The elastic interaction of screw dislocations and a star crack with a central hole

The elastic interaction of screw dislocations and a star crack with a central hole was investigated. The complex potential of the present problem was obtained from that of an internal crack in an infinite medium using the conformal mapping technique. The stress field, image force and strain energy of dislocation, and stress intensity factor at the crack tip were derived. The critical stress intensity factor for dislocation emission was calculated based on the spontaneous dislocation emission criterion. The influence of the ratio of crack length to hole radius, crack number, and dislocation source on the above mechanical variables were studied. The present solution was reduced to several special cases previously reported in the literature.     

Edge dislocations near a cracked sliding interface

The edge dislocations near a cracked sliding interface were investigated. A continuous distribution of edge dislocations with Burgers vector along the y direction was used to simulate a crack of finite length along the sliding interface. From the dislocation distribution the stress field in the entire space was obtained. The stress intensity factors at both crack tips and image force on the edge dislocation were derived. The effects of the dislocation source and shear modulus ratio on both stress intensity factors and image force were also studied. Only mode I stress intensity factors at both tips were found in the composite materials with a sliding interface. The edge dislocations with Burgers vector along the y direction emitted from the crack always shield it to prevent propagation. The above results may reduce to an edge dislocation near a semi-infinite crack along a sliding interface including a sliding grain boundary. This revised version was published online in August 2006 with corrections to the Cover Date.     

Stress intensity factor for a Griffith crack interacting with a coated inclusion

Stress investigation for the interaction problem between a coated circular inclusion and a near-by line crack has been carried out. The crack and the coated inclusion (a coated fiber) are embedded in an infinitely extended isotropic matrix, with the crack being along the radial direction of the inclusion. Two loading conditions, namely, the tensile and shear loading ones are considered. During the solution procedure, the crack is treated as a continuous distribution of edge dislocations. By using the solution of an edge dislocation near a coated fiber as the Green's function, the problem is formulated into a set of singular integral equations which are solved by Erdogan and Gupta (1972) method. The expressions for the stress intensity factors of the crack are then obtained in terms of the asymptotic values of the dislocation density functions evaluated from the integral equations. Several numerical examples are given for various material and geometric parameters. The solutions obtained from the integral equations have been checked and confirmed by the finite element analysis results.     

Dislocation emission criterion for a wedge crack under mixed mode loading

Dislocation emission criterion for a wedge crack under mixed mode loading was investigated using Airy stress function. The order of singularity at the wedge crack tip due to remote loading was found to vary with the loading mode. The plastic zones for plane stress and plane strain were studied based on von Mises' and Tresca criteria. The dislocation emission criterion was examined for both loading modes. The mechanism of crack propagation was believed to be controlled by dislocation emission. Under an action of Mode I loading, the wedge tip movement occurred when a pair of edge dislocations of Burgers vectors be ⁱ and –be ^–i were emitted from the wedge tip where b and were the magnitude of Burgers vector and the angle between the positive x axis and the line connecting from the tip to dislocation. Similarly, under an action of Mode II loading, the wedge crack tip moved as soon as either an edge dislocation of Burgers vector along the x direction was emitted from its tip or a pair of edge dislocations of Burgers vectors be ⁱ and be ^–i were emitted from the wedge tip. The conventional mechanism of crack propagation based on the energy release rate was not expected to occur. The calculated results for a few special cases were presented and compared with those reported in the literature.     

The effect of material combinations and relative crack size to the stress intensity factors at the crack tip of a bi-material bonded strip

Several types of singular stress fields may appear at the corner where an interface between two bonded materials intersects a traction-free edge depending on the material combinations. Since the failure of the multi-layer systems often originates at the free-edge corner, the analysis of the edge interface crack is the most fundamental to simulate crack extension. In this study, the stress intensity factors for an edge interfacial crack in a bi-material bonded strip subjected to longitudinal tensile stress are evaluated for various combinations of materials using the finite element method. Then, the stress intensity factors are calculated systematically with varying the relative crack sizes from shallow to very deep cracks. Finally, the variations of stress intensity factors of a bi-material bonded strip are discussed with varying the relative crack size and material combinations. This investigation may contribute to a better understanding of the initiation and propagation of the interfacial cracks.     

Stress intensity solutions for the interaction between a hole edge crack and a line crack

The principle of superposition is used to solve the problem and the original problem is converted into two particular hole edge crack problems. The remote stresses are applied at infinity in the first problem. Meantime, a dislocation distribution is assumed outside the hole contour in the second problem. Singular integral equation is proposed for the solution of the second problem, in which the right hand side of the integral equation is obtained from the solution of the first problem. The first problem as well as the elementary solution of the second problem are solved by means of the rational mapping approach. Finally, numerical examples with the calculated results of stress intensity factors are presented.     

A study of the influence of grain boundaries on short crack growth during varying load using a dislocation technique

The propagation of short cracks in the neighbourhood of grain boundaries have been investigated using a technique were the crack is modelled by distributed dislocation dipoles and the plastic deformation is represented by discrete dislocations. Discrete dislocations are emitted from the crack tip as the crack grows. Dislocations can also nucleate at the grain boundaries. The influence on crack growth characteristics of the distance between the initial crack tip and the grain boundary has been studied. It was found that crack growth rate is strongly correlated to the dislocation pile-ups at the grain boundaries.     

Some applications of singular fields in the solution of crack problems

This paper reviews some recent developments in superposition methods for calculating linear elastic stress intensity factors and eigenvalues for cracks and notches, presents some new results for pairs of edge cracks and provides new insights into the nature of the errors in these processes. The procedure requires a numerical solution to the full cracked problem and a second solution on the same mesh using the known form of the singularity in an infinite region. This is equivalent to the well-known Subtraction of Singularity (SST) method. The advantages of this procedure over conventional SST are: (1) no modifications need to be made to a standard computer program; (2) multiple crack tips may be analysed without the difficulty of unknown rigid body displacements at the crack tips; (3) solutions with different boundary conditions on the same mesh may be obtained simply in one step by re-using one singular field solution; The singular crack tip field may also be studied independently leading to estimates of the eigenvalues and some insight into mesh-induced errors. The additional computational cost of a two-step procedure is minimal since the solution matrix from step one may be re-used with a new right-hand side. Numerical experiments using the boundary element method demonstrate the accuracy and simplicity of the superposition approach for notches, simple cracks, mixed-mode cracks, two edge cracks of different lengths and eigenvalues under various boundary conditions. © 1998 John Wiley & Sons, Ltd.     

On contact zone models for an electrically impermeable interface crack in a piezoelectric bimaterial

An electrically impermeable interface crack between two semi-infinite piezoelectric planes under remote mechanical tension-shear and electrical loading is studied. Assuming the stresses, strains and displacements are independent on the coordinate x ₂ the expressions for the elastic displacement and potential jumps as well as for the stresses and electrical displacement along the interface via a sectionally holomorphic vector function are found. Introducing an artificial contact zone at the right crack tip and assuming the materials possess the symmetry class 6 mm the problem is reduced for a wide range of bimaterial compounds to a combination of combined Dirichlet–Riemann and Hilbert boundary value problems which are solved analytically. From these solutions clear analytical expressions for characteristic mechanical and electrical parameters are derived. As particular cases of the above mentioned solution the classical (oscillating) and contact zone solutions are obtained. Further, a comparison with an associated solution for an electrically permeable crack has been performed. The fracture mechanical parameters for all models via the remote loads are found analytically and important relationships between these parameters are obtained. Due to these relationships an important algorithm of a numerical method applicable for the investigation of an interface crack in a finite sized piezoelectric bimaterial is suggested.     

Stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes

The stresses around a crack in an interfacial layer between two dissimilar elastic half-planes are obtained. The crack is parallel to the interfaces. The material constants of the layer vary continuously within a range from those of the upper half-plane to those of the lower half-plane. An internal gas pressure is applied to the surfaces of the crack. To derive the solution, the nonhomogeneous interfacial layer is divided into several homogeneous layers with different material properties. The boundary conditions are reduced to dual integral equations, which are solved by expanding the differences of the crack face displacements into a series. The unknown coefficients in the series are determined using the Schmidt method, and a stress intensity factor is calculated numerically for epoxy-aluminum composites.     

Shear loaded interface crack under the influence of friction: a finite difference solution

Formulation of the elastic two‐dimensional problem of contact with friction is presented. Two‐dimensional equilibrium equations and boundary conditions in an orthogonal curvilinear co‐ordinate system are written explicitly. The above formulation is solved with the aid of the finite difference technique. An iterative algorithm which does not require load increments is employed for solving interface fracture problems with contact and friction subjected to a monotonically increasing load. The J‐integral is extended for problems in which there is friction along the crack faces. Stress intensity factors are calculated by means of the J‐integral, as well as an asymptotic expansion of the tangential shift. Two problems are analysed: (1) a crack in homogeneous material in the presence of friction involving stationary contact; and (2) an interface crack in the presence of friction involving receding contact. Results are compared to those found by analytical and semi‐analytical methods which are presented in the literature, as well as to those obtained by means of the finite element method. The accuracy of the results establishes the reliability of the finite difference analysis, as well as the post‐processors. In addition, a problem involving stick conditions is considered. It is observed that with increasing friction, the normal gaps and tangential shifts decrease. The size of the contact zone increases and values of the stress intensity factor decrease. Copyright © 2004 John Wiley & Sons, Ltd.     

A dislocation and point force approach to the boundary element method for mixed mode crack analysis of plane anisotropic solids

Abstract

This study investigates the feasibility of enhancing steam‐driven ejector performance. Initially, a one‐dimensional ejector theory is used to examine the effects on ejector performance of three isentropic efficiencies: nozzle efficiency η_m , mixing efficiency η_m, and diffuser efficiency η_m . Theoretical analysis demonstrates that mixing efficiency profoundly affects ejector performance, but that the other two efficiencies have slightly influenced ejector performance. This finding suggests that efficient mixing can promote ejector performance. This study also attempts to improve mixing efficiency using a petal nozzle. The behavior and characteristics of a petal nozzle are investigated by testing the nozzle under various operating conditions, i.e. primary pressure, secondary pressure, and back pressure. In addition, the study compares the experimental and theoretical results. These results prove that using a petal nozzle can improve ejector performance. The shadowgraph method was used to visualize the inner flow field of an ejector. The flow patterns observed should help to further improve ejector performance.     

The interaction of mode I crack with multi-inclusions in a three-phase model

An approximately close form solution has been developed for mode I crack interacting with multi-inclusions in composite materials. The crack-tip stress intensity factor is evaluated in a three-phase model, which combines the present knowledge that the inclusions only in the immediate neighborhood of the crack-tip have strong effect on the stress intensity factor and that the far inclusions have an overall effects which can be estimated by effective properties of the composites. As validated by numerical examples, the solution has good accuracy for a wide range of the modulus ratios between the inclusion and matrix material.     

BEM for crack‐inclusion problems of plane thermopiezoelectric solids

The problem of interactions between an inclusion and multiple cracks in a thermopiezoelectric solid is considered by boundary element method (BEM) in this paper. First of all, a BEM for the crack–inclusion problem is developed by way of potential variational principle, the concept of dislocation, and Green's function. In the BE model, the continuity condition of the interface between inclusion and matrix is satisfied, a priori, by the Green's function, and not involved in the boundary element equations. This is then followed by expressing the stress and electric displacement (SED) and elastic displacements and electric potential (EDEP) in terms of polynomials of complex variables ξ_t and ξ_k in the transformed ξ‐plane in order to simulate SED intensity factors by the BEM. The least‐squares method incorporating the BE formulation can, then, be used to calculate SED intensity factors directly. Numerical results for a piezoelectric plate with one inclusion and a crack are presented to illustrate the application of the proposed formulation. Copyright © 2000 John Wiley & Sons, Ltd.     

Elastodynamic stress intensity factors for a semi-infinite crack due to three-dimensional concentrated shear loadings on the crack faces

The dynamic stress intensity factors for a semi-infinite crack in an otherwise unbounded elastic body is investigated. The crack is subjected to a pair of suddenly-applied shear point loads on its faces at a distance l away from the crack tip. This problem is treated as the superposition of two problems. The first problem considers the disturbance by a concentrated shear force acting on the surface of an elastic half space, while the second problem discusses a half space with its surface subjected to the negative of the tangential surface displacements induced by the first problem in the front of the crack edge. A fundamental problem is proposed and solved by means of integral transforms together with the application of the Wiener–Hopf technique and Cagniard–de Hoop method. Exact expressions are then derived for the mode II and III dynamic stress intensity factors by taking integration over the fundamental solution. Some features of the solutions are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

A time‐dependent formulation of dual boundary element method for 3D dynamic crack problems

In this paper, the dual boundary element method in time domain is developed for three‐dimensional dynamic crack problems. The boundary integral equations for displacement and traction in time domain are presented. By using the displacement equation and traction equation on crack surfaces, the discontinuity displacement on the crack can be determined. The integral equations are solved numerically by a time‐stepping technique with quadratic boundary elements. The dynamic stress intensity factors are calculated from the crack opening displacement. Several examples are presented to demonstrate the accuracy of this method. Copyright © 1999 John Wiley & Sons, Ltd     

Thermoelasticity for the analysis of crack tip stress fields — a review

A comprehensive review is given of methods to determine the stress intensity factor at crack tips using thermoelastic stress analysis. In order to obtain accurate results a number of areas of experimental procedure need to be considered and these are discussed in detail. The paper concludes with a discussion on the future potential of the use of thermoelasticity for the analysis of cracks.     

The impact response of a half plane crack in a transversely isotropic solid due to 3-D mixed mode loading

Three-dimensional analysis of a half plane crack in a transversely isotropic solid is performed. The crack is subjected to two opposed pairs of shear line loads on its faces. Transform methods are used to reduce the boundary value problem to a set of coupled integral equations that can be solved by the Wiener-Hopf technique. The Cagniard-de Hoop method is employed to invert the transforms. Exact expressions are derived for the mode II and III stress intensity factors as functions of time and position along the crack edge. Some features of the solutions are discussed through numerical results.     

Axisymmetric crack terminating at the interface of transversely isotropic dissimilar media

In this paper, the axisymmetric elasticity problem of an infinitely long transversely isotropic solid cylinder imbedded in a transversely isotropic medium is considered. The cylinder contains an annular or a penny shaped crack subjected to uniform pressure on its surfaces. It is assumed that the cylinder is perfectly bonded to the medium. A singular integral equation of the first kind (whose unknown is the derivative of crack surface displacement) is derived by using Fourier and Hankel transforms. By performing an asymptotic analysis of the Fredholm kernel, the generalized Cauchy kernel associated with the case of `crack terminating at the interface' is derived. The stress singularity associated with this case is obtained. The singular integral equation is solved numerically for sample cases. Stress intensity factors are given for various crack geometries (internal annular and penny-shaped cracks, annular cracks and penny-shaped cracks terminating at the interface) for sample material pairs.