DOI: 10.1029/jb084ib05p02210. The stability of a rapid mode II shear crack with finite cohesive traction

The stability of a rapid mode II shear crack with finite cohesive traction

10.1029/jb084ib05p02210

Crossref journal-article

American Geophysical Union (AGU)

Journal of Geophysical Research: Solid Earth (13)

Abstract

It has been found in numerical simulations by Andrews [1976] that a growing mode II shear crack may at first rapidly accelerate toward the Rayleigh wave speed vR and then after a short period of readjustment start running at a speed slightly greater than (2)½vS, where vS is the shear wave speed. In order to throw some light on this phenomenon we study in detail the steady motion of a semi‐infinite crack which is driven by a following point load which remains at constant distance d from the crack tip. A cohesive traction which is a function of relative displacement acts in the Dugdale type tip region [Dugdale, 1960] which is small in comparison with d. We consider crack speeds vC in the range vC < vP, the P wave speed, and find that for vC < vR and for vS < vC < (2)½vS the load is a decreasing function of vC, while for (2)½vS < vC < vP the load increases with vC. The former situation is interpreted as instability, and the latter as stability. The range vR < vC < vS appears to be forbidden. This is in agreement with, and partially explains, Andrews's results. It also agrees with an earlier analytic solution obtained by Craggs [1960] for vC < vR. We find that for vC < vR the displacement in the tip region has a shape independent of vC but suffers a contraction analogous to a Lorentz contraction so that the length goes to zero as vC ↑ vR.

Bibliography

Burridge, R., Conn, G., & Freund, L. B. (1979). The stability of a rapid mode II shear crack with finite cohesive traction. Journal of Geophysical Research: Solid Earth, 84(B5), 2210â2222. Portico.

Authors 3

R. Burridge (first)
G. Conn (additional)
L. B. Freund (additional)

References 7 Referenced 150

Dates

Type	When
Created	17 years, 6 months ago (Feb. 6, 2008, 2:39 p.m.)
Deposited	1 year, 11 months ago (Sept. 23, 2023, 3:37 a.m.)
Indexed	1 week, 3 days ago (Aug. 12, 2025, 5:48 p.m.)
Issued	46 years, 3 months ago (May 10, 1979)
Published	46 years, 3 months ago (May 10, 1979)
Published Online	12 years, 11 months ago (Sept. 20, 2012)
Published Print	46 years, 3 months ago (May 10, 1979)

Funders 0

None

BibTeX

@article{Burridge_1979, title={The stability of a rapid mode II shear crack with finite cohesive traction}, volume={84}, ISSN={0148-0227}, url={http://dx.doi.org/10.1029/jb084ib05p02210}, DOI={10.1029/jb084ib05p02210}, number={B5}, journal={Journal of Geophysical Research: Solid Earth}, publisher={American Geophysical Union (AGU)}, author={Burridge, R. and Conn, G. and Freund, L. B.}, year={1979}, month=may, pages={2210–2222} }

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  "abstract": "<jats:p>It has been found in numerical simulations by Andrews [1976] that a growing mode II shear crack may at first rapidly accelerate toward the Rayleigh wave speed v<jats:sub>R</jats:sub> and then after a short period of readjustment start running at a speed slightly greater than (2)<jats:sup>\u00bd</jats:sup>v<jats:sub>S</jats:sub>, where v<jats:sub>S</jats:sub> is the shear wave speed. In order to throw some light on this phenomenon we study in detail the steady motion of a semi\u2010infinite crack which is driven by a following point load which remains at constant distance d from the crack tip. A cohesive traction which is a function of relative displacement acts in the Dugdale type tip region [Dugdale, 1960] which is small in comparison with d. We consider crack speeds v<jats:sub>C</jats:sub> in the range v<jats:sub>C</jats:sub> &lt; v<jats:sub>P</jats:sub>, the P wave speed, and find that for v<jats:sub>C</jats:sub> &lt; v<jats:sub>R</jats:sub> and for v<jats:sub>S</jats:sub> &lt; v<jats:sub>C</jats:sub> &lt; (2)<jats:sup>\u00bd</jats:sup>v<jats:sub>S</jats:sub> the load is a decreasing function of v<jats:sub>C</jats:sub>, while for (2)<jats:sup>\u00bd</jats:sup>v<jats:sub>S</jats:sub> &lt; v<jats:sub>C</jats:sub> &lt; v<jats:sub>P</jats:sub> the load increases with v<jats:sub>C.</jats:sub> The former situation is interpreted as instability, and the latter as stability. The range v<jats:sub>R</jats:sub> &lt; v<jats:sub>C</jats:sub> &lt; v<jats:sub>S</jats:sub> appears to be forbidden. This is in agreement with, and partially explains, Andrews's results. It also agrees with an earlier analytic solution obtained by Craggs [1960] for v<jats:sub>C</jats:sub> &lt; v<jats:sub>R.</jats:sub> We find that for v<jats:sub>C</jats:sub> &lt; v<jats:sub>R</jats:sub> the displacement in the tip region has a shape independent of v<jats:sub>C</jats:sub> but suffers a contraction analogous to a Lorentz contraction so that the length goes to zero as v<jats:sub>C</jats:sub> \u2191 v<jats:sub>R.</jats:sub></jats:p>",
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