Energy release rate calculations for an interface mode III edge crack based on a conservation integral

The M-integral is applied to the calculation of energy release races for interface edge cracks of the Mode III type. Specifically, for an edge crack along the interface between two elastic wedges of different opening angles and dissimilar elastic properties, and that is subjected to point loads at the apex, a relation is derived among the length of the crack, the energy release race of the crack, the applied loads, the wedge angles and the material parameters.     

Stress singularities in composite materials with an arbitrarily oriented crack meeting an interface

The plane, bending and antiplane strain elastostatic problems for two bonded half planes containing an arbitrarily oriented semi-infinite crack meeting the interface, are examined. A simple analogy between the interfacial continuity conditions for the plane and bending problems is derived and its implications are discussed. Using the eigenfunction-expansion method the crack tip stress singularities for various crack orientations and material combinations are compared for the three problems. It is shown that, under certain conditions, singularities are no longer present in the stress field. In the case of the antiplane strain problem subsequent paths of crack propagation are predicted.

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Résumé On examine des problèmes élasto-statiques en déformation plane, de flexion, et antiplanaire rencontrés dans deux demi-plans solidaires comportant, dans leur interface, une fissure semi-infinie orientée arbitrairement. On tire une analogie simple entre les conditions de continuité et interfaciales qui se présentent dans le cas des problèmes plans et flexionnels; ses implications sont discutées. En utilisant une méthode d'expansion d'une eigenfonction, on peut comparer les singularités de contraintes aux extrémités de la fissure, pour diverses orientations de la fissure et de combinaisons de matériaux différents. On montre que, sous certaines conditions, le champ de contraintes peut ne plus présenter de singularités. On peut par ailleurs prédire les chemins de la propagation d'une fissure dans le cas d'une déformation antiplanaire.

     

A new conservation integral for an arbitrarily kinked interfacial crack

A new conservation integral consisting of the path and area integral, for an arbitrarily kinked interfacial crack is proposed. The new conservation integral is shown to have the physical meaning of the energy release rate. We present two numerical examples to verify its usefulness; one is the problem of an interfacial crack with a parabolic-curved kink, and the other is the problem of a circular arc-shaped interfacial crack with a straight kink.     

An interface integral equation method applied to a crack impinging upon a bimaterial,frictional interface

A crack impinging upon a frictional, bimaterial interface is studied theoretically. Specifically we consider the problem of an infinitely long, cracked, two-dimensional fiber, which is embedded in an infinite plane with distinct elastic properties. The composite is subjected to tensile loading parallel to the fiber. An interface integral equation method is developed to solve this problem. This method, involving to-be-determined distributions of line forces, reduces the specific problem considered here to four coupled integral equations which are solved numerically. The bimaterial effect appears to be significant with respect to the length of the slip zone along the interface and the interfacial shear stress. However, the blunting of the crack by the frictional interface is virtually independent of the bimaterial effect.     

Stress singularities in a periodically layered composite near interface crack tips

The paper deals with the asymptotic analysis of stresses near interface crack tips in the periodically two-layered elastic composites. The problem is investigated for the plane state of strain within the framework of the homogenized model with microlocal parameters. The angular dependence of stresses at the crack tip is presented for different mechanical and geometrical properties of the composite.     

The singular function boundary integral method for biharmonic problems with crack singularities

We use the singular function boundary integral method (SFBIM) to solve two model fracture problems on the plane. In the SFBIM, the solution is approximated by the leading terms of the local asymptotic solution expansion, which are also used to weight the governing biharmonic equation in the Galerkin sense. The discretized equations are reduced to boundary integrals by means of the divergence theorem and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multipliers. The main advantage of the method is that the leading stress intensity factors (SIFs) are calculated directly together with the Lagrange multipliers, i.e. no post-processing of the numerical solution is necessary. The numerical results for the two model problems show the fast convergence of the method and compare well with those of the collocation Trefftz method.     

Reinitiation of a crack reaching an interface

We consider here a bi-material made of two layers bonded together by an interface. The specimen is loaded in tension parallel to the interface and the existence of a mode I crack is assumed. The crack initiated in just one layer reaches the interface normally. We then study the second of the two possible cases: the crack crosses the interface and goes straight into the second layer, in mode I also; or the crack debonds the interface before reinitiating in the second layer at the debond tip.In the present study the conditions of the reinitiation of the crack in the second layer after debonding of the interface are presented. The maximum debond distance is calculated by means of a Shear Lag analysis associated with a damage constitutive equation.Qualitative rules for design are pointed out to make the interface a location of crack arrest or at least of crack growth delay. These rules are mainly: small thickness of the possibly cracked layer, strong interface and tough substrate.     

The interaction of a crack with an interface crack as a theoretical model for debonding

A complex integral equation has been derived which describes the interaction of a crack with an interface crack as well as the limiting case of a kinked interface crack. With the help of this solution a model of the debonding process has been set up. Critical ratios of the energy release rates of the interface and the matrix material have been calculated for three different material combinations. These values can be used as estimates for interface design.     

Thermal crack problems for a bimaterial with an interface crack and internal defects subjected to a heat source

The interaction between internal defects and an interface crack in a bimaterial subjected to a thermal load, in particular a heat source, is examined. Attention is focused on the construction of the associated integral equations.     

Thermal crack problems for a bimaterial with an interface crack and internal defects subjected to a heat source

The interaction between internal defects and an interface crack in a bimaterial subjected to a thermal load, in particular a heat source, is examined. Attention is focused on the construction of the associated integral equations.     

Interaction between an interface crack and a parallel subinterface crack

In this paper, the pseudo-traction method addressed thoroughly in homogeneous cases is combined with the edge dislocation method to solve the interaction problem of an interface crack with a parallel subinterface crack. After deriving the fundamental solutions for a typical interface crack loaded by the normal and tangential concentrated tractions on both crack surfaces and the fundamental solutions for an edge dislocation beneath the interface, the interaction problem is reduced to a system of singular integral equations which can be solved numerically with the aid of the Chebyshev polynomial technique. Numerical results for the stress intensity factors are shown in the figures in which six kinds of material combinations presented by Hutchinson et al. [1] are considered.     

Application of conservation integrals to interfacial crack problems

Properties of the J, L and M integrals, proposed by Knowles and Sternberg for homogeneous materials are explored here for bi-material interfaces. The integrals are shown to satisfy the conservation law under certain conditions on the interfaces. Relations between the stress intensity factors and the conservation integrals for interfacial cracks in isotropic, linear-elastic materials are derived. The conservation integrals for some interfacial cracks are applied to get the stress intensity factors in a very simple way without solving the complicated boundary value problems. For interfacial cracks in finite-sized medium some numerical computations are carried out to verify the usefulness of the conservation integrals.     

Stress singularities for crack normal to and terminating at bimaterial interface on orthotropic half-plates

The problem of a crack normal to and terminating at an interface in two joined orthotropic plates is considered and the eigenequation for the asymptotic behavior of stresses at the crack tip on the interface is given in an explicit form. It is found that the singular stress field around the crack tip can be separated into two independent fields, respectively of the mode I and II. Also it is found that for both the mode I and II deformations the effects of elastic constants on the stress singularity order can be respectively expressed by three material parameters, two of which are the same for both the mode I and mode II deformations.     

Stress solution for a crack at an arbitrary angle to an interface

Two-dimensional elasticity solution and the stress intensity factors are determined for a finite crack in one of the materials of a bimaterial composite. The crack has an arbitrary orientation and distance from the straight interface. The solution for general stress boundary conditions on the crack surface is presented in the form of coupled Fredholm integral equations of the second kind. Numerical values of the stress intensity factors are computed for various crack orientations, distances from the interface, and different combinations of material properties when the boundary conditions are uniform pressure and uniform shear stress.     

Contour integral method for stress intensity factors of interface crack

A general Betti's reciprocal work theorem with interface cracks of a bimaterial is established in this paper, and a path independent contour integral method for the stress intensity factor (SIF) of the interface crack was obtained. When the stress and displacement fields in a specimen are calculated by the finite element method, the SIF K _I and K _II of interface cracks can be obtained immediately by a contour integral. Some solutions of interesting examples, such as two collinear interface cracks, are also given.Presented at the Far East Fracture Group (FEFG) International Symposium on Fracture and Strength of Solids, 4–7 July 1994 in Xi'an China.     

Applications of conservation integral to indentation with a rigid punch

When a substrate of the brittle material is indented by a relatively rigid, square-ended punch, a singular stress field and K-dominant region will arise at the near-surface adjacent to the punch corners. The singularity of this stress field is identical with the mode I crack. The stress intensity factor in this case represents the intensification of the stress fields induced by indentation. In present article, a new method to determine the stress intensity factors of the indentation problems is developed based on the conservation law. The physical meanings of the proposed method and some numerical analysis have been investigated.     

Orthogonal crack approaching an interface

We consider the problem of a tensile crack approaching a sliding interface in the direction normal to it in an attempt to find the mechanisms that control the crack offset. The crack in a plane free of loading is driven by uniform load applied to its faces. The interface is assumed to have no resistance to opening. The common conception is that as the crack approaches the interface it creates a zone of opening. When the crack touches the interface this opening zone eventually arrests the crack such that the continuation of the crack growth through the interface is only possible from an offset position. Our computer simulations conducted for frictionless interface and supported by a simple analytical model show that the situation is more complex. As the crack tip gets close, the zone of opening shrinks and the opening displacement increases. After the crack tip touches the interface, the opening zone disappears. Frictionless interface produces concentration of this stress only at the ends of the interface which physically corresponds to the points where sliding is artificially arrested.