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Sometimes cracks stop completely for a large number of cycles sometimes cracks only decelerate, both resulting in an additional number of life time cycles.
Grain A with the initial crack is surrounded by grain B.
In fact grain A with the initial notch is surrounded by grain B.
Firstly we only consider the information we normaly have from two grains and a grain boundary: The orientation of both grains which form the grain boundary and the inclination angle d between the grain boundary and the loading axis.
Now we can calculate the Schmid-factors for all slip planes and systems of grain A and grain B.

By evaluating the number of abrasive grains which pass through a unit length of a sample surface for each grinding pass, they revealed that only 1/5 of abrasive grains work effectively in the conventional one.
Discussions The number of abrasive grains passed through a unit length of sample surface, �g is calculated to evaluate working effective abrasive grains.
The value of �g is the total number of abrasive grains on that Archimedes' spiral and is calculated as: �g = LA.za.R (2) where LA is Archimedes' spiral length, and za abrasive grains in a unit area (about 30 grains / mm2 for present case).
Surface roughness, Ra versus number of abrasive grains that passed through a unit length of a sample surface, �g for each grinding pass.
Normally, smoother ground surfaces are obtained by large number of working abrasive grains passing through the surface.

Isothermes of grain boundary tension and grain boundary adsorption in Cu-Sn system Vaganov Danil1,a and Zhevnenko Sergey 1,b 1 Moscow State Institute of Steel and Alloys (Technological University), 4, Leninsky pr., Moscow, 119049, Russia a vaganov_d_v@pochta.ru, b sergeyng@mail.ru Keywords: Grain boundary tension; Grain boundary adsorption; Free surface tension; Zero creep method Abstract.
Today, there is a lack of such data due to the limited number of the measuring methods and possibilities of apparatus.
The groove is formed at the place of grain boundary exit to the surface.
The average grain size was 115 µm.
It is possible to evaluate the number of sites in surface monolayer A A m N N V Г 3 2 max −       = (5) 0)1ln( γ γ ++−= bc zRTdc d Г γ RT c −= bc1zbc + =Г 47.0)30001ln(102.0 ++ −= c GBγ 81.1)100001ln(148.0 ++ −= c sγwhere Vm is the tin molar volume and Na is the Avogadro number.

The initial austenite grain size plays an important role in the obtained ferrite nucleation number, and the potential nucleation cells are increased.
Fig.4 shows the ferrite nucleated cell number as a function of austenite grain size.
As shown in this figure, as the initial austenite grain size is increased, the ferrite nucleated number is decreased.
Therefore, as the initial austenite grains size become small, the nucleated ferrite grain numbers large.
Thus, increasing potential nucleation number and improving nucleation probability of each nucleation position can be helpful in obtaining fined ferrite grains.

The normalised cumulative number of nuclei/grains, as generated in the simulation, has been plotted as function of the simulated transformed fraction in Fig. 3 b).
For decreasing ratios of SGB V / ˙NO (and the same nucleation rate ˙NV , see above), the same number of nuclei must form on a more and more restricted grain-boundary area and therefore nuclei are more likely to appear close to each other.
This positive correlation of nucleation positions is exhibited in Fig. 1 c) and is the reason for the retardation of the transformation kinetics as observed (Fig. 1 a): The closer to each other nuclei form, the sooner they impinge which leads to slow transformation kinetics and a high number of small grains.
Moreover, for such parent microstructures, the last part of the transformation is further slowed down because there are a number of very large parent grains (which can be transformed only by product grains nucleated at grain boundaries of these grains).
fraction as function of the transformed fraction predikted by the JMAK-like model and b) normalised cumulative number of nuclei/grains during the simulation as function of simulated transformed fraction.

Briefly, the microstructure to be modeled is discretized, and the orientation number at each grid point is associated with a 3-parameter crystallographic orientation.
Each voxel i in a simple cubic lattice of N=100x100x100=10 6 elements was assigned an orientation number Si=500.
The misorientation distribution (MDF) was quantified by counting the number of voxels adjacent to a different grain and sorting them by misorientation type.
Journal Title and Volume Number (to be inserted by the publisher) 5 (i) (ii) Fig. 3.
Journal Title and Volume Number (to be inserted by the publisher) 7 Figure 6 illustrates the behavior of several systems.

The grain growth behavior depends on the roughening of the interfaces as indicated by the grain and grain boundary shapes.
With increasing impurity content-in particular SiO2-in the alumina powder, abnormal grain growth becomes more pronounced with increasing number of flat grain boundaries.
As shown in Fig. 1, the grain shapes and the grain growth behavior changed with the amount of B added.
The number fraction of the large grains exceeding 2.5 times of the average size appeared to increase with sintering time.
These grain shapes, grain boundary shapes, dihedral angles, and grain size distributions are same as those observed earlier by Park and Yoon [30] and Cho et al. [31] 0 2 4 6 Percentage of Grains (%) 0 8 10 12 0 Normalized Grain Radius 2 4 6 0B 1B 2B 3B 4B 0 2 4 6 Percentage of Grains (%) 0 8 10 12 0 Normalized Grain Radius 2 4 6 0B 1B 2B 3B 4B Fig. 2.

In order to understand why these factors, i.e. the number density and potency of the inoculant particles, affect grain size we need to understand the role of constitutional supercooling (CS).
The important properties of the nucleant particles, whether naturally present in the alloy melt or deliberately added as inoculants, are their nucleation potency, defined by DTn, and their distribution and number density, which define the spacing xSd between nucleants.
A representation showing the relationship between composition as defined by Q and the components that contribute to the grain size. xSd is constant if the number density of nucleant particles does not change with composition as shown in this figure (from [7]).
It has been found that G may decrease as the number of layers increase due to heat build-up in the component.
The ideal conditions for creating an equiaxed grain structure are: • an alloy with solute elements that generate a very high Q value and nanoparticles that slow grain growth and the diffusion rate in the liquid; • a melt inoculated with the most potent particles at a high number density; • a temperature gradient as low as possible; and • optimised processing parameters such as scan speed and any other processing parameters that promote nucleation.

Polycrystalline materials typically contain a very large number of grains whose surrounding grain boundaries evolve over time to reduce the overall energy of the microstructure.
Thin polycrystalline films are typically composed of a large number of small grains, and the surrounding grain boundaries largely determine the microstructure of the material.
Although applications typically involve polycrystalline specimens containing a very large number of grains, it is instructive to consider small idealized systems, such as special bicrystalline systems, which can be studied in detail [2, 4, 11].
(b) The grain boundary XIII.
(b) The grain boundary XIII.

The number of faces per grain f and the average number of faces of each grain’s nearest neighbors m(f) is counted.
Fig. 2 shows the distribution of the number of grain faces in the system.
Fig. 3 plots the average number of faces of each grain’s nearest neighbors, m(f), vs. the number of faces per grain.
A distribution in the average number of faces of a grain’s neighbors is observed for a given topological class f.
Fig.3 Plot of the average number of faces of the nearest-neighbor grains, m(f), vs. the number of faces of the grains, f.