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In addition to the macroscopic grain subdivision, microscopic grain subdivision also occurred within the matrix to form an ultrafine grained structure in the single crystal specimen after high strains.
Introduction It is well known that severe plastic deformation (SPD) of bulky metallic materials can produce ultrafine grained (UFG) microstructures having submicrometer grain size.
It is an effective way to use a single crystal having no initial grain boundary as the starting material for SPD, in order to get a deeper understanding of grain subdivision.
Additionally, several numbers of deformation bands inclined at about 20 degrees to the rolling direction (RD) were also observed within the deformed matrix and the bands subdivided the crystal.
Many fine "grains" surrounded by high-angle boundaries can be seen.

The dynamic recrystallization coefficient can be defined as the capacity to decrease the dislocation density via the growth of fresh grains; this coefficient equals the difference between the number of subgrains with sufficient energy for grain nucleation Nnucl (from whom grain growth occurs) and the number of growing grains Ngrowth, divided by Ngrowth [5].
Grain growth is a thermally activated process, thus Ngrowth follows an Arrhenius form, where the energy barrier for grain growth QDRX is composed by the difference between the energy induced by the boundaries motion when grains are growing (Edisp) and the strain energy to drive grain growth once high-angle grain boundaries form (EHAGB).
(3) The onset for dynamic recrystallization occurs when high-angle grain boundaries (HAGBs) form via the accumulation of dislocations leading to grain nucleation [6].
In analogy to a previous analysis for cell formation [3], dynamic recrystallization can be considered to start when the stored energy at the boundaries (Esub) equals to (i) the necessary energy to nucleate dislocation-free grains (Egrain); (ii) the displacement energy for boundary-dislocations to onset grain growth Edisp and (iii) the equivalent slip energy of dislocations migrating from the grain interior to the boundaries (Eint) [5].
The model results show good agreement in the dynamic recrystallization onset range, number of oscillations before undergoing steady state and the steady state stress for strain rates below 2.7 × 10−1 s−1.

Equal channel angular pressing (ECAP) is useful method to obtain the ultra-fine grained and the high hardened metal.
The as-deformed metals retained high dislocation densities, a large number of low angle sub-grain boundaries, and showed being in non-equilibrium configurations [7].
The grain of as-heat treated Al exhibited an equi-axial, uniform, and coarse structure.
The grains were elongated, having an angle of 15 - 30 degrees to the ECAPed out direction.
Rotated Goss component, {110}<110>, increases with the number of passes ECAP, decreases with annealing.

With increasing number of ECAP passes this difference decreased.
Fig. 2 The fraction of high-angle grain boundaries (HAGBs) in the crept samples as a function of the number of ECAP passes.
It is important to note that there is a difference in the appearance of the creep curves between the unpressed and the pressed materials and there is a difference in the fracture strain levels for the pressed material with different numbers of ECAP passes: pressed samples are denoted by the numbers B1-B12 where the numeral denotes the number of ECAP passes.
This softening may be related to the increase in the spacing of HAGBs at approximately constant subgrain size with increasing number of ECAP passes, resulting in the fraction of low-angle grain boundaries decreasing considerably (Fig. 2).
Fig. 5 Standard creep curves for unpressed (coarse-grained) state and states after various number of ECAP passes for: (a) Al, (b) Cu, (c) Al-0.2wt.

A small number of crystal plasticity simulations and tensile tests are carried out with the aim of demonstrating that control of twinning can improve the uniform elongation of magnesium based alloys.
A number of authors have recently drawn attention to this fact in their analysis of Mg-3Al-1Zn subjected to Equal Channel Angular Pressing [2,3].
Fraction of Grains Undergoing Twinning - Sachs Analysis The fraction of grains undergoing twinning, XT, is determined, in part, by the texture.
Assuming that only one deformation mode is active in each grain, the grains expected to twin can be estimated by combining a Schmid factor (SF) analysis with the fact that twinning only works in one direction.
That is, more grains should undergo twinning under uniaxial compression, compared with tension, for a random aggregate.

Most models that simulate or calculate the microstructural evolution at the particle scale focus on a very small number of particles.
E = 1 2 1"# qi,qj( )( )j=1 n $i=1 N $ (1) where i is each site, N is the total number of sites in the system, j is each neighbor of site i, n is the total number of neighbors of each site, qi is the state of the grain or pore at site i and qj is the state of the nearest neighbor at site j and δ is the Kronecker delta with δ(qi = qj) = 1 and δ(qi ≠qj) = 0.
Time in a kMC model is measured in units of Monte Carlo step; 1MCS corresponds to N attempted changes where N is the total number of sites in the system.
Images obtained from the numbered points indicated will be used for model validation.
Sintering was simulated by attempting Ng (number of grainsite) grain growth step, Np (number of poresite) pore migration step, and vacancy annihilation with a frequency given by Eq. 3.

Journal Title and Volume Number (to be inserted by the publisher) Fig 2.
Each lattice site is assigned a number, Si, which corresponds to the orientation of the subgrain in which it is embedded.
The number of distinct subgrain orientations is dependent on the measuring step size and area.
A grain boundary energy Ji is attached to the grain boundary sites and zero energy for sites in the grain interior, according to ( )∑δ−⋅= nn j SS i I i ji1JE
(3) Journal Title and Volume Number (to be inserted by the publisher) where ijδ is the Kronecker delta, the sum is taken over nearest neighboring(nn) sites and Ji is a positive grain boundary energy.

A significant grain refinement was observed by using the solute Ta together with stochiometric grain refiner (Al-2.2Ti-1B).
The grain size in Alloy 1 is about 700 µm.
The measured grain size in Alloy 2 is about 223 µm, while the measured grain size in Alloy 3 was approximately 140 µm.
The grain size can be refined to be less than 140 µm, which is much smaller than the grain size that can be achieved using Al-5Ti-1B grain refiner. 2.
StJohn, An analysis of the relationship between grain size, solute content, and the potency and number density of nucleant particles, Metall.

However, arbitrary number of crystal orientation can be described by only two order parameters.
The KWC model also allows for the grains to rotate.
Hslam et al., in their Molecular-dynamics (MD) studies [21-23], have indicated that both grain rotation and grain boundary migration occur during grain growth in nanocrystalline material.
In the case of grain of region A, we can see many high angle grain boundaries and high dislocation density distributions.
On the other hand, in grain B, the high angle grain boundaries and the high dislocation density are observed only around the original grain boundaries.

A gradient nature of changes in the number of stress concentrators when moving away from the failure surface was defined.
The scalar density of dislocations in grains without a band structure was about 3.3x1010 cm -2 .
However, broken sub-boundaries are often observed in grains with a chaotic dislocation structure.
The scalar density of dislocations in grains without a band structure was about 3.6x1010 cm -2 .
The scalar density of dislocations in grains without a band structure was about 3.1x1010 cm -2 .