Thermal fracture analysis of a functionally graded orthotropic strip with a crack

This paper is concerned with the thermal fracture problem of a functionally graded orthotropic strip, where the crack is situated parallel to the free edges. All the material properties are assumed to be dependent only on the coordinate y (perpendicular to the crack surfaces). By using Fourier transform, the thermoelastic problem is reduced to those that involve a system of singular integral equations. Numerical results are presented to show the effects of the crack position and the material distribution on the thermal stress intensity factors.     

Transient analysis of a piezoelectric strip with a permeable crack under anti-plane impact loads

The problem of a through permeable crack situated in the mid-plane of a piezoelectric strip is considered under anti-plane impact loads for two cases. The first is that the strip boundaries are free of stresses and of electric displacements, and the second is that the strip boundaries are clamped rigid electrodes. The method adopted is to reduce the mixed initial-boundary value problem, by using integral transform techniques, to dual integral equations, which are further transformed into a Fredholm integral equation of the second kind by introducing an auxiliary function. The dynamic stress intensity factor and energy release rate in the Laplace transform domain are obtained in explicit form in terms of the auxiliary function. Some numerical results for the dynamic stress intensity factor are presented graphically in the physical space by using numerical techniques for solving the resulting Fredholm integral equation and inverting Laplace transform.     

Finite strip with a central crack under tension

In this study, a symmetrical finite strip with a length of 2L and a width of 2h, containing a transverse symmetrical crack of width 2a at the midplane is considered. Two rigid plates are bonded to the ends of the strip through which uniformly distributed axial tensile load of magnitude 2hp₀ is applied. The material of the strip is assumed to be linearly elastic and isotropic. Both edges of the strip are free of stresses. Solution for this finite strip problem is obtained by means of an infinite strip of width 2h which contains a crack of width 2a at y = 0 and two rigid inclusions of width 2c at y = ±L and which is subjected to uniformly distributed axial tensile load of magnitude 2hp₀ at y = ±∞. When the width of the rigid inclusions approach the width of the strip, i.e., when c → h, the portion of the infinite strip between the inclusions becomes identical with the finite strip problem. Fourier transform technique is used to solve the governing equations which are reduced to a system of three singular integral equations. By using the Gauss–Jacobi and the Gauss–Lobatto integration formulas, these integral equations are converted to a system of linear algebraic equations which is solved numerically. Normal and shearing stress distributions and the stress intensity factors at the edges of the crack and at the corners of the finite strip are calculated. Results are presented in graphical and tabular forms.     

Stress intensity factors for a mixed mode center crack in an anisotropic strip

An approach based on the continuous dislocation technique is formulated and used to obtain the Mode I and II stress intensity factors in a fully anisotropic infinite strip with a central crack. First, the elastic solution of a single dislocation in an anisotropic infinite strip is obtained from that of a dislocation in an anisotropic half plane, by applying an array of dislocations along the boundary of the infinite strip, which is supposed to be traction-free. The dislocation densities of the dislocation array are determined in such a way that the traction forces generated by the dislocation array cancel the residual tractions along the boundary due to the single dislocation in the half plane. The stress field of a single dislocation in the infinite strip is thus a superposition of that of the single dislocation and the dislocation array in the half plane. Subsequently, the elastic solution is applied to calculate the stress intensity factors for a center crack in an anisotropic strip. Crack length and material anisotropy effects are discussed in detail.     

Impact response of a strip composite with a finite crack

The dynamic response of a central crack in a strip composite under normal impact is analyzed. The crack is oriented normally to the interfaces. Laplace and Fourier transform techniques are used to reduce the elastodynamic problem to a pair of dual integral equations. The integral equations are solved by using an integral transform technique and the result is expressed in terms of a Fredholm integral equation of the second kind. 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, the material properties and the geometrical parameters is discussed.     

Stress-intensity factor and crack opening for a linearly viscoelastic strip with a slowly propagating central crack

The stress-intensity factor and the size of the crack opening have been calculated for a linearly viscoelastic strip with a slowly propagating central crack. The edges of the infinitely long strip are displaced normal to the crack and both clamped and shear-free strip edges have been investigated. The results are based on the solution to the problem of a suddenly loaded strip with a stationary crack. The resulting integral equation has been solved numerically for arbitrary crack length and analytical solutions in form of asymptotic series are given for crack length up to about half the strip width. The response to a propagating crack is found by superposition.This work represents part of a Ph.D. Thesis submitted to the California Institute of Technology. The author gratefully acknowledges the support of this work by the National Aeronautics and Space Administration under Research Grant NGL-05-002-005, GALCIT 120.     

Wedge loading of a semi-infinite strip with an edge crack

The problem of a semi-infinite strip containing an edge crack is considered. It is assumed that the strip is loaded by a frictionless rigid wedge pressed into the crack. The resulting crack-contact problem is formulated in terms of a system of singular integral equations. The behavior of the solution near the singular points is studied in detail. A series of numerical examples is given and the results are compared with those obtained by the method of boundary collocation and by the simple beam theory.

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Résumé Le problème d'une tôle mince semi-infinie contenant une fissure latérale est considérée. On suppose que le feuillard est soumis à une charge par un coin rigide et sans friction appliqué dans la fissure. On formule le problème du contact de fissure qui en résulte en termes d'un système d'équations intégrales singulières. Le comportement de la solution correspondant aux points singuliers est étudié dans le détail. Une série d'exemples numériques est fournies et les résultats sont comparés avec ceux obtenus par la méthode de collocation des frontières et par la théorie simple des poutres.

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This work was supported by NASA-Langley under the Grant NGR 39-007-011 and by NSF under the Grant ENG 77-19127.     

Stress analysis of crack problems with a three-dimensional,time-dependent computer program

A three-dimensional, time-dependent computer program is used for the stress-strain analysis of elastic-plastic materials subjected to tensile loads. Several geometries are considered. The capabilities and advantages of this explicit finite difference computer program are demonstrated, and recommendations for future applications are made.

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Résumé Un programme de calcul à 3 dimensions et indépendant du temps a été utilisé pour l'analyse en tension-déformation des matériaux élasto-plastiques sujets à des contraintes et des tractions. On considère différents types de géométries. Les possibilités et les avantages que présente ce programme de calcul par différence finie explicite sont démontrés et l'on a fait des recommandations pour ses applications futures.

     

A half plane and a strip with an arbitrarily located crack

The paper introduces a technique to deal with the problem of an elastic domain containing an arbitrarily oriented internal crack. The problem is formulated as a system of integral equations for a fictitious layer of body forces imbedded in the plane along a closed smooth curve encircling the original domain. The problems of a half plane with a crack in the neighborhood of its free boundary and of an infinite strip containing a symmetrically located internal crack with an arbitrary orientation are considered as examples. In each case the stress intensity factors are computed and are given as functions of the crack angle.     

Enriched finite element analysis for a delamination crack in a laminated composite strip

Edge delamination cracks in laminated composite strips are analyzed with the aid of the enriched finite element method, wherein the asymptotic singular solution for a delamination crack is incorporated into finite elements. The strip is assumed to be in the state of generalized plane deformations including extension (compression), bending or torsion. Comparison of the numerical results with those from other methods is made to confirm the solution. The crack growth stability is examined for a couple of ply orientations in terms of the energy release rate and mode mixity.This work has been partially supported by the Agency for the Defense Development in Republic of Korea: under the Grant No. ADD-92-5-004.     

Stress analysis of a debonding and a crack around a circular rigid inclusion

A model of a debonding and a crack occurring from a circular rigid inclusion in an infinite plate is analyzed as a mixed boundary value problem under uniform tension. A mapping function represented in the form of a sum of fractional expressions and complex stress functions are used. The stress distribution, stress intensity factors at the tip of a crack, and stress singular values at a debonded tip are presented. By using these stress singular values, the intensity of the debonded tip is also considered.

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Résumé On analyse un modèle de décollement et de fissuration au départ d'une inclusion rigide circulaire dans une tôle infinie, en le considérant comme un problème mixte de valeurs aux limites sous une tension uniforme. On utilise des fonctions complexes de la contrainte et une représentation sous forme d'une somme d'expressions fractionnelles. La distribution des contraintes, des facteurs d'intensité de contraintes à l'extrémité de la fissure, et les valeurs des contraintes singulières à l'extrémité de la zone décollée, sont présentées. En utilisant ces valeurs de contraintes singulières, on prend également en compte l'étendue de cette zone décollée.

     

Transient thermoelectroelastic response of a functionally graded piezoelectric strip with a penny-shaped crack

Transient response of a penny-shaped crack in a plate of a functionally graded piezoelectric material (FGPM) is studied under thermal shock loading conditions. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the crack faces are completely insulated. By using both the Laplace and Hankel transforms, the thermal and electromechanical problems are reduced to a singular integral equation and a system of singular integral equations which are solved numerically. The intensity factors vs. time for various crack size, crack position and material nonhomogeneity are obtained.     

Dynamic mode-III interface crack in a bi-material strip

An interfacial crack is placed within a two-phase elastic strip subjected to an out-of-plane loading. In the unperturbed state, the crack propagates with a constant speed V along the interface. The Dirichlet boundary conditions are applied to the upper and lower sides of the strip. The exterior boundary is subjected to a regular small perturbation; in addition, it is assumed that the crack speed changes by a small amount ${\varepsilon \phi^{\prime}(t)}$ , where ${\phi}$ is a smooth function of time t. The asymptotic model presented in this paper delivers an approximation for the stress-intensity factor and an integro-differential equation for the perturbation function ${\phi}$ . A particular feature of the model is in the use of skew-symmetric dynamic weight functions, attributed to the interfacial crack problem in a strip.     

Transient response of a crack in an anisotropic strip

Summary The problem of an anisotropic elastic strip containing a crack which is opened by stresses suddenly applied on the crack faces is considered here. The problem is reduced to a set of simultaneous Fredholm integral equations of the second kind which may be solved iteratively. Once the solutions of these integral equations are obtained, the dynamic stress intensity factors may be evaluated numerically. Numerical results are obtained for a particular transversely isotropic strip.With 1 Figure     

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.     

Analysis and computations of oscillating crack propagation in a heated strip

This paper presents a computational analysis and several simulations of an existing experiment, which deals with a quasi-static thermal crack propagation in a glass plate. The experimental observation was that a straight or oscillatory crack propagation occurred depending on the plate width and thermal loading. The goal here is to simulate this experiment with the recent numerical tool such as XFEM. First, the analysis of the settings of the experiment is developed by providing the computed energy release rate of the crack for a wide range of experiment settings parameters. Second, different crack propagations are simulated, and show a good agreement with the experimental observation of straight or oscillatory paths. Third, a study of the results given by the fracture criteria (maximum hoop stress and Local Symmetry criteria) is also presented for this particular experiment in order to evaluate their differences.     

Impact response of a finite crack in an orthotropic strip

Summary The elastodynamic response of a finite crack in an infinite orthotropic strip under normal impact is investigated in this study. The crack is situated symmetrically and oriented in a direction normal to the edges of the strip. Laplace and Hankel transforms are used to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution to the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. Numerical values on the dynamic stress intensity factor for some fiber-reinforced composite materials are obtained and the results are graphed to display the influence of the material orthotropy.