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It was concluded that the fatigue damage could be evaluated by the EBSD measurements using the relationship between the total strain range, the number of cycles and the crystal grain size.
The number of cycles to failure (Nf) was defined as the instant when the maximum stress during the cycle dropped below 75% of the maximum stress at half of the number of cycles [7].
Definition of crystal grain is shown in Fig. 3(c), and the calculation procedure can be summarized as follows: The number of points included in a single crystal grain is calculated for each grain and defined as Pi.
The total number of points, Pg, is calculated by summing all Pi within the measurement range.
The average crystal grain area is expressed by SA as the following equation: g A NSS = (2) where Ng is the number of grains within the measurement range.

Q is the total number of the orientations, and Si corresponds to the orientation of the grain in typical grain growth simulations.
Each set of contiguous sites with the same orientation number forms a grain in the microstructure.
The total energy is computed via the Hamiltonian: , (2) in which N is the total number of lattice sites, z is the lattice coordination (26 for a cubic voxel, considering 1st, 2nd and 3rd nearest neighbors), J(Si,Sj) is the grain-boundary energy per unit area and δ is the Kronecker delta.
The orientation number at each site was initialized at random and the inert pinning particles were randomly placed (and were not allowed to touch) until the prescribed volume fraction is reached 0.02, 0.04, 0.06, 0.08, 0.10 and 0.12.
(b) Grain Size Distributions based on the logarithm of the normalized grain size as a function of simulation time. 3.2 The effect of 2nd phase particles on the grain size distribution As described above, the size of the simulation box was 2563 and all orientation numbers were initialized at random.

This work suggests that it may be possible to see past a grain growth episode to estimate the original grain shape and grain size of the polycrystal, and perhaps even reconstruct the grain boundary kinematics.
Many natural examples of this type of microstructure have been described in the literature [3,10,11,12]. 1 http://www.microstructure.uni-tuebingen.de/elle Journal Title and Volume Number (to be inserted by the publisher) 3 Figure 1.
Journal Title and Volume Number (to be inserted by the publisher) 5 Discussion The numerical simulations presented here predict that virtually all grains undergoing normal grain growth will preserve a remnant core of unswept material, and that if these cores can be identified, then it is possible to estimate the grain size, shape and chemistry of the primary material.
The variety of natural samples found suggests that finding unswept cores may not be that difficult, however, in order to apply this result to natural systems there are a number of issues that need to be addressed.
Thus the evolution of grain and grain boundary chemistry can be tracked in systems such as grain growth where the dynamics of the grain boundaries are relatively straightforward.

The information on the grain microstructure with respect to grain size and number of grains composing different texture components obtained by orientation imaging with EBSD is given in Table 1.
A magnetic annealing also alters the number of grains in the different grain subsets.
Grain numbers, grain number fractions (% in brackets) and mean grain sizes for subsets based on orientation criteria in specimens annealed at 700°C for 180 min at zero field and in a magnetic field of 17 T.
Grain subsets Out of magnetic field In magnetic field All measured grains 10607 4857 Overall mean grain size 21.6 µm 35.3 µm Subset A (0, 35, 0) grains number (fraction%) 510 (6.6%) 217 (5.5%) mean grain size 25.6 µm 40.9 µm Subset B (0, 35, 30) grains number (fraction%) 1307 (9.8%) 585 (7.4%) mean grain size 21.7 µm 30.8 µm Subset R (including A+B) grains number (fraction%) 5318 (40.4%) 1886 (26.3%) mean grain size 21.5µm 32.0 µm Subset C* (180, 35, 0) grains number (fraction%) 494 (7.1%) 378 (15.9%) mean grain size 26.2 µm 48.9 µm Subset D* (180, 35, 30) grains number (fraction%) 1294 (9.8%) 788 (14.7%) mean grain size 21.8 µm 36.3 µm Subset L* (including C+D) grains number (fraction%) 5289 (59.6%) 2971 (73.7%) mean grain size 21.7 µm 37.4 µm Grains of size > 70µm in subset R 53 (0.5%) 100.3 µm 89 (1.8%) 93.1 µm Grains of size > 70µm in subset L* 59 (0.6%) 104.2 µm 296 (6.1%) 105.8 µm The EBSD analysis also showed that the
An increase in the fraction number of abnormally grown grains is observed for both favourably (180,35,0) and unfavourably (0,35,0) oriented grains.

Grain size or/ and continuous annealing process may affect the number of grain boundary segregation carbon atoms.
Cottrell has shown that the kinetics of bake hardening is dependent on the amount of solute carbon and the number of free dislocations.
But a great number of carbon atoms segregating to grain boundaries have a big affect on bake hardening property because final cooling was at low temperature (20-400 oC).
Discuss the effect of grain size on grain boundary segregation of carbon atoms.
As the grain size increasing accompanied by a reduction in the actual number of grains, the total area of boundary was reduced, the total amount of carbon stored in the grain boundaries should be lower than fine grain structure.

Finally, statistical analyses were made such as the number of grain boundaries, the diameter and area of grains.
A certain number of points would be chosen as grain cores and each core was assigned with a grow velocity.
Fig. 2 Simulated result for 16 grains A statistical analysis of the number of grain edges in the microstructures simulated in Fig.2 and 3 was conducted and the results were shown in Table 1 and 2.
The previous research indicated that the average number of edges for a grain was nearly 5.143 under equilibrium which meant most of grains were like a pentagon or a hexagon.
With the ratio equal to 1.8, polygons with different number of edges appeared.

Each site has a grain number for the identification of individual grains.
And each grain number has orientation information which consists of three Euler angles (φ1, ω, φ2).
When these two randomly-selected sites have a different orientation number, the orientation number of the selected lattice site is replaced by that of the selected nearest neighboring site.
The number of a central grain represents the Goss orientation which has a potential to grow abnormally under favorable conditions.
When a central Goss grain contains sub-boundaries, the central grain is divided into 8 sub-grains, which have slightly different Goss orientation numbers with sub-boundary energy of 0.05.

As with other metallic engineering alloys, a refinement in prior-β grain size in cast titanium alloys is believed to improve a number of properties including strength, ductility and fatigue resistance [1] as well offer a number of other benefits [2, 3].
A number of articles by the authors have investigated a variety of different alloying elements in titanium with a core focus on grain refinement.
Various grain refining elements were investigated in a number of studies including Si [20], B [21], Cr and Fe [22] and Be [19].
According to the model proposed by Easton and StJohn [12], the slope of the trendline through the data indicates that the particles are semi-potent, as relatively low solute additions are sufficient to activate a number of the particles.
[12] Easton, M.A. and StJohn, D.H. (2005) An analysis of the relationship between grain size, solute content, and the potency and number density of nucleant particles, Metallurgical and Materials Transactions 36A, 1911 - 1920

Therefore, those simulations were terminated to small grains in order to keep the number of grains adequately for statistically analysis.
In the present 3D simulations we choose the number of MCU's of the simulated grain structures as 150x150x150.
Figure 3: a - Simulated GSDF versus x after 500 MCS compared to the analytic approximation Eq. 3. b - Number of neighbouring grains s versus grain size x after 500 MCS.
Figure 4: a - Simulated 3D GSDF versus x after 500 MCS compared to the analytic approximation Eq. 3. b - Number of neighbouring grains s versus grain size x after 500 MCS.
In Fig. 4b the number of neighbouring grains of grains of size x is plotted after 500 MCS.

Grain Boundary Migration in Nanocrystalline Iron T.
A number of experimental techniques used for the investigations of GB properties in traditional materials (coarse grained) are not applicable to nanomaterials.
The colour intensity indicate coordination number (number of the nearest neighbours), which equals 14 for atom at the site in perfect BCC lattice.
For the calculation of the energy of GB, EGB the following equation can be applied [9]: EGB = N (Ea - Ea(s))/A. (1) where N is a total number of atoms in the system, Ea(s) is an energy per atom for the single-crystal at particular temperature and A represents the surface area of the grain boundary.
It has been observed that for low-angle grain boundaries grain rotation occurs at sufficiently high rates such that GB misorientation may saturate long before the grain disappears due to grain boundary migration.