Torsional impact response of a penny-shaped crack lying on a bimaterial interface

The torsional impact response of a penny-shaped crack lying on a bimaterial interface is considered in this study. Laplace and Hankel transforms are used to reduce the problem to the solution of a pair of dual integral equations. The solution to the dual integral equations is expressed in terms of a Fredholm integral equation of the second kind with a finite integral kernel. A numerical Laplace inversion routine is used to recover the time dependence of the solution. The dynamic stress intensity factor is determined and its dependence on time and material constants is discussed.     

Stress fields around a crack lying parallel to a free surface

A method of stress analysis for a two dimensional crack, which is subjected to internal gas pressure, and situated parallel to a free surface of a material, is presented. It is based on the concept of continuously distributed edge dislocations of two kinds, i.e. one with Burgers vector normal to the free surface and the other with Burgers vector parallel to it.Stress fields of individual dislocations are chosen so as to satisfy stress free boundary conditions at the free surface, by taking account of image dislocations. Distributions of both kinds of dislocations in the crack are derived so as to give the internal gas pressure and, at the same time, to satisfy shear stress free boundary conditions on the crack surface. Stress fields _xx, _yy and _xy in the sub-surface layer are then determined from them. They have square root singularities at the crack-up.

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Résumé On présente un méthode d'analyse de contrainte dans le cas d'une fissure bidimensionnelle soumise à la pression d'un gaz interne et située parallèlement à une surface libre d'un matériau. La méthode est basée sur un concept de dislocation-coin distribuée de manière continue et de deux types, c'est-à-dire l'une présentant un vecteur de Burgers normal à la surface libre et l'autre comportant un vecteur de Burgers parallèle à cette surface libre.On choisit le champ de contrainte de dislocations individuelles de telle manière qu'il satisfasse à des conditions de frontières libres de contrainte à la surface libre et en tenant compte des dislocations images. On en tire les distributions des deux types de dislocation dans la fissure de manière à fournir la pression interne des gaz et, dans le même temps, à satisfaire les conditions d'absence de contraintes de cisaillement aux frontières, sur la surface de la fissure. On en détermine les champs de contrainte et dans la couche subsuperficielle. Ces champs présentent des singularités d'ordre 1/2 à la face supérieure de la fissure.

     

Optimization of a circular thin-film piezoelectric actuator lying on a clamped multilayered elastic plate

A system consisting of a circular multilayered thin-film elastic plate and a piezoelectric actuator, which is generally used for ultrasound generation in air, is studied in this paper. Effects of the electrode dimension of a circular thinfilm piezoelectric actuator lying on a clamped multilayered elastic plate are discussed theoretically, while the first-order theory of asymmetrically laminated piezoelectric plates with consideration of coupled extension and flexure of the reference plane is used. Numerical results show that the deflection of the elastic plate can be optimized by adjusting the radius of the top electrode.     

Kinked crack in a bending trapezoidal plate

The interaction problem of a kinked crack and the edges of a bending trapezoidal plate which takes the effects of transverse shear deformation into account is presented. The research method is based upon the complex potential technique of Muskhelishvili using conformal mapping. Furthermore, for the analysis of the moment intensities at the tips of the kinked crack, the concept of dislocation distribution is applied. The integral equations for the stress disturbance problem along the line that is the presumed location of the kinked crack are then obtained as a system of singular integral equations with simple Cauchy kernels. As a consequence, the variation of moment intensity factors at the crack-tips is also illustrated.     

A note on the problem of edge crack in a semi-circular plate

International Journal of Fracture -     

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.

     

Study on crack propagation behavior in a quenched glass plate

Crack pattern transition and crack propagation behavior in a quenched glass plate are investigated. Theoretical analysis indicates that the distance between the crack tip and the cold front is closely related to the crack pattern transition. This theoretical result is examined experimentally using instantaneous phase-stepping photoelasticity. As expected theoretically, when the crack tip remains close enough to the cold front, crack propagation remains straight. When this distance reaches a given value, the crack oscillates. These experimental results are in good agreement with the theory of crack pattern transition. Therefore, present theoretical analysis is valid in predicting the instability of crack propagation. The crack tip stress field is also examined by the present experimental method. In particular, in the oscillating regime, the mode-I stress intensity factor frequently becomes larger than the fracture toughness, and the mode-II stress intensity factor has a nonzero value during propagation. For the former result, some reasons are discussed, but the cause of this problem is still unknown. However, the latter result can be explained by the theoretical analysis of an infinitesimal kinked edge crack just after crack initiation.     

Dynamic crack response to a localized shear pulse perturbation in brittle amorphous materials: on crack surface roughening

Linear Elastic Fracture Mechanics (LEFM) provides a coherent framework to evaluate quantitatively the energy flux released at the tip of a growing crack. However, the way in which the crack chooses its path in response to this energy flux remains far from completely understood: the growing crack creates a structure on its own as conveyed by crack surface roughening even in brittle amorphous materials such as glass. We report here experiments designed to uncover the primary cause of surface roughening in brittle amorphous materials. Therefore, we investigate the response of a growing crack to local perturbation introduced as a shear wave pulse of controlled duration, amplitude, frequency and polarization. This pulse is shown to induce a local mode III perturbation in the loading of the crack front, which makes it twist locally, without fragmenting. This response is linear both in amplitude and frequency with respect to the perturbation, and disappears with it. We also show that shear wave pulses are emitted when the propagating crack encounters the heterogeneity. Implications of these observations for possible sources of roughening are finally discussed.     

State of stress in a patched plate containing a crack

Summary The state of stress and strain is examined for a plate containing a curvilinear crack reinforced by a finite patch. The elastic patch covers the crack completely and is rigidly connected to the infinite plate only along its edge. It is assumed that the plate and patch are in a general state of planar strain. The boundary-value problem is reduced to a system of three singular integral equations, which is solved by mechanical quadrature. Numerical results are given for a plate containing a crack in the form of an arc of a parabola and reinforced with an elliptical patch for various orientations of the tensile forces at infinity. The stress intensity coefficients at the crack vertices have been calculated along with the contact forces at the junction.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 27, No. 4, pp. 33–40, July–August, 1991.     

CTOD for the through-the-thickness crack in a plate of arbitrary thickness

The sectional thickness of plate-like components has a significant influence on the fatigue and fracture properties. This effect is primarily due to the differences in the through-the-thickness stresses prevailing at the tip of a crack in a finite-thickness plate or shell. Characterization of this effect to date has remained largely empirical. The current paper presents new analytical results for CTOD for the through-the-thickness crack in infinite plates with various thicknesses. These results are based on a recently developed solution for an edge dislocation in infinite plate of arbitrary thickness. The analytical predictions of the CTOD and the constraint factor are compared with the three-dimensional FE results. It is shown that the analytical and the numerical results are in good agreement when the numerical calculations are not affected by the size of the FE mesh and by the boundaries of the FE model.     

A crack originating from a triangular notch on a rim of a semi-infinite plate

Stress analysis of a semi-infinite plate with a triangular notch and a crack originating from a triangular notch are carried out. Muskhelishvili's method is used for stress analysis and rational mapping functions of a sum of fractional expressions are used. The obtained solution is exact for the shape represented by the rational mapping function and is in the closed form. Stress distributions and stress intensity factors for some angles of a notch and crack length are analytically calculated and investigated. An approximate expression of the stress intensity factor is presented.     

On the dynamic propagation of a griffith crack in a finite rectangular plate

A preliminary analysis of crack initiation and dynamic crack propagation of a Griffith crack in a finite rectangular plate is performed. The problem is simulated using an improved two-dimensional finite difference code—the SMF2D code—thus yielding more accurate and reliable results. The results are then presented and discussed.