Two bonded strips containing an infinite row of interface cracks

The plane strain problem of two bonded dissimilar isotropic elastic strips is considered. It is assumed that the composite strip contains an infinite row of interface cracks located symmetrically on the centerline. The case in which each of the cracks is opened out by the same constant pressure is discussed in detail and numerical results are reported for quantities of practical interest.     

The elastostatic problem of an infinite strip containing a periodic row of line cracks

The two dimensional problem of an infinite strip containing a periodic row of line cracks, each subjected to arbitrary but identical pressure distribution, is solved by superposing two solutions: the problem of a row of line cracks in an infinite medium and the solution of an infinite strip loaded at the edges. This procedure leads to a system of simultaneous integral equations. The solution is obtained by reduction of these equations into algebraic equations with the help of Fourier expansion of involved functions. An analytic expression for the stress-intensity factor is also derived. Boundary conditions are later modified to get the solution of the problem of an infinite sheet containing doubly periodic array of line cracks.     

The problem of internal cracks in an infinite strip having a circular hole

Summary. The elastostatic plane problem of an infinite strip having a circular hole and containing two symmetrically located internal cracks perpendicular to the boundary is formulated in terms of triply coupled integral equations. The solution of the problem is obtained for various crack geometries and for uniaxial tension applied to the strip away from the crack region. Quantities of physical interest are displayed in graphical forms.     

A laminate composite with an infinite row of parallel cracks normal to the interfaces

Under the assumption of plane strain, the distribution of stresses in a laminate composite due to the presence of an infinite row parallel cracks situated normal to the bond lines is obtained. Using an integral transform technique, the problem is reduced to that of solving a Fredholm integral equation of the second kind. The singular stress field near the tip of a crack is then derived. The effects on the stress intensity factor due to the presence of many cracks in a laminate-composite are illustrated graphically.     

Fracture of crystalline solids with an infinite row of collinear cracks as a result of plastic flow

The paper considers a fracture model consisting of an infinite row of collinear cracks formed as a result of plastic flow. Bullough-Gilman and Zener-Stroh type cracks are studied using an energy criterion. The results are compared with those for an isolated crack derived by Bullough. Numerical calculations in a first approximation shows good agreement with the experimental orientation dependence of the fracture stress of zinc single crystals by lleruyttere and Greenough.

---

Zusammenfassung Der Artikel betrachtet ein Bruchmodell, bei dem eine unendliche Reihe hintereinanderliegender Risse durch plastisches Fliessen verursacht wird. Unter Benutzung eines Energie-Kriteriums werden Brüche betrachtet, wie sie Bullough-Gilman and Zener-Strop angegeben haben. Die Ergebnisse werden mit denen verglichen, die von Bullough für einen isolierten Riss abgeleitet wurden. Numerische Abschätzung erster Näherung zeigt eine gute Übereinstimmung mit der experimentell von Deruyttere and Greenough erhaltenen Orientierungsabhängigkeit der Bruchspannung bei Zinkeinkristallen.

---

Résumé A partir d' un modèlle de fracture constitué d' une rangée infinie de fissures colinéaires résultant de la déformation plastique, on etudie des fissures de types Bullough-Gilman et Zener-Strop en utilisant un critère d'énergies Les résultats sont compares à ceux obtenus par Bullough pour une fissure isolée. Des calculs numeréques approchés sont en bon accord avec la dépendance en orientation de la contrainte de fracture de monocristaux de zinc, obtenue experimentalement par Deruytters et Greenough.

     

An approximate analysis of an internally loaded elastic plate containing an infinite row of closely spaced parallel cracks

The stress transfer which occurs in an internally loaded infinite elastic plate containing an array of closely spaced parallel cracks of finite width is examined. The internal loading corresponds to a doublet of concentrated forces which act at finite distances from the cracked region. The solution presented is approximate to the extent that the state of stress in the strip regions contained between adjacent cracks is considered to be one-dimensional. Such a simplification enables the derivation of certain general results for the stress distribution in a strip region contained within internally loaded half-planes of differing elastic characteristics. These solutions are obtained by Fourier transform methods. Attention is particularly focussed on the estimation of the stress magnification which occurs in the strip region.     

Theoretical stress analysis for a non-isotropic body of cylindrical configuration containing a row of cracks

A problem of stress analysis for a long circular cylinder has been dealt with in this paper by analytical methods. The cylinder is assumed to be made of an elastic material which is not isotropic but the elastic properties are considered to be similar in directions perpendicular to the axis of the cylinder. The body under consideration is supposed to contain an infinite row of penny-shaped cracks which are parallel to each other and located periodically along the cylinder-axis. All the cracks are assumed to be opened by the same distribution of internal pressure on their surfaces. By choosing appropriate potential functions the problem is treated mathematically through the use of integral equation approach. Numerical results for the stress-intensity factor, the strain energy and the critical pressure, obtained on the basis of the analysis are also given.     

Stress concentration of a cylindrical bar with a V-shaped circumferential groove under torsion, tension or bending

The stress concentration of a cylindrical bar with a V-shaped circumferential groove is analyzed by the body force method. The stress field due to a ring force in an infinite body is used to solve this problem. The solution is obtained by superposing the stress fields of ring forces in order to satisfy the given boundary conditions. The present results for semi-circular notches are in close agreement with Hasegawa's results. As a result of the systematic calculation of a 60° V-shaped notch, it is found that the stress concentration factors obtained by Neuber's trigonometric rule used currently have non-conservative errors of about 10% for a wide range of notch depths. The stress concentration factors are illustrated in charts so they can be used easily in design or research.     

Thermal stresses in a laminate composite with infinite row of parallel cracks normal to the interfaces

Under the assumption of plane strain, some linear thermoelastic problems concerning a laminate composite containing an infinite row of parallel cracks situated normal to the bond lines are solved by the use of integral transform technique. The thermal stresses are caused by a uniform heat flow disturbed by the presence of the cracks and the interfaces. The problem is reduced to that of solving a Fredholm integral equation of the second kind which is solved numerically by the use of Gaussian quadrature formulas. The effect of various quantities of physical interest on the stress intensity factor is shown graphically.Calculations are also carried out for the stress intensity factor for a laminate composite with a crack normal to the interfaces. This is accomplished by taking the limiting case of a laminate composite with an infinite row of parallel cracks normal to the interfaces.     

Three collinear cracks in an infinite elastic medium

The plane strain problem of determining the distribution of stress in the vicinity of three cracks embedded in an infinite isotropic elastic medium is considered. The cracks are collinear, the two side cracks are equal in length and located symmetrically with respect to the middle crack. The surface tractions acting on the cracks are completely arbitrary. Some special cases of the loading are discussed in detail.     

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.     

An infinite row of collinear cracks at the interface of two bonded dissimilar elastic half planes

The problem of determining the stress and displacement fields in the vicinity of an infinite row of collinear Griffith craks, located at the interface of two bonded dissimilar elastic half planes, when these cracks are subjected to internal pressure is considered. By making use of finite Fourier transforms the problem is reduced to a set of simultaneous dual series relations which in turn is shown to be equivalent to a Hilbert problem. In the special case of uniform internal pressure, closed formulae and some diagrams are given for the resulting shape of cracks and for the stresses in their neighborhood.     

Thermal stresses in an infinite non-isotropic plate having a penny-shaped crack

Of concern in the paper is the distribution of thermal stresses in the vicinity of a penny-shaped crack in a thick elastic plate made of a non-isotropic material. The problem pertains to the situation where the crack is opened by a prescribed normal pressure and a prescribed heat-flux or a prescribed temperature.     

An electro-magneto-thermo-visco-elastic problem in an infinite medium with a cylindrical hole

A magneto-thermo-visco-elastic problem of an infinite isotropic medium is considered in this problem. The analysis encompasses Lord–Shulman and Green–Lindsay theories of generalized thermo-elasticity to account for the finite velocity of heat equation. The problem is solved by taking Laplace transform techniques and the inversion of the Laplace transform is carried out using a numerical approach.