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DU School of Materials Science and Engineering, Central South University, Changsha 410083, China a wealth9733221@sohu.com Key words: void growth; FEM simulation; aluminum; single crystal; crystallographic orientation Abstract: Void growth in aluminum single crystals is simulated using the finite element method, to illustrate the effect of grain orientation on void growth, a rate dependent crystal plasticity constitutive theory is implemented as a user-defined plasticity subroutine.
The computed results for several grain orientations are compared, which have shown that crystallographic orientation has significant influence on growth behavior of void.
Simulation model The kinematics of crystal plasticity theory presented here follows the classical developments of Hill [8], Hill and Rice [9], and Asaro [10-12], the velocity gradient L is separated into non-plastic and plastic parts: pe LLL += (1) The plastic contribution Lp is assumed to arise from slip on a finite number of slip systems: ∑∑ +=+= α αα α αα γ γ )()( )()( w P WDL & &p pp (2) e ee WDL += (3) Where the superscript α represents a quantity with respect to the αth slip system, )(α γ& is the slip rate of the αth slip system, D p and W p are the plastic rate of deformation and the plastic spin. ) ( 2 1 )()()()( )( α α α α α smmsP ⊗+⊗= (4) ) ( 2 1 )()()()( )( α α α α α smmsw ⊗−⊗=
Fig.5 Contour plots of equivalent plastic strain for the one-void specimens with strain εX: (a) 0.05, (b) 0.1 and (c) {111} pole figure for G {011}<100> at εX =0.1 θAVE Frequency (a) (b) Fig.6 Inhomogeneous deformation of {011}<100> at εX=0.1: (a) in whole single, (b) near the void Frequency θAVE Figs.2-5 show the deviation from the original crystallographic orientation, which indicates grains rotated during deformation.

Firstly, hydrogen is absorbed by the RE-rich phase located at the grain boundaries and then by the hard magnetic phase [2-3].
For the former: (1) where ni, Pi and Ti are number of mols, the H2 pressure and temperature before the beginning of the absorption process, respectively, V is the volume of system which encloses the gas and R is the universal constant of gases.
Based on these considerations, it is possible to write: (2) where nf and Pf are the final number of mols and the H2 pressure in the system, respectively.
Regarding the real gases equation, the number of mols of hydrogen in the system was determined using the well known Van der Waals equation [6, 7]: (3) where a and b are constants referent to H2.
This is attributed to the grain growth on annealing.

%Ge alloy inoculated with Al-Ti-B grain refiner.
P is the solutal peclet number and it is given as P = RV/2D
Hence for a measured growth rate, V, and a solute level, Cf, measured at a finite distance, Z, ahead of the dendrite tip, we calculate the Peclet number, P; composition at the tip, Ct; tip radius, R; global undercooling, ∆TT; and tip temperature, Tt.
Experimental In-situ X-ray imaging experiments were conducted at BM05 at the European Synchrotron Radiation Facility (ESRF) using aluminum-germanium samples, Al-12wt%Ge, inoculated with an Al-5wt%Ti-1wt%B grain refiner (to give 0.0025wt%Ti).

The average grain sizes ranged from 20 to 100 nm.
Distribution of grain size of mechanically alloyed La-Ni alloy (a).
This can be achieved for magnets, which do not have a paramagnetic, isolating phase in grain boundaries and have a grain size smaller than 40 nm.
The latter coefficient strongly depends on the grain size dz.
wavelength [nm] e goal of the technological efforts is to produce vast number of quantum dots of uniform size and shape and geometrically selforganised.

Grain growth occurred during reheating, forming and cooling; however, the average grain sizes are still in the region of 10-20 µm.
The thickness of the final component can be adapted by the number of thermal spray prepregs that are laminated.
The grains of the aluminum rich phase show a shape that is close to the globular grains of the thermally sprayed and reheated material, comp.
Fig. 3 (right), while the grain sizes are larger due to the slow cooling process in the heated die, which supports grain coarsening.
However, there are also a number of drawbacks that still prevent the realization of these alternative technologies in industrial applications.

The size of grains depends upon the energy loss during interaction.
At low fluence (9 x 1010 ions/cm2) of lithium beam, growths of grain like structures are exhibits.
With increasing fluence, the growths of grain like structures are observed at ion fluence of 3 x 1011 ions/cm2.
The number of carbon atoms per cluster can be calculated by following relation [37]: Eg = 34.3/√N eV (5) Where, N is the number of carbon atoms per cluster and Eg is the energy band gap.
Linkage between adjacent grains or coalescence induced by ion irradiation increases the charge transport.

Finally the hot strip is coiled and cooled down to room temperature, before it is cold rolled in a number of passes with or without inter-annealing to final gauge.
Unlike conventional texture models like the common Taylor approach, the GIA-model considers the deformation of an aggregate of eight brick-shaped grains so as to take grain-to-grain interaction into consideration [10].
The novel method to determine earing profiles from sheet texture was validated with a number of examples covering a wide range of sheet textures typically encountered in commercial Al sheet products [3,5].
Conf. on Recrystallization and Grain Growth, eds.
Conf. on Recrystallization and Grain Growth, eds.

The experiment conditions are: grain mesh: 80,grain type :garnet ,cutting material: A3 steel, cutting angle: 90°.
It is easy to determine the number of neurons in the input layer and the output layer during applications.
However it is not so easy to choose the appropriate number of neurons in the hidden layer for there is currently no definite rule to determining it except through experimentation.
The BP neural network can be effective for analyzing a system containing a number of variables, to establish patterns and characteristics not previously known.
However, there are some problems need to be well discussed in the applications of BP neural network, such as the choice of the preset training precision and the proper number of hidden neurons etc.

Substantial plastic strain or grain boundary sliding can cause the nucleation of larger grain boundary cracks or cause preexisting cracks to grow in a stable manner, until an increased length of one of these cracks coupled with higher stress due to work hardening leads to unstable propagation of the cleavage crack.
Such cracking occurs along the grain boundaries and is called intergranular, when most of the second phase particles, where voids are formed, is located on grain boundaries.
If the distribution of second phase particles is relatively uniform, the cracking occurs through grains and is called transgranular.
If the number of finite elements is increased than it is obvious that the number of system equations should be also increased.
There are a number of variants of the CG method.

This study focused on the effect of grain size and the concentration of Mn0.25Fe2.75O4@SiO2 core-shell on mercury absorption efficiency.
The characterization using XRD, VSM, and FTIR was conducted to determine grain size, properties, and material functional groups proving that SiO2 was successfully covered on Fe3O4 surface.
FTIR results showed the sample had a functional group of the main components of Fe-O and SiO2 at wave number of 420-507 cm-1 and 801 cm-1 (stretching) and 1078 cm-1 (bending), respectively.
The results of mercury absorption test indicated that the smaller the grain size and the higher the concentration of TEOS, the percentage of mercury uptake would increase.
Based on Figure 2, the results of FTIR characterization of the two samples have a valley at wave number of 415-516 cm-1 which was a vibration of the Fe-O bond as in the results of the characterization of the Mn0,25Fe2.75O4 sample and have a similarity with previous research [19,20].