Interplay between Process Zone and Material Heterogeneities for Dynamic Cracks

Abstract

Using an elastodynamic boundary integral formulation coupled with a cohesive model, we study the problem of a dynamic rupture front propagating along an heterogeneous plane. We show that small-scale heterogeneities facilitate the supershear transition of a mode-II crack. The elastic pulses radiated during front accelerations explain how microscopic variations of fracture toughness change the macroscopic rupture dynamics. Perturbations of dynamic fronts are then systematically studied with different microstructures and loading conditions. The process zone size is the intrinsic length scale controlling heterogeneous dynamic rupture. The ratio of this length scale to asperity size is proposed as an indicator to transition from quasihomogeneous to heterogeneous fracture. Moreover, we discuss how the shortening of the process zone size with increasing crack speed brings the front to interact with smaller details of the microstructure. This study shines new light on recent experiments reporting perturbations of dynamic rupture fronts, which intensify with crack propagation speed. DOI: 10.1103/PhysRevLett.119.144101 Introduction.-Our modern understanding of fracture arose from Griffith [1] and Irwin [2] which viewed crack propagation as a thermodynamic process where, at equilibrium, the energetic cost of creating new surfaces in the material is balanced by the release of strain energy subsequent to crack advance. This theoretical framework known as linear elastic fracture mechanics (LEFM) has been successfully used over the last 50 years to predict the stability of flaws in engineering materials. Consequently LEFM was extended to cracked bodies far from equilibrium, i.e., to dynamic fracture mechanics [3,4]. Experiments on brittle solids showed that this dynamic theory of fracture gives good prediction for slow crack propagation but is unsuitable to describe fast rupture events where the crack front speed is a significant fraction of material shear wave speed c s . In particular, linear elastic theory overestimates the propagation speed and significantly underestimates the dissipated energy. For a review of dynamic fracture experiments, the reader is referred to [5][6][7][8][9]. A three-stage transition is universally observed within brittle materials, usually referred to as "mirror," "mist," and "hackle" in reference to the postmortem appearance of fracture surface. At low rupture velocity, fracture surfaces are planar and smooth (mirror) and crack dynamics is thereby well predicted by LEFM theory. As crack speed increases, the rupture remains in plane but fracture surface roughens (mist), followed by a stage characterized by the formation of out-of-plane microbranches (hackle), and finally the onset of macroscopic branching. This transition observed in various brittle materials [7,10] and at different scales [11,12] explains how linear elasticity fails at describing fast rupture events where the front starts to interplay with the microstructure and/or dynamic instabilities

Robust Estimation of Rupture Properties at Propagating Front of Laboratory Earthquakes

“…First, we have assumed that slight fluctuation of stress or frictional properties does not significantly affect the overall rupture behavior, which allows for a simplified numerical modeling of laboratory earthquakes. One should bear in mind that this condition may not always be satisfied in laboratory earthquakes, and special care needs to be taken when strongly heterogeneous features emerge (Barras et al, ; Bayart et al, ). Second, we have only modeled one half of symmetrically expanding ruptures to reproduce the major rupture phase of laboratory earthquakes in a selected time window.…”

Supershear bursts in the propagation of a tensile crack in linear elastic material

“…At t = 0, the crack reaches the critical size L c where G(v = 0, L = L c ) exactly equates the fracture energy G H c and starts to propagate dynamically at a speed v > 0. L c corresponds then to the largest stable crack size [39,43,48] given by where E and ν respectively denote the Young's modulus and Poisson's ratio of the elastic solid, and G H c is the fracture energy of the homogeneous portion of the fracture plane. In an infinite homogeneous solid, Freund [1] showed that the energy release rate evolves with propagation speed as G…”

“…Similarly to supersonic aircraft, elastic waves radiated from supershear cracks gather to form shock wave fronts, also referred to as Mach cones, leading to particularly violent earthquakes [32][33][34][35][36]. Several studies have described how local variation in toughness or elastic properties can precisely favor the supershear transition of a mode II crack [37][38][39][40][41][42][43]. Despite the relative rarity of supershear earthquakes reported in nature, recent experiments [44] suggest that shortlived supershear events may frequently occur at small scales of crustal fault, out of the resolution of seismic inversion, yet significantly impacting the rupture dynamics.…”

Brittle Fracture Theory Describes the Onset of Frictional Motion

“…Later numerical work [10] found that a sufficiently strong shear stress peak can overcome interfacial strength and nucleate a daughter crack that could propagate at supershear velocities. Supershear ruptures have been observed along natural fault planes [34,55], in laboratory experiments [26,85,99,111,127,151,154] and have been extensively investigated by numerical simulations [1,4,20,43,58,65,67,87,88,118]. A further description, however, is beyond the scope of this review.…”