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Slightly curved or kinked cracks

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Abstract

A solution is presented for the elastic stress intensity factors at the tip of a slightly curved or kinked two-dimensional crack. The solution is accurate to first order in the deviation of the crack surface from a straight line and is carried out by perturbation procedures analogous to those of Banichuk [1] and Goldstein and Salganik [2, 3]. Comparison with exact solutions for circular arc cracks and straight cracks with kinks indicates that the first order solution is numerically accurate for considerable deviations from straightness. The solution is applied to fromulate an equation for the path of crack growth, on the assumption that the path is characterized by pure Mode I conditions (i.e., K II=0) at the advancing tip. This method confirms the dependence of the stability, under Mode I loading, of a straight crack path on the sign of the non-singular stress term, representing tensile stress T acting parallel to the crack, in the Irwin-Williams expansion of the crack tip field. The straight path is shown to be stable under Mode I loading for T<0 and unstable for T>0.

Résumé

On présente une solution pour les facteurs d'intensité de contrainte élastique à l'extrémité d'une fissure bi-dimensionnelle légèrement incurvée ou croquée.

La solution est exacte au premier degré pour la déviation à la surface de la fissure à partir d'une ligne droite, et est mise en oeuvre à l'aide de procédures de perturbations analogues à celles de Banichuck, et de Goldstein et Salganik.

Une comparaison avec les solutions exactes dans le cas de fissures en arc de cercle et de fissures droites avec un croquage indique que la solution du premier ordre est numériquement exacte pour des déviations déjà importantes par rapport à une fissure purement droite.

La solution est appliquée à la formulation d'une équation décrivant le parcours de la croissance d'une fissure, en supposant que ce parcours est caractérisé des conditions de Mode I pures (càd. K h=0) à l'extrémité de la fissure.

Cette méthode confirme la dépendance de la stabilité sous une mise en charge de Mode I d'un parcours d'une fissure droite par rapport aux signes du terme de contrainte non singulière représentant la contrainte de traction agissant parallèlement à la fissure dans un champ de Irwin-Williams décrivant l'expansion à l'extrémité de celle-ci. On montre que le chemin en ligne droite est stable sous une mise en charge de Mode I lorsque T est inférieur à O et instable lorsque T est supérieur à O.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Sydney, Sydney, Australia

    B. Cotterell (Visiting Associate Professor)

  2. Division of Engineering, Brown University, 029111, Providence, R.I., U.S.A.

    J.R. Rice

Authors
  1. B. Cotterell
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  2. J.R. Rice
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Research supported by the U.S. National Science Foundation/Materials Research Laboratory at Brown University.

Research supported by the U.S. National Science Foundation/Materials Research Laboratory at Brown University.

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Cotterell, B., Rice, J. Slightly curved or kinked cracks. Int J Fract 16, 155–169 (1980). https://doi.org/10.1007/BF00012619

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  • DOI: https://doi.org/10.1007/BF00012619

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