Reply
The factor of 3 appearing in the stability criterion given by Dienes (1983) did indeed seem puzzling, and the author is most grateful to Rice (this issue) for pointing out that when traction on the crack boundary is accounted for in the energy balance, the stability criterion involves simply the square of the stress difference, (sigma - tau)/sup 2/, rather than (sigma - tau)(sigma - 3tau). His analysis of the shear crack problem using the uniformly stressed state as a reference rather than the unstressed state leads to an elegant alternative to his original stability analysis. The material of Appendix A was included in order to show that the strain energy has the form A (sigma - tau)/sup 2/, an assumption that a reviewer did not consider obvious. The author is indebted to Rice (this issue) for pointing out that an expression for strain energy involving integration only over the crack surface was previously obtained by Rice and Drucker (1967), and they point out that this significantly simplifies the calculation of strain energy. However, neither their paper nor that of Murrell (1964), which also contains that result, discusses the problem of a crack with finite traction acting on its surface, to which (A8) applies. As pointed out in my paper, it follows from (A8) that the strain energy does not in general have the simple stress dependence of (sigma - tau)/sup 2/, this form being valid only for simple closed cracks.
- Research Organization:
- Los Alamos National Lab., NM
- OSTI ID:
- 6687162
- Journal Information:
- J. Geophys. Res.; (United States), Vol. 89:B4
- Country of Publication:
- United States
- Language:
- English
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