Rupture velocity of plane strain shear cracks

Abstract

Propagation of plane strain shear cracks is calculated numerically by using finite difference equations with second-order accuracy. The rupture model, in which stress drops gradually as slip increases, combines two different rupture criteria: (1) slip begins at a finite stress level; (2) finite energy is absorbed per unit area as the crack advances. Solutions for this model are nonsingular. In some cases there may be a transition from rupture velocity less than Rayleigh velocity to rupture velocity greater than shear wave velocity. The locus of this transition is surveyed in the parameter space of fracture energy, upper yield stress, and crack length. A solution for this model can be represented as a convolution of a singular solution having abrupt stress drop with a 'rupture distribution function.' The convolution eliminates the singularity and spreads out the rupture front in space-time. If the solution for abrupt stress drop has an inverse square root singularity at the crack tip, as it does for sub-Rayleigh rupture velocity, then the rupture velocity of the convolved solution is independent of the rupture distribution function and depends only on the fracture energy and crack length. On the other hand, a crack with abrupt stress drop propagating faster than the shear wave velocity has a lower-order singularity. A supershear rupture front must necessarily be spread out in space-time if a finite fracture energy is absorbed as stress drops.

Modeling Slope Instability as Shear Rupture Propagation in a Saturated Porous Medium

“…Here, rupture propagation is below the Rayleigh wave speed c r (for u = 0.483 , c r 0.95c s ) until about the last time step plotted in Figure 3b where the rupture begins a transition to rupture propagation beyond the shear wave speed (so-called supershear rupture), first in the downslope direction and shortly followed by a transition in the upslope direction (not shown). (Andrews 1976) and here r = 0.32 (note r = 1 / (1 + S) where S is a similar measure commonly used in earthquake rupture studies).…”

Electromechanical influence of crack velocity at bifurcation for poled ferroelectric materials

“…Moreover, it is doubtful that local stress state is one of pure in-plane shear despite the fact that it prevails globally at distances far away from the crack tip. Should the main crack be macroscopic and the nucleated crack be microscopic [2], then there is no valid reason why the same event would not occur for an in-plane extensional crack. Equally unconvincing is the explanation offered by the finite cohesive traction shear crack model [3] where a finite peak shear stress was developed ahead of the tip.…”

Dynamic Propagation Problems of Mode Iii Semi-Infinite Crack

“…However, a lot of engineering structures are under the conditions of dynamic loadings and the static theory can't effectually III resolve a series of dynamic queries, so it is indispensable to study the fracture dynamics problems (Sih, 1968;Kostrov, 1964;Freund, 1998;Sih and MacDonald, 1974;Srolovitz and Source, 1997). A lot of researches on mode III crack dynamic propagation problems were performed cautiously (Freund, 1998;Sih and MacDonald, 1974;Srolovitz and Source, 1997;Gao, 1996;Andrew, 1976;Rosakis et al, 1999;Tang and Sih, 2004). In view of the complexity, cockamamie and difficulty in mathematical operations, fracture dynamics problems are not investigated enough thoroughly (Sih, 1968;Kostrov, 1964;Freund, 1998;Sih and MacDonald, 1974;Srolovitz and Source, 1997;Broberg, 1960;RubinGonzalea and Mason, 2000) and numerical solutions acquired (Sih and MacDonald, 1974;Sih, 1973;1991;Fedelinski et al, 1997;Wang et al, 1992;Knauss, 1987;Wang, 1992;Ranjith and Narasimhan, 1996) were much more than analytical solutions (Nian-Chun et al, 2004;2005;2006).…”