Strip yield analysis of two collinear unequal cracks in an infinite sheet

Plastic zone sizes and crack tip opening displacements (CTODs) are obtained for two collinear cracks in an infinite sheet subjected to known remote stress. Analysis is conducted by assuming the crack accompanying plastic zones as a fictitious crack and formulating integral equations based upon traction free and no stress singularity conditions. In addition, critical remote stress, plastic zone sizes, and CTODs when the adjacent plastic zones touched are obtained by assuming the coalesced fictitious cracks as a single fictitious crack and formulating integral equations based upon no stress singularity and zero coalesced point displacement conditions. Extensive numerical results are presented.     

Thermoelasticity problem of an orthotropic plate with two collinear cracks

In this article a rigorous formulation of, and an exact solution to the plane thermoelasticity problem of an orthotropic plate having two collinear cracks are presented. Explicit expressions for the temperature, thermal displacements, thermal stresses and thermal stress intensity factors are obtained assuming that uniform or linear heat flow has been applied on the crack surfaces. Numerical values of thermal stress intensity factors and thermal crack sliding displacements and other quantities are worked out and presented in graphic form. A number of conclusions of practical significance are derived from the above results, including the assertion that an extremely large magnitude of stress singularity may occur in the geometry of two closely neighbouring cracks under the action of linear heat flow.

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Résumé On présente une formulation rigoureuse et une solution exacte d'un problème de thermo-élasticité plane dans une tôle orthotrope comportant deux fissures colinéaires. On obtient les expressions explicites de la température, des dilatations thermiques, des contraintes thermiques et des facteurs d'intensité des contraintes thermiques en supposant appliquer un flux de chaleur uniforme ou linéaire sur les faces de la fissure. On élabore les valeurs numériques des facteurs d'intensité des contraintes thermiques, des déformations thermiques de la fissure par glissements, et d'autres grandeurs, et on les présente sous une forme graphique. On tire de ces résultats un certain nombre de conclusions pratiques, y compris la constatation que des singularités de contraintes d'extrêmmeent grande amplitude peuvent se rencontrer dans une géométrie de deux fissures très voisines sujettes à un flux de chaleur linéaire.

     

On paths of two equal collinear cracks

In a previous paper an analysis of the path prediction for a single line crack in sheets of brittle material has been performed. In this work, the analysis is extended to a system of two collinear cracks embedded in an infinite medium subjected to biaxial loading. The interaction between the crack paths is shown. The effects of biaxial loading as well as of crack inclination on the stability of trajectories are pointed out.     

Dugdale models for two collinear unequal cracks

In this paper the Dugdale model is applied to determine the plastic zones developed in the case of two collinear and unequal cracks within an homogeneous, Isotropic, elastic-perfectly plastic infinite plate. The cracks are subjected to a normal loading, acting at the infinity. It was assumed that the type of plastic deformation was of the cross-slip mode creating narrow plastic enclaves, case for which the original Dugdale model for a single crack is valid. The case of plastic coalescence between the collinear cracks was derived as a special case of the general problem.     

Interaction between an elastic circular inclusion and two symmetrically placed collinear cracks

This paper investigates the fracture toughness of a flat large elastic cracked plate containing an elastic circular inclusion, using the plane stress crack-tip stress intensity factor as a criterion for fracture. In this plane stress geometry, each of the two collinear finite cracks is located on either side of the elastic circular inclusion and the geometry is subjected to uniform stresses at infinity. The analysis is based on the two-dimensional theory of clasticity by using the Muskhelishvili complex variable approach. Numerical calculations are reported for the case of simple tension normal to the crack direction, and show the variation of the stress intensity factor with the configuration and elastic properties of the plate and the inclusion.

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Résumé On étudie la ténacité à la rupture d'une grande plaque plane et élastique comportant des fissures et une inclusion élastique circulaire, en utilisant comme critère de rupture le facteur d'intensité des contraintes en état plan de tension. Dans ce type de géométrie, on aligne une paire de fissures linéaires et finies de part et d'autre de l'inclusion circulaire, et on soumet cette disposition à une contrainte uniforme à l'infini. L'analyse est basée sur la théorie de l'élasticité bidimensionnelle grâce à l'approche par variables complexes due à Muskhelishvili. Les calculs numériques sont effectués pour le cas de la traction simple normale à la direction des fissures et montrent la variation du facteur d'intensité des contraintes avec la configuration de la tôle et de l'inclusion ainsi qu'avec leurs propriétés élastiques.

     

Elastic behavior of an edge dislocation inside the nanoscale coating layer

The problem of an edge dislocation inside the nanoscale coating layer accounting for the interface effects is addressed. By combining the sectionally holomorphic function, Laurent series expansion techniques and the complex variable function method, the stress fields in the coating layer and the image force acting on the edge dislocation are derived analytically. The results indicate that an additional repulsive force or attractive force will act on the edge dislocation for considering the interface effects, and there exists more than one stable (unstable) dislocation equilibrium point. The material elastic dissimilarity, the coating thickness, the interface stress as well as the relative position of the dislocation have great influence on the force acting on the edge dislocation in the coating layer. The present solutions contain previously several known results, which can be shown to be special cases.     

Complex variable-based analysis for two semi-permeable collinear cracks in a piezoelectromagnetic media

The problem of two equal collinear cracks weakening a poled transversely isotropic piezo-electro-magnetic plate is addressed under semi-permeable electro-magnetic boundary conditions on the crack faces. The problem is formulated employing Stroh formalism and solved using a complex variable technique. Closed form analytical expressions are derived for various fracture parameters. An illustrative numerical case study is presented for poled BaTiO₃ ? CoFe₂O₄ ceramic cracked plate to study the effect of prescribed electric load, magnetic load, and inter-crack distance on fracture parameters. Moreover, a comparative study is done of volume fraction, impermeable, and semi-permeable boundary conditions on fracture parameters.     

Growth and coalescence of two collinear indentation cracks in glass

Subcritical growth and coalescence of two collinear cracks of different lengths were investigated using small Knoop indentation cracks in glass. Indentation cracks subjected to bending in water showed anomalous crack growth in terms of the stress intensity factor, K_I. The crack growth velocity, dc/dt, was initially high, decreased and thereafter increased with increasing K_I. The effective stress intensity factor, K_I,eff, was calculated by adding a term describing the state of residual stress to explain this anomalous growth. Before crack coalescence, a large crack showed a crack velocity higher than expected from the coalescent crack. The coalescent crack velocity increased with K_I,eff and the slope of dc/dt−K_I,eff curves differed from that for a single crack, depending on the crack length.     

Non-singular stresses effects on two interacting equal collinear cracks

An analysis of the effect of the interaction between two equal collinear cracks embedded in an infinite elastic plane medium on the fracture response is considered.The expressions of the stress intensity factors under general biaxial loading to infinity are worked out by using the expressions known in the case of a normal stress as well as of a shear stress which are perpendicular and parallel respectively to the cracks line.After noting that the non-singular term of the local circumferential stress is expressed in the same way as the simple line crack, the effects of the stress parallel to the cracks line on the prediction of the angle of initial crack extension, on the fracture loci and on the critical applied loads are studied.     

Elastic circular inclusion in an infinite plane containing two cracks

The elastic fields in an elastic circular inclusion and surrounding infinite matrix containing two cracks symmetrically situated, are determined when the matrix is subjected to loads at infinity. In this problem, the elastic properties of inclusion could differ from those of the matrix. The Muskhelishvili's technique is used. The solution depends upon two sets of suitable complex potentials Φ_m(z), Ψ_m(z), Φ_i(z), Ψ_i(z) for matrix and inclusion respectively, which solves the problem.     

Elastic cracks and screw dislocation pile-ups crossing a bimaterial interface

The concept of continuously distributed dislocations is employed to study the behavior of anti-plane shear cracks crossing a bimaterial interface. The governing equations of the dislocation distribution function are dual singular integral equations. It is noticed that close to the tip, the crack opening displacement behaves as if the crack were imbedded in a homogeneous medium. C onsequendy, the stress in the immediate vicinity of the crack tip varies with the inverse square root of the distance from the tip. Moreover, the stress intensity near the crack tip in the comparatively harder phase is higher than that in the softer phase. The present method of analysis can be applied to the study of screw dislocation pile-ups crossing a phase boundary.     

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.     

Exact solutions of two semi-infinite collinear cracks in a strip

The stress intensity factors (SIFs) are calculated for an infinitely long strip of finite height containing two straight semi-infinite collinear cracks, which is a very useful model in simulating the interaction of faults in the study of tectonic earthquake. The new solutions are obtained by complex function method. It is shown that two well-known exact solutions for the crack problems are the limiting cases of the present results.     

Weight functions and strip yield solution for two equal-length collinear cracks in an infinite sheet

The problem of two equal-length collinear cracks in an infinite sheet is treated using the weight function method. Exact weight functions for the inner and outer crack tips are derived based on the crack opening displacement solution for a reference load case. These weight functions are used to calculate stress intensity factors for different load cases, plastic zone sizes and crack tip opening displacements of the strip yield model. The approach is validated by the perfect agreement between the present strip yield model solutions and Collins and Cartwright’s analytical results based on the direct complex stress function formulation.     

Elastic fields due to an edge dislocation in an isotropic film-substrate by the image method

The stress and displacement fields due to an edge dislocation in a linearly elastic, isotropic film-substrate are derived using the method of image dislocations. The key features of the developed method are (1) a decomposition scheme in which the interfacial conditions are satisfied a priori, (2) all singular integrals are eliminated from the governing equations, (3) the elastic fields are obtained in the form of series, the terms of which can be exactly evaluated via integral transforms, and (4) the solutions converge satisfactorily with only three terms of the series. It is shown that the film thickness and dislocation position have a significant influence on the image force acting on the dislocation, and that the film thickness variation due to an accumulation of dislocations may degrade the performance of optical films.     

Dynamic interaction of collinear cracks

Summary The method of caustics was used to investigate the dynamic problem of interaction of two collinear edge cracks in plane PMMA specimens. By varying the externally applied strain rate and the initial crack lengths, useful conclusions were derived on the instability of interacting cracks, their paths of propagation, the variation of the crack propagation velocities and the stress intensity factors.With 14 Figures     

Discrete dislocation analysis of pre-existing cracks

The discrete dislocation method is employed to determine the dislocation configurations associated with a continuous plastic crack subjected to both loading and unloading. The concept of anticrack dislocations is introduced in order to satisfy the free surface boundary conditions on the surfaces of the unloaded crack associated with lattice dislocations in its plastic zone. Various configurations of the unloaded crack, which incorporate a zipping action of the crack surfaces to reduce surface energy, are illustrated schematically wherein the discrete dislocation analysis is utilized. The results are obtained for both a tensile and a shear crack.

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Résumé On utilise la méthode de dislocations discrètes pour déterminer la configuration des dislocations associées à une fissure plastique continue soumise à une charge et à déchargement. Le concept de dislocation d'anti-fissure est introduit en vue de satisfaire les conditions aux limites de surface libre sur les faces de la fissure non chargée, associées aux dislocations des réseaux dans la zône plastique. Des configurations variées de fissures non soumises à sollicitation qui comportent une action de fermeture des surfaces de fissure en vue de réduire l'énergie de surface, sont schématiquement illustrées dès lors que l'analyse par dislocations discrètes peut être utilisée. Des résultats sont obtenus pour des fissurations sous tension et sous cisaillement.