Torsion of an elastic medium containing a nanosized penny-shaped crack with surface effects

International Journal of Fracture - Theoretical and experimental studies have revealed that at small length scales, surface effects contribute significantly to overall elastic deformation. In this...     

Thermal stresses near a penny-shaped crack in an elastic sphere embedded in an infinite elastic space

This paper gives an analysis of the distribution of thermal stresses in a sphere which is bonded to an infinite elastic medium. The thermal and the elastic properties of the sphere and the elastic infinite medium are assumed to be different. The penny-shaped crack lies on the diametral plane of the sphere and the centre of the crack is the centre of the sphere. By making a suitable representation of the temperature function, the heat conduction problem is reduced to the solution of a Fredholm integral equation of the second kind. Using suitable solution of the thermoelastic displacement differential equation, the problem is then reduced to the solution of a Fredholm integral equation, in which the solution of the earlier integral equation arising from heat conduction problem occurs as a known function. Numerical solutions of these two Fredholm integral equations are obtained. These solutions are used to evaluate numerical values for the stress intensity factors. These values are displayed graphically.     

Antiplane vibration of an elastic layer with a midplane crack

The oscillations of an elastic layer excited by antiplane tractions of uniform intensity along the faces of a midplane crack are investigated. A singular integral equation is derived and solved numerically by Gauss-Chebyshev integration technique. The stress intensity factor and crack surface response are computed as functions of frequency and layer thickness-to-crack length ratio, and the resonant frequencies of the cracked layer are determined.     

Green’s functions for the periodic four-phase elastic space with an interface crack or a linear rigid inclusion

We construct fundamental solutions of the problem of antiplane deformation of an unbounded composite body with interface cut or a linear rigid inclusion subjected to the action of concentrated forces. The periodic cell of the composite contains four different elements with rectangular cross sections. The problem is studied by the method of homogenization with microlocal parameters. The formulas for the stress intensity factors are obtained in the analytic form and investigated. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 2, pp. 25–32, March–April, 2007.     

Torsion of a semifinite nonuniform cylinder with a crack

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 4, pp. 75–80, July–August, 1990.     

On solutions of crack surface opening displacement of a penny-shaped crack in an elastic cylinder subject to tensile loading

A simple analytical expression for the surface displacement of a penny-shaped crack in an elastic cylinder subject to remote tensile loading is proposed based on a modified shear-lag model. The results are then compared with the dilute solution [1] and those of finite element calculation. It is found that the present work gives much better result than the dilute model.     

Twisting of an elastic plate containing a crack

The stress distribution caused by twisting an infinite plate containing a finite crack is analyzed in terms of Reissner's theory for the bending of thin plates. The singular character and the detailed structure of the stresses near the ends of the crack are determined in closed form. Numerical results are given for the magnitudes of the stress couples and stress resultants for a range of plate thicknesses.

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Zusammenfassung Due Spannungsvertcilung, hervorgerufen durch die Torsion einer unendlichen Platte mit einem Ri\ begrenzter Länge, wird mit Hilfe der Reissner-Theorie für die Biegebeanspruchung dünner Platten untersucht. Der singulare Charakter und die genauc Verteilung der Spannungen in Nähe der Ri\enden werden bestimmt. Zahlenmä\ige Ergebenisse für die Gro\e der Spannungsparre und ihrer Resultanten werden für eine Reihe von Plattenstärken angegeben.

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Résumé La distribution des contraintes dans une plague infinie comportant une fisure finic et soumise à torsion est analysée au moyen de la théorie de Reissner pour la flexion des tôles minces.Le caractère singulier, et la structure de détail des contraintes au voisinage des extrémités de la fisure sont explicités.Des résultats numériques sont fournis en ce qui regarde les grandeurs des couples de contraintes et de leurs résultantes, pour une certaine gamme d'éspaisseur de tôles.

     

Partially stiffened elastic half-plane with an edge crack

A technique, using the Brazilian disk specimen, for measuring the fracture toughness of unidirectional fiber-reinforced composites, over the entire range of crack-tip mode mixities, was developed. The fracture toughness of a graphite/epoxy fiber-reinforced composite was measured, under both mode-I and mode-II loading conditions. We found that for certain material orientations the mode-II fracture toughness is substantially higher than the mode-I toughness. The complete dependence of the fracture toughness on the crack-tip mixity was determined for particular material orientations and the phenomenological fracture toughness curves were constructed. Using the Brazilian disk specimen, together with a hydraulic testing machine, the fracture toughness of the composite under moderate loading rates was measured. We observed that the mode-I fracture toughness was not sensitive to the loading rate at the crack tip, K, while the mode-II ‘dynamic’ fracture toughness increased approximately 50 percent over the quasi-static fracture toughness. A qualitative explanation of the dependency of fracture toughness on crack-tip loading rate is discussed. Finally, a mechanical fracture criterion, at the microscopic level, which governs the crack initiation under mixed-mode loading conditions is presented; these theoretical predictions closely follow the trend of experimental measurements. This revised version was published online in August 2006 with corrections to the Cover Date.     

Torsion of an infinite composite elastic cylindrical shell

Summary The problem considered is that of the torsion of a semi-infinite composite elastic cylindrical shell composed of two materials of different rigidity modulus. It is assumed that there is perfect bonding at the common cylindrical surface. The problem is solved by means of the use of Fourier transforms.     

Edge crack in a strip of an elastic solid

The problem of determining the distribution of stress and the deformation of a long strip of an elastic material, damaged by a crack normal to an edge of the strip, is investigated. The strip is deformed by pressure applied to the faces of the crack. The stress intensity factor is calculated and its variation with the depth of the crack, relative to the width of the strip, in the special case of uniform pressure, is illustrated.     

Three-dimensional elastic stress analysis of a fracture specimen with an edge crack

A numerical stress analysis of an elastic three-dimensional specimen similar to the compact tension specimen used in fracture investigations is presented. The numerical results are achieved using singular integral equations which are analogous to Green's boundary formula in potential theory. The analysis yields details of the stresses near the crack tip and clearly shows their three-dimensional character. Some results are also given to indicate the influence of thickness and Poisson's ratio on the stresses.

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Zusammenfassung Es wird für eine dreidimensionale elastische Probe, ähnlich der kompakten Zugprobe für Bruchuntersuchungen, eine zahlenmässige Analyse der Spannungen dargelegt. Die numerischen Ergebnisse wurden über singulare Integralgleichungen analog den Greenschen Formeln in der Potentialtheorie ermittelt. Die Untersuchung ergibt Einzelheiten über die Spannungen in der Umgebung der Rißspitze und zeigt klar deren dreidimensionalen Charakter. Es werden auch einige Resultate mitgeteilt die den Einfluß der Dicke und des Poissonschen Moduls auf die Spannungen herausstellen.

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Résumé On présente une analyse numérique des contraintes dans une éprouvette à trois dimensions en sollicitation dans le domaine élastique, éprouvette similaire à l'éprouvette de traction utilisée dans les études de mécanique de rupture.Les résultats numériques sont obtenus en recourant à des équations à intégrales singulières, qui sont analogues à l'équation aux limites de Green dans la théorie du potentiel.L'analyse conduit à fournir la distribution complète des contraintes au voisinage de l'éxtremité de la fissure et démontre clairement le caractère tridimensionnel de celle-ci.L'influence de l'épaisseur et du module de Poisson sur les contraintes est également dégagée de certains résultats qui ont été obtenus.

     

Energy analysis of crack interaction with an elastic inclusion

This paper gives an energy analysis of an elastic solid with a crack which penetrates an elastic inclusion. The purpose of our work is to evaluate the energy release rates (ERR) associated with crack tip extension while the inclusion is stationary, and to evaluate the ERR due to inclusion translation, rotation and expansion with respect to the crack tip. Reduction and increase in the crack ERR caused by an inclusion (shielding and amplification effects of the inclusion) are expressed in terms of the inclusion elastic properties normalized by Young's modulus of the bulk material. The variation in ERR as a crack approaches and passes through a circular inclusion is also examined.     

Interactions of a sub-surface crack with a center of dilatation in an elastic half-plane

This paper examines the interaction between a crack parallel to the free surface of an elastic half-plane and an internal center of dilatation. The problem is decomposed into two auxiliary problems. When the center of dilatation approaches the crack tip, two kinds of singularity are analytically obtained. If the overburden stress and the friction on crack surface are neglected, both modes I and II stress intensity factors (K_I and K_II) are induced at the crack tips. The maximum of K_I and K_II occurs when the center of dilatation is located in front of the crack tips. The tensile cracking is likely to be prohibited by the overburden stress, while shear cracking remains possible even including the effects of both overburden and friction on the crack surface.     

Surface-breaking crack in an elastic half-space

A semi-infinite crack terminating at the boundary of an elastic half-space is considered. It is assumed that the crack is subjected to a mode-I load applied in a finite region remote from the crack plane, and the boundary of the half-space and the crack surfaces are free of tractions. The problem is formulated in terms of a hypersingular integral equation with respect to the relative crack-face separation defined over the region occupied by the crack. The behaviour of the solution near the corner point where the crack edge intersects the boundary is analysed and results which show the dependence of the stress singularity exponent on the angle of inclination of the crack edge are presented.     

Torsion of an elastic layer by two circular dies

Two circular discs of rigid material and of different radii are bonded to the opposite faces of an infinite elastic layer. The torques T₁ and T₂ have been calculated when the discs are rotated through different angles.     

Dependence of a crack growth path on the elastic moduli of an anisotropic solid

One of the ways to increase the resistance of a structure to catastrophic fracture is to force a main line crack to deviate from its path. For this reason the influence of the elastic moduli of an anisotropic material on crack rotation are studied. In particular a linear elastic problem for a straight Mode I crack, located on a symmetry axis of an orthotropic plane is considered. The strength properties of the material are assumed to be isotropic. Several crack models are considered for studying the direction of a crack growth path. It is shown that a crack modeled as a thin, elongated, elliptical hole leads to more plausible results concerning crack rotation conditions than an ideal cut model. The maximal tensile stresses are taken as a crack growth criterion. It is shown that for a class of orthotropic materials a crack deviates from the straight path just after it starts to grow, even in the conditions of uniaxial normal tension. The problem of the stability of a straight crack path under Mode I loadings is also considered. This problem is reduced to the problem of the fracture direction determination for thin, elongated, elliptical cavities slightly inclined to the initial direction. The conditions of instability are obtained within the framework of the proposed approach. It is shown that for a class of orthotropic materials a straight crack path is unstable in the conditions of uniaxial normal tension. This class of materials is larger than the one for which a crack deviates from the straight crack path just after its start.