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Interrelation Between Constitutive Laws and Fracture in the Vicinity of Friction Surfaces

  • Chapter
Physical Aspects of Fracture

Part of the book series: NATO Science Series ((NAII,volume 32))

Abstract

It is well known that cracks can produce stress singularities in linear elastic materials. One common type of stress singularity is \( \sigma \propto K/\sqrt r \) where r is the distance from the crack tip and K is the stress intensity factor. The stress intensity factor approach is very effective in structural design. In particular, a popular fracture criterion is formulated in the form K = K c where K c is a critical value of the stress intensity factor, a material constant. In the present paper the general concept of the stress intensity factor is adopted for fracture analysis in the vicinity of maximum friction surfaces (surfaces where the frictional stress attains its maximum possible value). The basic constitutive law is the rigid/perfectly plastic solid. In this case the equivalent strain rate, ξ eq , is describable by nondifferentiable functions in the vicinity of maximum friction surfaces and its behavior is given by \( \xi _{eq} \propto D/\sqrt {x_3 } \) where x 3 is the distance from the friction surface. Most fracture criteria in metal forming involve the equivalent strain rate in such a manner that they would immediately predict fracture initiation at the maximum friction surface since the behavior of a fracture parameter is singular and its value approaches infinity at the friction surface. Therefore, by analogy with the mechanics of cracks, it is natural to assume that the intensity of the strain rate singularity can be used to predict fracture in the vicinity of maximum friction surfaces. In the present paper the equivalent strain is used as the fracture parameter. The strain intensity factor E, which controls the magnitude of the equivalent strain in the vicinity of a maximum friction surface, is introduced and then a fracture criterion is postulated in the form E — E c where E c is assumed to be a material constant. The effects of temperature, pressure dependence of the yield condition, viscosity, and strain hardening on the behavior of solution in the vicinity of the maximum friction surface are discussed. A few examples are proposed to illustrate the approach.

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Authors and Affiliations

  1. Alcoa Technical Center, 100 Technical Drive, Alcoa Center, PA, 15069-0001, USA

    S. Alexandrov

  2. Institute for Problems in Mechanics Russian Academy of Science, 101 Prospect Vernadskogo, 117526, Moscow, Russia

    S. Alexandrov

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  1. S. Alexandrov
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Editors and Affiliations

  1. Service de Physique et Chimie des Surfaces et des Interfaces, Direction des Sciences de la Matière, CEA, Saclay, France

    Elisabeth Bouchaud

  2. Centre de Morphologie Mathématique, Unité Mixte de Recherche CNRS, Ecole des Mines Paris, France

    Dominique Jeulin

  3. Université Paris 13 and Laboratoire Mécanique des Sols, Structures et Matériaux, Unité Mixte de Recherche CNRS, Ecole Centrale Paris, France

    Claude Prioul

  4. Laboratoire Surface du Verre et Interfaces, Unité Mixte de Recherche CNRS, St-Gobain, France

    Stéphane Roux

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© 2001 Springer Science+Business Media Dordrecht

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Alexandrov, S. (2001). Interrelation Between Constitutive Laws and Fracture in the Vicinity of Friction Surfaces. In: Bouchaud, E., Jeulin, D., Prioul, C., Roux, S. (eds) Physical Aspects of Fracture. NATO Science Series, vol 32. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0656-9_14

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  • DOI: https://doi.org/10.1007/978-94-010-0656-9_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-7147-2

  • Online ISBN: 978-94-010-0656-9

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