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Contained plastic deformation near cracks and notches under longitudinal shear

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International Journal of Fracture Mechanics Aims and scope Submit manuscript

Abstract

An exact linear elastic-perfectly plastic solution is presented for the problem of a sharp notch (or, when the notch angle is zero, a crack) in a plane of finite width subjected to anti-plane stresses inducing a stress and deformation state of longitudinal shear. General solutions for physical coordinates corresponding to given stresses, position of the elastic-plastic boundary, and accompanying displacements are given in terms of finite single integrals.

The case of cracks is treated in detail and closed form solutions are presented in terms of elementary and elliptic functions. Numerical results are given and applications of the solution to the development of fracture mechanics failure criteria, as well as some inherent difficulties, are discussed.

Résumé

Une solution linéaire exakte, élastique — parfaitement plastique, est présentée pour le problème d' une entaille aigue (ou, quanó l' angle de 1' entaille est égal a zéro, und fissure), dans un plan d' étendue finie, sujette ã des contraintes antiplanes qui induísent une contrainte et une déformation de eisaillement longitudiaale. de la limite élastique — plastique, et les déplacements qui en résultent sont données sous forme d' intégrales simples finies.

Le cas des fissures est discuté en détail et des solutions de forme férmée présentées en terme de functions elementaires et élliptiques. Les résultats numériques sont données et les applications de la solution au développement d' un critère de fracture ainsi que quelques difficultés inherentes sont discutées.

Zusammenfassung

Eine exakte linear elastisch-perfekt plastische Lösung wird für das Problem einer scharfen Kerbe (oder, wenn der Winkel der Kerbe null ist, für einen Anriss), in einer Ebene mit endlicher Breite gezeigt, die mit einer Längsschubspannung beansprucht wird. Allgemeine Lösungen für Koordinaten die den gegebenen Soannungen entsprechen, für den Ort der elastisch-plastischen Grenze Bowie für die dazuge hörendea Verformungen werden in Form von endlichen Einfachintegralen gegebenen.

Der Fall der Risse wird im Detail behandelt. Die Lösungen sind in geschlossener Form, in elementaren und elliptischen Funktionen angegeben.

Numerische Resultate werden gegeben und die Anwendung der Lösungen zur Entwicklung der Kriterien der Bruchmechanik, Bowie einige anhaftende Schwierigkeiten werden besprochen.

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Authors and Affiliations

  1. Assistant Professor of Engineering, Brown University, Providence, R.I.

    James R. Rice

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  1. James R. Rice
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Assistant Professor of Engineering, Brown University, Providence, R.I.

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Rice, J.R. Contained plastic deformation near cracks and notches under longitudinal shear. Int J Fract 2, 426–447 (1966). https://doi.org/10.1007/BF00183821

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  • DOI: https://doi.org/10.1007/BF00183821

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