Intersonic Bilateral Slip

Abstract

S U M M A R YSymmetric "bilateral slip at constant intersonic velocity is investigated. Linear isotropic elasticity is assumed, and the idealization of a point-sized process region is adopted. The energy release rate is calculated for a slip propagation velocity equal to lh times the S-wave speed, which is the intersonic velocity for which stresses and strains are square-root singular in this idealization. The result shows a smaller energy release rate than at low subRayleigh velocities, but in general not much smaller: it equals approximately the energy release rate at about 95 per cent of the Rayleigh wave velocity for Poisson's ratio around 0.25. For other intersonic velocities the results were modified to include a finite process region, by using previously obtained results concerning steady-state propagation. In this way the energy flow to the process region can be obtained as a function of the slip propagation velocity in the whole intersonic region for each set of process region characteristics assumed. Numerical calculations, assuming a Barenblatt process region model, indicate little sensitivity to process region size and a somewhat flat maximum close to f i times the S-wave speed.

Transition of mode II cracks from sub-Rayleigh to intersonic speeds in the presence of favorable heterogeneity

“…We note that propagation of a secondary crack before the intersonic transition is not only nonlinear (due to friction) but also highly unsteady dynamic process and its analytical treatment, beyond qualitative arguments provided in this study, may be rather difficult. However, once crack tips become intersonic, their behavior is consistent with analytical inferences for intersonic cracks (e.g., Burridge et al, 1979;Freund, 1979;Broberg, 1994Broberg, , 1995Huang and Gao, 2001;Samudrala et al, 2002;Antipov and Willis, 2003).…”

“…Significant advances have been made in understanding various theoretical aspects of crack propagation with speeds larger than c R (e.g., Burridge et al, 1979;Freund, 1979;Broberg, 1994Broberg, , 1995Huang and Gao, 2001;Samudrala et al, 2002;Antipov and Willis, 2003). In part, it has been established that cracks cannot propagate with speeds in the interval ½c R ; c s due to energetic constraints, and that intersonic cracks in models with finite tractions, constant fracture energy, and uniform prestress would tend to accelerate to the dilatational wave speed c p .…”

Identifying the unique ground motion signatures of supershear earthquakes: Theory and experiments

“…Close scrutiny of the entire class of self-similar analytical solutions for supershear ruptures (for example Burridge, 1973;Broberg, 1994) also reveals that a secondary rupture travels behind the main crack tip at speeds approaching the Rayleigh wave speed. This feature, herein referred to as a trailing Rayleigh rupture, also accompanies spontaneously propagating ruptures and cannot be captured by steady-state models.…”

“…Problems of this type are better addressed by a more-general class of self-similar analytical solutions for supershear ruptures (for, e.g., Burridge, 1973;Broberg, 1994), which incorporate unsteady cohesive zone models. Experimental investigations presented in this chapter confirm the presence of the trailing Rayleigh rupture and examine the ground motion induced by this rupture following the passage of the leading supershear rupture.…”

Transient near tip fields in crack dynamics

“…Therefore, for moving cracks speed is another important factor that is affecting the SIF approximation accuracy. Having this in mind one may wish to revise Freund's solution for the limiting speed of crack propagation [22] for mode I cracks and solutions for permitted speeds for shear cracks [4,[22][23][24][25]. Though we are unlikely to question the fact that C R is the limiting speed for mode I cracks in problems without local scale and microstructure, as there are other physical and empirical reasons why mode I cracks cannot propagate with greater speeds, obviously, revision of solutions for shear crack propagation can help better understand recent experiments on ultrasonic dynamic cracking [26].…”