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Introduction Twinning is an important deformation mechanism in most hcp metals because of an insufficient number of independent dislocation slip systems.
It is further seen that twinning proceeds in the studied parent grain families in accordance with the Schmid factors, i.e. the fastest in {10.0}|| grains, and slowest in {11.0}|| grains.
This post-yielding decrease in the AE activity has been previously attributed to the increasing number of dislocations and thus decreasing free length for dislocation movement as well as exhaustion of twinning activity [7].
That means that twins in one grain can lead to the nucleation of twins in neighbouring grains via an increase in the local stress at the grain boundary due to impinging on the grain boundary.
It stands to reason that a considerably higher number of twins nucleate at the onset of plasticity in the fine-grained alloy.

The fine β grains (lighter phase, about 2μm) are dispersed homogeneously in the α2 grains.
The number of cavities decreased with the decrease of strain rate.
At high strain rate 1.7×10-3s-1, a number of small cavities with the pattern of short stick are non-uniformly distributed near the fracture tip.
As previous stated the finer grain could provide better accommodating deformation due to grain boundary sliding, so more cavities were founded in larger grain size at 940℃.
Number of cavities decreased with the decrease of deformation strain rate.

The distributions of grain sizes were obtained by taking at least 200 different grain images for the sample and estimating the mean diameters of individual grains by using the J-image software.
Table 1 shows the average grain sizes observed from FeSEM.
Average grain size of samples sintered at varied temperatures.
The increased of μ΄ value with increasing of sintering temperature is attributed to the increase of grain sizes, where larger grains diminish the number of grain boundaries [8].
Therefore, the domain wall will easily move in the larger grains.

After 390℃ extrusion the alloy grain size（as shown in Fig. 3-d） is significantly larger than the that extruded at other temperatures grains of alloy extruded at 290℃ very unevenly, mainly for coarse grains within a partial area, while in other regions, grains are particularly small (Fig. 3-a), the grain sizes not the uniformity which will usually result in the unevenness of the material properties.
With increasing post extrusion temperature grain gradually becomes uniform.
Therefore, for thermal deformation at a lower temperature, the grains will have a large number of the twin tissues (Fig. 3-a).
There are a large number of large and deep dimples on the fracture surface(Fig. 5-b).
The interior of the crystal grains of the alloy in the post extrusion exist a large number of twinned organizations, which is reduced with extrusion temperature rising. 3) The aging treatment can further improve the Mg-6Zn-Si-0.25Ca’s mechanical properties after the post extrusion.

Addition of grain refiner and modifier is an alternative for this problem, through the control of solidification process that results in grain refining and microstructure modification.
The Ti grain refiner was varied 0.063, 0.083 and 0.108 wt. % Ti and added at the holding furnace prior to LPDC process.
One of the alternative to overcome this problem is by addition of modifier and grain refiner.
The solute elements restrict the grain growth by segregating to the newly formed solid surface.
The total number of cylinder heads produced during the trial was 764 pieces for each of the standard and the modified alloy.

The fracture toughness of hot press sintered Al2O3 was, therefore, higher than that of pressureless sintered Al2O3, because the total amount of bridging stress and stress shielding effect increased with increasing magnitude of microcrack deflection and the number of interlocking grains.
Total number of nodes and elements were about 70,000 and 17,000, respectively.
Crack face bridging, i.e., grain bridging, was rarely observed.
The fracture toughness of hot press sintered Al2O3 was, therefore, higher than that of pressureless sintered Al2O3, because the total amount of bridging stress and stress shielding effect were increased with increasing magnitude of microcrack deflection and the number of interlocking grains.
(4) The total amount of bridging stress and stress shielding effect were found to increase with increasing magnitude of microcrack deflection and the number of interlocking grains.

The number of deformation cycles (passes) at an angle of 90 0 between the channels was N=2 (ε ≈ 2.3) for both temperatures of ECA pressing, and, at an angle of 120° between the channels, this number was N = 3 (ε ≈ 2.0 ) at T=20 0C for the initially ferritic-pearlitic structure and N = 4 (ε ≈ 2.5 ) at T=300 0C for the initially martensitic structure.
We observed also isolated coarse grains of ~200 nm in size.
The fraction and size of grains in the samples increase.
The structure is characterized by the grain nonuniformity.
The dislocation density inside the grains is relatively low.

The waveforms created in this way are downloaded via an interface and stored in a file with a controlled number of samples.
In addition a number of standard voltage waveforms are available including sine, square, triangle, ramp and pulse.
Moreover, the number of minor loops can equally be observed increasing with the increase of switching frequency.
Measured iron losses, under SPWM excitation at fundamental frequency of 50 Hz and switching frequency of 5 kHz. __...__...: non oriented grain laminations (large grain) ------: non oriented grain laminations (small grain) _______: grain oriented laminations Fig. 10.
Measured hysteresis loop for non oriented grain (large grain) laminations under SPWM excitation at fundamental frequency of 50 Hz and switching frequency of 1 kHz Fig. 11 shows the hysteresis loop area of non oriented grain (large grain) material under SPWM excitation at fundamental output frequency at 50 Hz and switching frequency of 1 kHz.

Causality analysis of the differences in local toughness was done with samples marked with circles and sample number, as shown in Fig. 1.
Ferrite grains in this locality were coarse with mean grain size d= 0.250 mm.
The microstructure in the vicinity of the fracture and slab surface was coarse grained with mean grain size d= 0.177 mm.
For the brittle sample D22 the mean grain size was d = 0.0221 mm, while the ductile sample D21 had grain size d = 0.0156 mm.
Metallographic evaluation of seeming grain size

The random number generator is based on the Box-Muller transformation [11], a pseudo-random sampling method for generating standard normally distributed random numbers.
The cellular automata space is a grid of finite number of cells described by several internal variables and it can be represented by the array of integers.
Particular gains grow until the whole space is covered with grains.
Difference between circles/spheres and grains distributions.
After growth procedure (Fig. 5) grains increase their size in comparison to initial circle/sphere size and translate the grain size distribution to the right, towards higher mean average grain sizes.