Temperature distributions in semi-infinite and finite-thickness media as a result of absorption of laser light

A time-domain method is used to derive simple expressions for temperature distributions within media heated by a moving laser beam with a Gaussian power density profile. Various medium-absorption functions are considered. The solutions are given as single integrals with respect to time of simple functions. The expressions can be applied to multilayer media consisting of layers with different optical (light-absorbing) properties, provided that the layers have similar thermal properties. A number of optical recording examples have been examined in detail, and the results compared with those obtained by use of a more general (fast-Fourier-transform-based) approach.     

Temperature distributions in semi-infinite and finite-thickness media as a result of absorption of laser light: erratum

Errors in a paper published earlier [Appl. Opt. 36, 494 (1997)]are corrected. They comprise a corrected definition and line of pseudocode. In the paper "Temperature distributions in semiinfinite and finite-thickness media as a result of absorption of laser light,"(1) two errors appeared and are corrected as follows:     

A rectangular crack in an infinite solid,a semi-infinite solid and a finite-thickness plate subjected to tension

This paper is concerned with the tension problems of a semi-infinite solid with an embedded rectangular crack and a rectangular surface crack as well as an infinite solid with a rectangular crack as a special case. The analyses are based on the body force method, and are performed by generalizing the previous analyses of an embedded elliptical crack and a semi-elliptical surface crack. Furthermore, approximate results are given for a finite-thickness plate with an embedded rectangular crack, by superposing the effects of the free surfaces obtained in the above analysis for a semi-infinite solid.     

Antiplane shear in adhesively bonded semi-infinite media with transverse cracks

The elasiostatic antiplane shear problem of two half spaces bonded through an infinite layer all having transverse fatigue cracks is considered. The cases of three imbedded cracks, cracks terminating at the interfaces, completely broken layer, and a crack in the layer spreading into the half spaces are separately treated in detail. The Fourier transform is used to formulate the problem. Use of the mixed type conditions on the crack plane reduces the formulation to a system of singular integral equations with simple or generalized Cauchy kernels. Singular behavior of the solution at the irregular points on cracks is investigated. Numerical results given in the paper include stress intensity factors and crack opening displacements for material pairs of aluminum-epoxy and steel-aluminum.

---

Résumé On considère le problème de cisaillement élasto-statique anti-planaire de deux demi-espaces reliés par une couche infinie et comportant des fissures de fatigue transversales. On traite séparément, dans le détail, les cas suivants: trois fissures noyées, fissures se terminant à l'interface, couche complètement rompue et fissure dans la couche intermédiaire s'étendant dans les demi-espaces. Pour formuler le problème, on fait appel à la transformée de Fourier. En utilisant des conditions de type mixte sur le plan de la fissure, on peut réduire la formulation du problème à un système d'équations intégrales singulières à conditions aux limites de Cauchy simples ou généralisés. On étudie le comportement singulier de la solution dégagée aux points irréguliers des fissures. Les résultats numériques fournis dans le mémoire comportent les facteurs d'intensité de contrainte et les déplacements d'ouverture de la fissure pour des combinaisons de matériaux d'aluminium Epoxy et acier aluminium.

     

Conical crack problem in semi-infinite media with stress-free boundary conditions

In this study an axially symmetric conical crack problem in semi-infinite media is considered. Stress-free boundary conditions are satisfied at the boundary of the half-space. By using Papkovich-Neuber functions and Hankel transform techniques the problem is reduced to a system of two singular integral equations which are then solved numerically. The numerical examples are given for a constant pressure and constant shear stress on the crack surface separately. The stress intensity factors are evaluated and presented for various crack geometries and Poisson's ratios.

---

Résumé Dans cette étude, on considère le problème d'une fissure en forme de conique à symétrie axiale dans un milieu semi-infini. Les conditions d'absence de contraintes aux limites sont satisfaites à l'extrémité du demi-espace. En utilisant les fonctions de Papkovich-Neuber et une transformée de Hankel, on réduit le problème à un système de deux intégrales singulières, que l'on résout ensuite par voie numique.A titre d'exemples numériques, on considère une pression constante et une tension de cisaillement constante, agissant séparément sur la surface de la fissure.On évalue les facteurs d'intensité de contraintes et on les présente pour diverses géométries de fissures et pour diverses valeurs du module de Poisson.

     

Tension of a finite-thickness plate with a pair of semi-elliptical surface cracks

This paper deals with the tension of a finite-thickness plate with a pair of semi-elliptical cracks on both of the free surfaces. The analysis is performed in a similar manner to the previous single crack problem, by using the body force method and the boundary conditions expressed in terms of resultant forces and displacements of the boundary elements. The stress intensity factor at the maximum depth of the crack front is calculated for various values of the parameters and these results are fitted by a reliable polynomial formula for convenience of engineering applications.     

Light transport in three-dimensional semi-infinite scattering media

The three-dimensional radiative transfer equation is solved for modeling the light propagation in anisotropically scattering semi-infinite media such as biological tissue, considering the effect of internal reflection at the interfaces. The two-dimensional Fourier transform and the modified spherical harmonics method are applied to derive the general solution to the associated homogeneous problem in terms of analytical functions. The obtained solution is used for solving boundary-value problems, which are important for applications in the biomedical optics field. The derived equations are successfully verified by comparisons with Monte Carlo simulations.     

Temperature and displacement distributions in a half-space in the presence of a moving heat flux and convective cooling

Summary A solution has been obtained to the quasistationary conduction problem for an elastic half-space heated by a source moving with a constant velocity over the boundary, with the heat flux distributed over a finite segment. It is assumed that there is convective heat transfer in accordance with Newton's law with the external medium outside the heated region.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 3, pp. 18–25, May–June, 1992.     

Stress intensity factors and weight functions for deep semi-elliptical surface cracks in finite-thickness plates

ABSTRACT Three-dimensional finite element analyses have been conducted to calculate the stress intensity factors for deep semi-elliptical cracks in flat plates. The stress intensity factors are presented for the deepest and surface points on semi-elliptic cracks with a/t -values of 0.9 and 0.95 and aspect ratios ( a/c ) from 0.05 to 2. Uniform, linear, parabolic or cubic stress distributions were applied to the crack face. The results for uniform and linear stress distributions were combined with corresponding results for surface cracks with a/t = 0.6 and 0.8 to derive weight functions over the range 0.05 ≤  a/c  ≤ 2.0 and 0.6 ≤  a/t  ≤ 0.95. The weight functions were then verified against finite element data for parabolic or cubic stress distributions. Excellent agreements are achieved for both the deepest and surface points. The present results complement stress intensity factors and weight functions for surface cracks in finite thickness plate developed previously.     

Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates

Surface cracks are among the more common flaws in aircraft and pressure vessel components. Accurate stress analyses of surface-cracked components are needed for reliable prediction of their crack growth rates and fracture strengths. Several calculations of stress-intensity factors for semi-elliptical surface cracks subjected to tension have appeared in the literature. However, some of these solutions are in disagreement by 50–100%.

In this paper stress-intensity factors for shallow and deep semi-elliptical surface cracks in plates subjected to tension are presented. To verify the accuracy of the three-dimensional finite-element models employed, convergence was studied by varying the number of degrees of freedom in the models from 1500 to 6900. The 6900 degrees of freedom used here were more than twice the number used in previously reported solutions. Also, the stress-intensity variations in the boundary-layer region at the intersection of the crack with the free surface were investigated.     

Dislocations and internal loading in a semi-infinite elastic medium with surface stresses

This paper presents analytical solutions for shear and opening dislocations in an elastic half-plane with surface stresses by using the Gurtin–Murdoch continuum theory of elastic material surfaces. The fundamental solutions corresponding to buried vertical and horizontal loads are also presented. Fourier integral transforms are used in the analysis. It is found that a characteristic length parameter that depends on the surface and bulk elastic moduli exists for this class of problems, and it represents the influence of surface stresses on the bulk elastic field. Selected numerical results are presented to demonstrate the influence of surface stresses on the bulk stress field. The fundamental solutions presented in this study can be used to develop boundary integral equation and other methods to analyze complicated fracture and boundary-value problems associated with nano-scale structures and soft elastic solids.     

Vibrations of elastic infinite and semi-infinite media containing cracks

The problems of stress distribution in an infinite medium and in an elastic half-plane containing line cracks, when the pressure which opens the crack is periodic in time, are considered. These are (1) a cruciform crack in an elastic infinite medium, (2) an edge crack perpendicular to the surface of an elastic half-plane, and (3) their corresponding “exterior” problems. The integral equations corresponding to these problems are obtained. Expressions for the stress intensity factor and the crack energy are derived and numerical results are presented. The equivalence of the stress intensity factor and the crack energy for “exterior” and “interior” problems as established by Stallybrass for the static case is obtained from the dynamic results by letting the frequency tend to zero.     

Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption

The problem of unsteady, two-dimensional, laminar, boundary-layer flow of a viscous, incompressible, electrically conducting and heat-absorbing fluid along a semi-infinite vertical permeable moving plate in the presence of a uniform transverse magnetic field and thermal and concentration buoyancy effects is considered. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. The obtained analytical results reduce to previously published results on a special case of the problem. Numerical evaluation of the analytical results is performed and some graphical results for the velocity, temperature and concentration profiles within the boundary layer and tabulated results for the skin-friction coefficient, Nusselt number and the Sherwood number are presented and discussed.     

Computation of electric-arc parameters taking account of convective and radiant losses

An approximate solution of the problem of an electrical arc in a turbulent argon stream is obtained, taking into account convective and radiant energy losses in the discharge channel at atmospheric pressure.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 4, pp. 673–680, October, 1971.     

One-dimensional propagation of discontinuities in non-homogeneous linear viscoelastic semi-infinite media

One-dimensional wave-propagation is analysed in a non-homogeneous, isotropic, linearly viscoelastic semi-infinite medium, by the theory of singular surfaces. The characteristics of the medium at any point are assumed to be dependent upon the position of the point. The solution for the stress field, which is valid even after the wave-front has passed, is obtained in the form of Taylor’s series by prescribing the time dependent stress boundary condition in the form of a Maclaurin’s series. Furthermore, it is shown that the higher order discontinuities satisfy the same propagation conditions as the stress waves and all the discontinuities decay as they traverse the material. An application of inhomogeneity varying exponentially with position has been analysed. Diagrams for the above example with arbitrarily chosen parameters are presented.     

Radionuclide adsorption upon convective and diffusional migration in disperse media

Equations and boundary and initial conditions of radionuclide transfer in disperse media are formulated taking into account diffusion, radioactive decay, adsorption, and convective transfer. Particular solutions of the system of equations under consideration are obtained in the case of linear Henry sorption isotherm and at constant diffusion coefficients and flow velocity. The problems are extended to the case of linear and inhomogeneous media for given sorption equations and transfer coefficients.Institute for Energy Problems of the Academy of Sciences of Belarus, Academic Scientific Complex A. V. Luikov Institute of Heat Mass Transfer, Academy of Sciences of Belarus, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, July–August 1995, pp. 660–677.     

AC losses in tubular superconducting composites with anisotropic surface structure

AC losses have been measured in prototype tubular composite conductors of a design proposed for superconducting ac power transmission lines. The conductors were of 15 and 19 mm diameter, with a niobium surface layer bonded to a copper substrate either directly or via an intermediate layer of niobium-titanium alloy. At a surface current density appropriate for the working conditions of a power transmission line (40 A mm^?1) the losses measured for current flow in the axial or circumferential directions differed by up to an order of magnitude, depending on details of the surface anisotropy of each sample.For purely topological anisotropy, manifest in practice as longitudinal corrugations, circumferential currents gave the lower losses. For largely compositional anisotropy, such as longitudinal welds or strips of degraded surface material, circumferential currents gave the greater losses. These results have been interpreted in terms of the surface current distribution in each case.     

Propagation of unipolar perturbations in hysteretic media with saturation of nonlinear losses

The propagation and evolution of unipolar perturbation pulses in hysteretic media with saturation of nonlinear losses have been theoretically studied. An exact analytical solution that describes the propagation and evolution of initially triangular pulses in these media has been obtained. Numerical and graphic analyses of the obtained solution are presented.     

Comparison of convective heat transfer models in porous media

A comparison of experimental data with theory has shown the applicability of both the one-temperature and the two-temperature models of convective heat transfer in porous media.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 60, No. 5, pp. 754–758, May, 1991.     

Behaviour of an edge dislocation in a semi-infinite solid with surface energy effects

The method of continuously distributed dislocations and the method of discrete distribution of dislocations have been used to determine the effect of surface energy on the surface boundary conditions of a semi-infinite solid containing an edge dislocation. The surface dislocation model which incorporates two surface dislocation arrays, the primary and the secondary, in order of importance, is used to study the effect of surface energy. The surface dislocation model in conjunction with the method of continuously distributed dislocations enables the exact determination of the dislocation distribution function of the primary and secondary dislocation arrays and the effect of surface energy tends to lower both the total Burgers vector associated with the surface arrays and dislocations in evaluating the effect of surface energy is illustrated and is compared with the method of continuously distributed dislocations. It has been found that the surface energy tends to lower both the total Burgers vector associated with the surface arrays and the length of the region within which they are spread on the surface. Although the effect on the primary surface arrays is not very large, the secondary surface arrays are completely eliminated with normal values of surface energy encountered in real solids. Thus, the effect of surface energy is to bring non-vanishing stress components to the surface. The surface is also non-uniformly stressed. The superiority of the surface dislocation model over the other methods hitherto used in the literature is illustrated.