The quasistatic extension of a shear crack in a viscoelastic medium *

Summary. We consider the quasistatic extension of an anti‐plane shear crack with a zone of slip‐weakening. The crack is imbedded in a medium that has a standard linear viscoelastic rheology; the Kelvin and Maxwell solids are limiting cases. In general, three different crack histories can be identified for a crack of a given initial length: if the stress drop is smaller than some lower critical value, the crack does not extend. For stress drops larger than some upper critical value, the crack extends at velocities close to the S ‐wave velocity; we call this an infinite rupture velocity and the crack appears to grow instantaneously. For a stress drop in the interval between these two bounds, the crack extends quasistatically with finite velocities. For the case of the standard linear viscoelastic body in the quasistatic regime, the crack increases to a finite length and the rupture velocity becomes infinite after a finite time interval; after a finite time interval, both the crack length and the rupture velocity tend to infinity for a Kelvin body; no matter how small the stress drop is, a crack in a Maxwell solid will eventually extend to a critical length, at which point rupture occurs instantaneously. The breakout time, which is the time required for a growing crack to accelerate to infinite rates of extension, decreases monotonically with increasing stress drop.