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This study will provide a stress - strain analysis based on molecular dynamics simulations of a series of metastable grain boundaries with identical crystal orientations but unique grain boundary characteristics.
The behaviour of grain boundaries (hereafter referred to as GBs) is complex.
Grain boundaries may be classified according to a characteristic known as the coincidence site lattice number (CSL) [7], also represented by ΣN.
Pond, On the interaction of crystal dislocations with grain boundaries.
McDowell, Asymmetric tilt grain boundary structure and energy in copper and aluminium.

The TRC strip (Fig. 1a) had a coarse dendritic columnar grain structure with an average grain size of 600 mm.
The Hunt map in Fig 2(b) predicts that TRC of Az31 alloy with adequate grain refiner addition produces a fully equiaxed grain structure.
A physical approach to grain refinement by MC process has been developed to provide grain refinement without addition of chemical grain refiners.
In the MC-TRC process, Mg-alloy melt has been intensively sheared to enhance nucleating particles with adequate number density, suitable size and distribution.
In the case of MC-TRC process is the solidification driven process, which can be controlled by the number density of potent nucleating oxide particles.

Post-mortem material characterization of the grain structure was also performed.
Calculating the grain area along the length of the simulated results showed that when the number of seeds (No) was 100, the CET was observed at 14.3cm (143 mm in fig. 3(i)).
When the number of seeds was increased to 500 in the simulation, the CET occurred at approximately 13.7cm (137 mm in fig. 3(ii)).
The number of seeds used in the simulations was approximated.
The seed data used in the simulation was selected to demonstrate the qualitative effect of increasing the number of seeds (that is, the effect of adding a grain refiner).

Internal gettering by EDs including stacking faults and grain boundaries is one possibility.
For the undecorated EDs, the minimum cross-sections defines the number of atoms per atomic plane.
Tsurekawa, "Electron-beam-induced current study of grain boundaries in multicrystalline silicon," J.
Gumbsch, "Interstitial iron impurities at grain boundaries in silicon: A first-principles study," Phys.
Yamamoto, "Tight-binding study of grain boundaries in si: Energies and atomic structures of twist grain boundaries," Phys.

Heavy deformation was introduced in the samples after a considerable number of ECAP passes, from 1 to 16.
The number of ECAP passes, namely 1, 4, 8, 12 and 16 promotes a significant grain refinement observed by transmission electron microscopy (TEM).
Fig. 2 Longitudinal wave velocity vs. the number of ECAP passes for nanostructured copper.
Fig. 3 Transversal wave velocity vs. the number of ECAP passes for nanostructured copper.
A bimodal grain size distribution developed for higher number of passes.

The recrystallization microstructures consisted of equiaxed grains and a large number of the annealing twins.
Texture evolution during the recrystallization and grain growth.
Then, in the subsequent grain growth stage, the similar preferential growth occurs on the grains with the same orientation as the as-rolled texture since these grains can form the 40˚<111> GBs with the grains in the primary recrystallization texture.
However, they did not find the texture return by the grain growth.
Regarding the texture evolution by the subsequent grain growth, observed was the tendency that the {110} texture components appeared during the grain growth [17].

The relatively large initial grain size permitted the identification of the fine DRX grains nucleated at the TJs of the original grains.
It is notable in Fig. 3 that TJ nucleation was already detectable at ε = 0.1 and that the number of new grains increased monotonically with strain.
In this strain range, no nucleation was observed either on grain boundaries or in the grain interiors.
Nature of grains nucleated The crystallographic orientations of the grains nucleated at the TJs at a strain of 0.2 were analyzed using OIM.
This revealed that more than 90% of the new grains had Σ3 relations with one of the surrounding grains, irrespective of the testing temperature.

To mimic the geometrical arrangement of AlN precipitates along austenite grain boundaries, a new model for precipitation at grain boundaries is used, which takes into account fast short-circuit diffusion along grain boundaries as well as the slower bulk diffusion of atoms from inside the grain to the grain boundaries.
Also, the number of available theoretical treatments of the precipitation process of AlN is rather limited.
To take into account the geometrical arrangement of AlN precipitates along austenite grain boundaries, a novel model for precipitation at grain boundaries is used [35].
A default grain size of 50 µm is used in all simulations unless stated otherwise.
Thus, the grain sizes used in the simulations are only estimated values.

The grain orientation texture and (grain) spatial distribution of, at minimum, 1 mm × 7 mm (RD × TD) EBSD maps of BR_HR and GR_A materials were compared.
This method reduces the total number of experimentally measured points to a set of 2000 equally weighted orientations.
Only the {123} <634> S-oriented grains are shaded in Fig. 3(a) since they constitute the highest volume fraction of grains in the BR_HR material.
Fig. 3(e) shows that the IA resulted in elongated, coarse grains which have an average grain size (determined from line intercepts) of 129 µm (compared to a mean size of 100 µm for all non-Cube, 15° tolerance, grains) and a volume fraction of ∼51%.
Acknowledgment This research was carried out under the project number MC4.05238 in the framework of the Research Program of the Materials innovation institute M2i (www.m2i.nl), the former Netherlands Institute for Metals Research.

Number 3 (m=0.3, T=750℃ V=0.5 mm/sec) shows the maximum load of the Z-axis.
Number 1 (m=0.1, T=750℃, V=0.5mm/sec) shows the maximum effective strain.
Number 2 (m=0.2, T=750℃, V=0.5mm/sec) shows the maximum effective stress.
The increasing temperature reduces effective stress from Number 3, 4, and 5.
Figure 9(b) shows the simulation of the grain boundaries, dislocation density, grain orientation, and grain orientation and grain boundaries simulation of Fig. 9. p1, p2, and p3 of the average grain size were 2.24642, 2.37440, and 2.18039 mm2/mm3, respectively, and p3 produced more detailed grain via the simulation.