Interactions of a penny-shaped crack with a center of dilatation in an elastic half-space

Kam Tim Chau, X. Yang, R. C.K. Wong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)


This paper considers the interaction between a penny-shaped crack and a center of dilatation in an elastic half-space. The problem is decomposed into two `Auxiliary Problems': (I) a half-space containing a center of dilatation and (II) a penny-shaped crack subject to tractions that cancel those induced by the Auxiliary Problem I. The fundamental solutions for penny-shaped crack subject to point forces on the crack surface are first derived, then they are used to generate the solution for Auxiliary Problem II. When the free surface is far from the crack and the center of dilatation, the results by E. Karapetian and M. Kachanov is recovered as a special case. If the overburden stress and the friction on crack surface are neglected, all modes I, II, and III stress-intensity factors (K1, K2and K3) are induced at the crack tips. In general, the maximum value of K2is observed when the center of dilatation is located in front of the crack tip at an elevation close to that of the penny-shaped crack. However, tensile cracking is likely to be prohibited by the overburden stress and friction on the crack surface, while shear cracking remains possible even when both overburden and friction on the crack surface are included. Generally speaking, the mode II stress intensity factor is larger than those for mode I and III cracking.
Original languageEnglish
Pages (from-to)645-662
Number of pages18
JournalMechanics of Materials
Issue number11
Publication statusPublished - 1 Jan 2000

ASJC Scopus subject areas

  • Instrumentation
  • General Materials Science
  • Mechanics of Materials


Dive into the research topics of 'Interactions of a penny-shaped crack with a center of dilatation in an elastic half-space'. Together they form a unique fingerprint.

Cite this