Semi-weight function method on computation of stress intensity factors in dissimilar materials

Semi-weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi-weight functions were obtained as virtual displacement and stress fields with eigenvalue-lambda. Integral expression of fracture parameters, K-I and K-II, were obtained from reciprocal work theorem with semi-weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi-weight function method is a simple, convenient and high precision calculation method.

Stress intensity factors calculation in anti-plane fracture problem by orthogonal integral extraction method based on femol

For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions (or between the derivatives of eigenfunctions) of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors (SIFs), so any order SIF can be extracted based on a certain known solution of displacement (an analytic result or a numerical result). Many numerical examples based on the finite element method of lines (FEMOL) show that the present method is very powerful and efficient.

High-resolution X-ray diffraction analysis of the Bragg peak integrated intensity in highly mismatched III-N epilayers

A new method of measuring the thickness of GaN epilayers on sapphire (0 0 0 1) substrates by using double crystal X-ray diffraction was proposed. The ratio of the integrated intensity between the GaN epilayer and the sapphire substrate showed a linear relationship with the GaN epilayer thickness up to 2.12 mum. It is practical and convenient to measure the GaN epilayer thickness using this ratio, and can mostly eliminate the effect of the reabsorption, the extinction and other scattering factors of the GaN epilayers. (C) 2003 Elsevier Science B.V. All rights reserved.

Intensity exaggeration of endohedral metallofullerenes in laser-desorption-ionization time-of-flight mass spectrometry

The laser-desorption-ionization time-of-flight mass spectrometry and desorption-electron-ionization mass spectrometry were employed for the characterization of metallofullerenes extract. it was found that the relative intensities of metallofullerenes in this positive-ion, negative-ion LD-TOF MS and DEI MS were much different. This phenomenon should have relationship with the peculiar ionization energies and electron affinities of metallofullerenes.

EFFECT OF THE CONCENTRATION OF THE ER3+ ION ON THE SPECTRAL INTENSITY PARAMETERS OF ER-YAG CRYSTALS

The absorption spectra of Er:YAG (YAG, yttrium-aluminium-garnet) crystals containing different concentrations of the trivalent erbium ion were measured and the spectral intensity parameters were calculated from these experimental spectra using the Judd-Ofelt model. The results indicate that the phenomenological intensity parameters, OMEGA(lambda) (lambda = 2, 4 and 6), vary as a function of the concentration of the Er3+ ion in the Er:YAG crystal, but no variation in the fluorescence-branching ratios as a function of the concentration of the Er3+ ion is found. An empirical formula is proposed to describe the relationship between the spectral intensity parameters and the Er3+ ion concentration in the Er:YAG crystal. The spectral intensity parameters exhibit a maximum in Er:YAG crystals containing about 1-1.5 at.% Er3+ ion. The effect of the Er3+ ion concentration on the spectral intensity parameters may be attributed to the inhomogeneous lattice distortion in the cell of the Er:YAG crystal caused by the dopant erbium ions.

Response of cyanobacterial carbon concentrating system to light intensity: a simulated analysis

Cyanobacteria possess a delicate system known as the carbon concentrating mechanism (CCM), which can efficiently elevate the intracellular inorganic carbon (Ci) concentration via active transportation. The system requires energy supplied by photosystems; therefore, the activity of the Ci transporter is closely related to light intensity. However, the relationship between CCM and light intensity has rarely been evaluated. Here, we present an improved quantitative model of CCM in which light is incorporated, and developed a CCM model that modified after Fridlyand et al. in 1996. Some equations used in this model were inducted to describe the relationship between transport capacity and light intensity, by which the response of the CCM to light change is simulated. Our results indicate that the efficiency of the carbon concentrating system is sensitive to light intensity. When the external Ci concentration was low, CO2 uptake dominated the total Ci uptake with increasing light intensity, while under high external Ci concentrations HCO3- uptake primarily contributed to the total Ci uptake. Variations in the ratio of energy allocated between the transport systems could markedly affect the operation of CCM. Indeed, our simulations suggest that various combinations of Ci fluxes can provide a possible approach to detect the way by which the cell distributes energy produced by the photosystems to the two active Ci transport processes. The proportion of the energy consumed on CCM to the total energy expenditure for the fixation of one CO2 molecule was determined at 18%-40%.

General Relationship Between Contact Stiffness, Contact Depth, and Mechanical Properties for Indentation in Linear Viscoelastic Solids Using Axisymmetric Indenters of Arbitrary Profiles

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. Although the same expression is well known for indentation in elastic and in elastic-plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. Furthermore, the same expression holds true for both fast loading and unloading. These results should provide a sound basis for using the relationship for determining properties of viscoelastic solids using indentation techniques.

Intensity Distribution Design for Laser-Induced Thermal Loading Based on Numerical Simulation

To accomplish laser-induced thermal loading simulation tests for pistons,the Gaussian beam was modulated into multi-circular beam with specific intensity distribution.A reverse method was proposed to design the intensity distribution for the laser-induced thermal loading based on finite element(FE) analysis.Firstly,the FE model is improved by alternating parameters of boundary conditions and thermal-physical properties of piston material in a reasonable range,therefore it can simulate the experimental resul...

Relationship Between Contact Stiffness, Contact Depth, and Mechanical Properties for Indentation in Linear Viscoelastic Solids Using Axisymmetric Indenters

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. Although the same expres

The relationship of SIF between plate and plane fracture problems and the effect of the plate thickness on SIF

In the present paper, it is shown that the zero series eigenfunctions of Reissner plate cracks/notches fracture problems are analogous to the eigenfunctions of anti-plane and in-plane. The singularity in the double series expression of plate problems only arises in zero series parts. In view of the relationship with eigen-values of anti-plane and in-plane problem, the solution of eigen-values for Reissner plates consists of two parts: anti-plane problem and in-plane problem. As a result the corresponding eigen-values or the corresponding eigen-value solving programs with respect to the anti-plane and in-plane problems can be employed and many aggressive SIF computed methods of plane problems can be employed in the plate. Based on those, the approximate relationship of SIFs between the plate and the plane fracture problems is figured out, and the effect relationship of the plate thickness on SIF is given.

Dynamic stress intensity factor of a functionally graded material under antiplane shear loading

The dynamic response of a finite crack in an unbounded Functionally Graded Material (FGM) subjected to an antiplane shear loading is studied in this paper. The variation of the shear modulus of the functionally graded material is modeled by a quadratic increase along the direction perpendicular to the crack surface. The dynamic stress intensity factor is extracted from the asymptotic expansion of the stresses around the crack tip in the Laplace transform plane and obtained in the time domain by a numerical Laplace inversion technique. The influence of graded material property on the dynamic intensity factor is investigated. It is observed that the magnitude of dynamic stress intensity factor for a finite crack in such a functionally graded material is less than in the homogeneous material with a property identical to that of the FGM crack plane.

Stress intensity factors for functionally graded solid cylinders

This paper presents the mode I stress intensity factors for functionally graded solid cylinders with an embedded penny-shaped crack or an external circumferential crack. The solid cylinders are assumed under remote uniform tension. The multiple isoparametric finite element method is used. Various types of functionally graded materials and different gradient compositions for each type are investigated. The results show that the material property distribution has a quite considerable in influence on the stress intensity factors. The influence for embedded cracks is quite different from that for external cracks.

Optimization Of Off-Null Ellipsometry For Air/Solid Interfaces

The optimization of off-null ellipsometry is described with emphasis on the improvement of sample thickness sensitivity. Optimal conditions are dependent on azimuth angle settings of the polarizer, compensator, and analyzer in a polarizer-compensator-sample-analyzer ellipsometer arrangement. Numerical simulation utilized offers an approach to present the dependence of the sensitivity on the azimuth angle settings, from which optimal settings corresponding to the best sensitivity are derived. For a series of samples of SiO2 layer (thickness in the range of 1.8-6.5 nm) on silicon substrate, the theory analysis proves that sensitivity at the optimal settings is increased 20 times compared to that at null settings used in most works, and the relationship between intensity and thickness is simplified as a linear type instead of the original nonlinear type, with the relative error reduced to similar to 1/100 at the optimal settings. Furthermore the discussion has been extended toward other factors affecting the sensitivity of the practical system, such as the linear dynamic range of the detector, the signal-to-noise ratio and the intensity from the light source, etc. Experimental results from the investigation Of SiO2 layer on silicon substrate are chosen to verify the optimization. (c) 2007 Optical Society of America.

Quasi-Dammann Grating With Proportional Intensity Array Spots

A quasi-Dammann grating is proposed to generate array spots with proportional-intensity orders in the far field. To describe the performance of the grating, the uniformities of the array spots are redefined. A two-dimensional even-sampling encode scheme is adopted to design the quasi-Dammann grating. Numerical solutions of the binary-phase quasi-Dammann grating with proportional-intensity orders are given. The experimental results with a third-order quasi-Dammann grating, which has an intensity proportion of 3:2:1 from zero order to second order, are presented. (C) 2008 Optical Society of America

Thermal fatigue on pistons induced by shaped high power laser. Part II: Design of spatial intensity distribution via numerical simulation

In the laser induced thermal fatigue simulation test on pistons, the high power laser was transformed from the incident Gaussian beam into a concentric multi-circular pattern with specific intensity ratio. The spatial intensity distribution of the shaped beam, which determines the temperature field in the piston, must be designed before a diffractive optical element (DOE) can be manufactured. In this paper, a reverse method based on finite element model (FEM) was proposed to design the intensity distribution in order to simulate the thermal loadings on pistons. Temperature fields were obtained by solving a transient three-dimensional heat conduction equation with convective boundary conditions at the surfaces of the piston workpiece. The numerical model then was validated by approaching the computational results to the experimental data. During the process, some important parameters including laser absorptivity, convective heat transfer coefficient, thermal conductivity and Biot number were also validated. Then, optimization procedure was processed to find favorable spatial intensity distribution for the shaped beam, with the aid of the validated FEM. The analysis shows that the reverse method incorporated with numerical simulation can reduce design cycle and design expense efficiently. This method can serve as a kind of virtual experimental vehicle as well, which makes the thermal fatigue simulation test more controllable and predictable. (C) 2007 Elsevier Ltd. All rights reserved.