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The Dynamic Behavior of Ultra-Fine-Grained Copper Fabricated by Equal Channel Angular Pressing Y.C.
Dalla-Torre et al. [6] reported the SRS of pure copper increased from 0.007 to 0.023 along with increasing the number of passes of equal channel angular extrusion (ECAE) from 1 to 12.
This phenomenon could be explained by a heavy increase of dislocation density along with a small number of ECAP passes.
Flow stress as a function of passes after ECAP deformation Fig. 5 demonstrates the variety of flow stresses versus the number of the ECAP passes, which shows that the flow stress was growing along with the accumulation of number of ECAP passes at any strain rate, and the strength enhanced with the increasing strain rate.
They showed that strain rate sensitivity increased with the reducing of grain size, although their studies have been focused on the coarse grain sizes.

The most effective way to reduce the stress concentration at grain boundary during deformation should be grain refinement.
The grain size (nominal grain size) of austenite was measured by quadrature method [7].
Grain size control of Fe-25Cr-1!
The effect of grain refinement becomes more significant when the grain size is reduced below 50 microns.
Figure 10 Relation between area fraction of intergranular fracture surface and grain size in Fe-25Cr-1N alloys. 300 400 500 600 700 800 900104 105 106 107 108 Maximum stress, σmax / MPa Number of cycles to failure, Nf / cycles Fe-25Cr-5Mn-1N (as-solution-nitrided) Fe-25Cr-5Mn-1N (grain-refined) ASTM F2229 100µm (a) d≒260µm 100µm (b) d≒60µm 30µm (c) d≒20µm 100µm (a) d≒260µm 100µm100µm (a) d≒260µm (a) d≒260µm 100µm (b) d≒60µm 100µm100µm (b) d≒60µm (b) d≒60µm 30µm (c) d≒20µm 30µm30µm (c) d≒20µm (c) d≒20µm Figure 9 SEM images showing fracture surface of tensile-tested Fe-25Cr-1N alloy as-solution-nitrided at 1473K for 43.2ks (a), grain-refined by reversion at 1473K for 0.9ks (b) and 0.12ks (c) after isothermal heat treatment at 1173K for 0.3ks. 300 0 10 20 30 40 50 60 70 800 50 100 150 200 250 Area fraction of intergranular fracture surface, A /% Grain size, d /µm Grain-refined materials As-solution-nitrided material 300 0 10

On the other hand, because the seepage in the slope body caused by rainfall carried the fine clay grains to the slope direction and the larger silt grains was left, then the laterite grains characteristic showed that the silt grains content increased and the clay grains content reduced with the slope altitude to increase.
Table 5 The density of slope’s soils number initial wet density / g/cm3 slope altitude / cm wet density / g/cm3 corresponding water content / % dry density / % Initial dry density / g/cm3 1 1.27 46 1.67 30.5 1.28 1.00 40 1.59 31.2 1.21 30 1.52 31.7 1.15 20 1.48 37.2 1.08 2 1.27 36 1.72 33.0 1.29 0.99 30 1.59 33.7 1.19 20 1.49 36.2 1.09 Table 6 The grain composition of slope’s soils number Initial silt content/ % location slope altitude / cm grain composition / % initial clay content / % silt content clay content 1 57.1 slope internal 46 61.4 38.6 42.9 40 63.3 36.7 30 61.6 38.4 20 61.6 38.4 10 58.7 41.3 0 59.6 40.4 slope surface 47 59.4 40.6 35 59.8 40.2 model tank front 0 64.4 35.6 tank surface -20 37.0 63.0 The change of shear strength of the laterite in the model slope under the effect of rainfall According to the above test results, the water content and density of the laterite in the each part of model slope have changed after a rainfall process.
These factors weakened the effect of the connection structure between the laterite grains and caused the connection force between the laterite grains to reduce, which would lead to the cementatory ability of the laterite grains to reduce.
In other words, the cementatory ability between the laterite grains was closely related to the density and the grain composition.
Then the raise of the contact point between the laterite grains made the embedding capacity between the laterite grains became stronger and the relative sliding between the laterite grains became very difficult.

With increasing number of passes the grains changed from an elongated shape to a more equiaxed structure, which was especially pronounced after 8 and 16 passes (Figs. 1, 2).
The fraction of high angle grain boundaries increased with rising number of passes, and a value of about 40% for the precipitated and about 50% for the supersaturated state was obtained after 16 passes (Fig. 3).
It was noticed that the higher the number of passes the softer the material became after annealing for 1 h.
For both alloy constitutions it was found that the formation of a new equiaxed microstructure progressed with increasing number of passes.
EBSD maps revealed that with increasing number of passes the fraction of the equiaxed grains in the microstructure had increased during annealing for 1 h.

During hot compression deformation of 1235 aluminum alloy, slidings occur sooner or later and the number is different for the difference of grain orientation, and so the distribution of grain orientation as well.
The time of occurrence and the number of slips differ for the difference of polycrystalline grain orientation during deformation.
From the charts, there are a large number of low-angle boundaries and high-angle boundaries with wealth distribution information in 1235 aluminum alloy after hot compression deformation.
At the strain rate for 50s-1, there are a larger number of small low-angle boundaries in grains (the percentage of angle less than 3° is 41.1%).
At strain rate for 0.1s-1, the major textures are Goss (G) textures, Brass (B) textures, Rotated cube textures, including a small number of R textures and cubic textures.

Form the model we can found that the larger the ultrasonic power and amplitude, conditions can be more easily satisfied; simlarly the higher the ultrasonic frequency, angle crossing number, grain structure defects, the longer action time to make greater fatigue, all this factors can also make the conditions more easily satisfied.
Further expand the Eq. 6 as δ ϕ ϕ ≥ ∂ ∂ + ∂ ∂ ),( )( )( ),( xtp x x x x xtp (7) and assuming the ultrasound as a plane harmonic longitudinal wave that pass through the grain spread along the x-axis positive, then the displacement fluctuation function can be written as )cos(),( kxtAxtp − = ω (8) where A is the input displacement amplitude of ultrasound, ω = 2πf is angular frequency, f is ultrasonic frequency, k = ω/c0 = 2π/λ is the angle wave number, λ is the wavelength of the ultrasound transmit in the grain, respectively.
In the factors that affecting the conditions of dendrite fragmentation, amplitude and angular wave number depend respectively on the ultrasonic power and frequency, while the variance ratio of grain cross-section M and the shape function φ(x) depend mainly on the defects of grain shape and size along the ultrasonic propagation direction.
From Eq. 12 we can found that the larger the ultrasonic power and amplitude, conditions can be more easily satisfied; simlarly the higher the ultrasonic frequency, angle crossing number, grain structure defects, the longer action time to make greater fatigue, all this factors can also make the conditions more easily satisfied.
Conclusions This article elaborated the forced movement of the particle within grains and its influence on the integrity of the grain itself, established the mathematical theory model of ultrasonic grain crushing.

With increase in the number of pass, the percentage of elongation increases slightly.
Hardness vs Number of passes Fig. 7.
Elongation % vs Number of passes Fig. 8.
Tensile strength vs Number of passes · The microstructure of the extruded specimen and ECAP specimen is compared.
· Tensile strength and hardness increases with the increase in limited number of passes

NA is the sites number of phase A.
NB is the sites number of nano-phase B.
NC is the smaller sites number of that of phase A or nano-phase B. nA is the phase A site number around one specific site of phase A(≤6). nB is the nano-phase B site number around one specific site of nano-phase B(≤6). nC is the nano-phase B site number around one specific site of phase A when NC is the phase A site number(≤6), otherwise, nC is the phase A site number around one specific site of nano-phase B when NC is the nano-phase B site number(≤6), nD is the pore phase site number around one specific site of phase A(≤6), nE is the pore phase site number around one specific site of phase B(≤6). δQiQj is the Kronecker delta function.
The number ratio of intra/intergranular nano-particles Grain growth and Densification.
With densification, the pinning effect of pores on grain growth is gradually weak because of the reduction of pores number, especially after 300 MCS, and grain growth is enhanced rapidly.

The average grain sizes (d) were determined by the linear intercept method, given by d=1.56L/MN, where d is the average grain size, L is the total length of test line used, N is the number of intercepts, and M is the magnification of the photomicrograph [12].
Zn2TiO4 assembled grain boundary and inhibited the grain growth of the ZnO varistors ceramics.
Larger average grain size means less grain number per unit thickness, which resulted in lower potential gradient.
Although increasing the amount of TiO2 addition can promote the grain growth of Zn-Bi varistors ceramics, more TiO2 addition will induce the abnormal grains, which results more small grains.
Therefore, the average grain size decrease and the grain boundary layers per unit increase, the potential gradients also increase.

Indentation was made at various positions, that is, on the grain boundary and about 210μm distant from the grain boundary.
As-aged specimen, not electropolished, showed low hardness near the grain boundary.
According as the surface was removed successively, the hardness number increased, particularly near the grain boundary.
After a removal of 100μm total thickness, the hardness became independent of the position of indentation relative to the grain boundary.
In Fig.2 stress amplitude is plotted against the number of cycles to failure for the Al-12%Zn alloy heat-treated in the same way as above.