International Journal of Fracture

, Volume 21, Issue 3, pp 229–240 | Cite as

A Griffith crack shielded by a dislocation pile-up

  • B. S. Majumdar
  • S. J. Burns
Article

Abstract

The dislocation free zone at the tip of a mode III shear crack is analyzed. A pile-up of screw dislocations parallel to the crack front, in anti-plane shear, in the stress field of a crack has been solved using a continuous distribution of dislocations. The crack tip remains sharp and is assumed to satisfy Griffith's fracture criteria using the local crack tip stress intensity factor. The dislocation pile-up shield the sharp crack tip from the applied stress intensity factor by simple addition of each dislocation's negative contribution to the applied stress intensity value. The analysis differs substantially from the well known BCS theory in that the local crack tip fracture criteria enters into the dislocation distributions found.

Keywords

Stress Intensity Factor Shear Crack Screw Dislocation Fracture Criterion Free Zone 

Résumé

On analyse la zone libre de dislocation qui est située à l'extrémité d'une fissure de cisaillement de mode III. On solutionne à l'aide d'une distribution continue de dislocations le problème de l'empilement de dislocation-vis parallèle en front de fissure et situé, en cisaillement antiplanaire, dans le champ de contraintes d'une fissure. On suppose que l'extrémité de la fissure demeure aiguë et qu'elle satisfait au critère de rupture de Griffith, en recourant au facteur d'intensité de contraintes local à fond d'entaille. L'empilement de dislocations protège l'extrémité aiguë de la fissure contre l'influence du facteur d'intensité des contraintes appliquées, du fait d'une addition simple des contributions négatives de chaque dislocation à la valeur de l'intensité de contrainte appliquée. L'analyse diffère substantiellement de la théorie BCS bien connue en ce que les critères de rupture à l'extrémité de la fissure entrent dans la distribution de dislocation trouvée.

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Copyright information

© Martinus Nijhoff Publishers 1983

Authors and Affiliations

  • B. S. Majumdar
    • 1
  • S. J. Burns
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of RochesterRochesterUSA

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