary (GB) plane is locating in the x-y planes.
Additionally, asymmetry in number of atoms arises by only deleting the atoms in one of the grains; to address the issue, same number of atoms must be deleted in both grains for atoms beneath the cut-off radius.

To improve the bioactivity of Ti surface, Ca/P-containing porous titania coating were prepared on the ultrafine-grained Ti and coarse-grained Ti by micro-arc oxidation (MAO) in Ca/P based solution.
The amounts of Ca, P and Ca/P ratio of the MAO coating formed on ultrafine-grained Ti were higher than those for coarse-grained Ti samples.
Influence of grain refinement on the MAO process.
From a thermodynamic point of view, the driving force for the MAO process is enhanced for the UFG-Ti phase, which contained a large number of defects and thus stored a large excess energy.
Conclusions Due to a high defect density and a large number of high-energy grain and sub-grain boundaries, the chemical reactivity of UFG Ti is significantly increased.

Then, the model is adapted from the case of spheroidal grains, considered initially, to the more general situation of ellipsoidal grains.
A combined effect of grain size, grain shape and texture on plastic anisotropy at yielding is illustrated in case of a rolled IF steel sheet.
For a given applied stress within the soft grain, the number n of dislocations piling up against the boundary with the hard grain increases proportionally to the distance dαs of the dislocation source.
This means that the softer grains undergo the following backstress: ταb ≡ (bα ⊗ mα) : σ − eτc0 = √µbτy πdαs (5)The theory was originally applied to equi-axed grains while assuming that the dislocation source is in the grain center.
Barnett: ''Modelling the combined effect of grain size and grain shape on plastic anisotropy of metals'', Int.

Gamma Profile Analysis for Stress, Texture and Grain Size Bob B.
He Bruker AXS Inc, 5465 East Cheryl Parkway, Madison, WI 53711, USA Bob.he@bruker-axs.com Keywords: 2D detector, Residual stress, Texture, Grain size Abstract.
The g-profile contains information on texture, stress, and crystal grain size.
Each diffraction cone corresponds to the diffraction from the same family of crystalline planes in all the participating grains.
The number of candies to fill the box depends on the size of the candy and candy box.