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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.

In recent years, it has been developed on the grain design for the solid rocket motor and complete star grain design is found in [2].
The star grain configuration considered is defined by the seven independent geometric parameters: grain outside radius, R, number of star points, N, web thickness, W, fillet radius, r1, cusp radius, r2, star angle, ζ, and star point semiangle, η.
To ensure neutral burning, for a given number of star points, the star point semiangle can be solved by using (2).
η = π/2 + π/N – tan (π/2 – η) (2) Star point semiangle with respect to the star point number is expressed in table II.
Grain outside radius, R = 150 mm Web thickness, W = 60 mm Fillet radius, r1 = 10 mm Cusp radius, r2 = 8 mm Number of star points, N = 6 Star angle, ζ = 25˚ Star point semiangle, η = 33.5295˚ As shown in table III and table IV, the numerical method gives close result as the geometrical method which gives the exact result.

Kanga Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea asjkang@kaist.ac.kr Keywords: grain boundary structure, grain boundary migration, microstructural evolution, grain growth model, abnormal grain growth, nonstationary grain growth Abstract.
If the deposition of an atom from the neighboring grain onto the growing grain is not stable, the atom should detach from the grain and return back to the neighboring grain.
Experimental Observations and Practical Applications There are a number of experimental results that demonstrate the correlation between grain growth behavior and grain boundary structure: normal in systems with rough boundaries and non-normal, in particular abnormal, in systems with faceted boundaries [9, 15, 16, 18-22, 24].
The number in a circle on the figure shows the percentage of the rough boundaries in the sample prepared under the corresponding oxygen partial pressure and donor concentration.
The number in the circle denotes the measured percentage of rough boundaries at the respective conditions.

Grain growth model Grain growth model(GGM) is the model for calculating grain growth speed model essentially, generally, which use the rate of average grain radius to characterize grain growth speed.
Grain growth model of solid phase sintering.
It is well known that the grain growth process at the end of the single-phase SPS is such process as the grain boundary migration between pores and grain boundary reaction; and the grain growth of polycrystalline material is the result of surface diffusion or grain boundary migration due to the system energy reduce.
When particles dissolve in the liquid phase, the number reduced.
Because LSW theory had not considered the solute concentration change around particles, and the effect of diffusion distance decrease due to the increase of the number of particles, then Ardell modified LSW theory by introducing volume fraction, the MLSW is given by Eq. 11

This is the natural boundary conditon for equilibrium of the Journal Title and Volume Number (to be inserted by the publisher) 2 Mullins Equation, a fact that may not be well known.
Journal Title and Volume Number (to be inserted by the publisher) 4 We conclude this section with a description of the critical events.
Loss of grain: some neighboring grain GN will absorb a small target grain GT.
Journal Title and Volume Number (to be inserted by the publisher) 5 Figure 1.
Depiction of a 3 D grain from an ensemble of about 500 grains.

This method gives the average grain size but no information is provided about the grain size distribution.
Ma et al [5] have observed the presence of a small number of grains with clearly larger sizes than the average.
The large amount of defects, the lack of clear grain boundaries and the superposition of grains (in the width direction) do not help in measuring the grain size.
Bright-field and corresponding SAD (a) and dark field (b) TEM images showing the grain structure in samples consolidated at 425ºC. 0 20 40 60 80 100 120 140 160 50 100 150 200 250 300 350 400 450 Number of grains Grain size (nm) CONSOLIDATION TEMPERATURE : 425ºC Number of grains: 422 Figure 4.
Bright-field TEM image and corresponding SAD showing grain structure of a sample consolidated at 475ºC. 0 20 40 60 80 50 100 150 200 250 300 350 400 450 Number of grains Grain size (nm) CONSOLIDATION TEMPERATURE : 475ºC Number of grains: 550 Figure 6.

Journal Title and Volume Number (to be inserted by the publisher) Consideration of crystallographic neighbourhood in magnetic sheets of Fe3%Si.
Behaviour prediction of grain growth from the texture function.
In this modified Monte-Carlo approach [13]: - A site is not characterized by an orientation number, but by a triplet (φ1, φ, φ2) corresponding to its orientation in Euler space
Table 2 Characteristics of considered Goss grains.
Fig.3 Goss grain growth kinetics in global matrix without (-a-) and with (-b-) texture consideration Goss grain growth in oriented matrixes The two components of texture have a different behaviour with regard to Goss grains.

Unfavourable influence of coarse-grain microstructure and favourable influence of its refinement on a number of mechanical properties place the problem of finding solutions for the effective grain refinement in the circle of fundamental issues for this group of alloys [9÷11].
The number of cycles was changed from 1 to 20.
Further increasing the number of cycles has slight effect on changes in size (Fig. 9a) and shape (Fig. 9b) of grain and relative surface area of its boundaries (Fig. 9c).
During the next cycles, a unique state of equilibrium between the number of undissolved lamellar precipitations of g phase and the number of grains is established.
Too low heating rate causes that the number of these precipitations is small, which affects lower grain refinement.

In order to quantify the plastic anisotropy of the ultrafine grained aluminium alloy AA6016 produced by accumulative roll-bonding (ARB) the Lankford parameter is measured by tensile testing as a function of the number of ARB cycles.
During ARB the coarse globular grain structure in the starting material changes to an ultrafine grained lamellar structure (Fig. 1).
increases steadily with increasing number of ARB cycles.
During deformation the coarse globular grain structure in the starting material changes to an ultrafine grained lamellar grain structure.
The key figure shows the position of the main texture components. 0 2 4 6 8 0 1 2 3 4 r number of cycles rRD r45° rTD Experiment 0 2 4 6 8 0 1 2 3 4 FC - Simulation r number of cycles rRD r45° rTD 0 2 4 6 8 0 1 2 3 4 r number of cycles rRD r45° rTD RC - Simulation 0 2 4 6 8 0 1 2 3 number of cycles 0 2 4 6 8 -4 -3 -2 -1 0 1 ∆∆∆∆r number of cycles ∆rFC ∆rRC ∆rexp Fig. 3: Lankford parameter r calculated for tensile deformation in different directions as a function of the number of ARB cycles, a) experiment, b) FC and c) RC Taylor model Fig. 4: Measured and simulated normal anisotropy (a) and planar anisotropy ∆r (b) as a function of the number of ARB cycles a) b) c) a) b) Conclusions Measurements of the Lankford parameter show that the plastic anisotropy of the ultrafine grained Al alloy AA6016 increases with the number of

The microstructure of the material is observed with increasing number of passes using optical microscopy (OM), laser microscope and scanning electron microscopy (SEM) electron backscattered diffraction (EBSD).
Moreover, the hardness of material also increasing up to 41Hv for the first pass and constantly increased with the increasing number of pressing.
The influence of NTE pass number on grain size and hardness properties of material was studied at first.
Grains are equiaxial after subjected to 4 passes of NTE.
Following that the grain size was measured by using linear intercept method.