Recent Milestones in Unraveling the Full-Field Structure of Dynamic Shear Cracks and Fault Ruptures in Real-Time: From Photoelasticity to Ultrahigh-Speed Digital Image Correlation

The last few decades have seen great achievements in dynamic fracture mechanics. Yet, it was not possible to experimentally quantify the full-field behavior of dynamic fractures, until very recently. Here, we review our recent work on the full-field quantification of the temporal evolution of dynamic shear ruptures. Our newly developed approach based on digital image correlation combined with ultrahigh-speed photography has revolutionized the capabilities of measuring highly transient phenomena and enabled addressing key ques- tions of rupture dynamics. Recent milestones include the visualization of the complete displacement, particle velocity, strain, stress and strain rate fields near growing ruptures, capturing the evolution of dynamic friction during individual rupture growth, and the detailed study of rupture speed limits. For example, dynamic friction has been the big- gest unknown controlling how frictional ruptures develop but it has been impossible, until now, to measure dynamic friction during spontaneous rupture propagation and to understand its dependence on other quantities. Our recent measurements allow, by simul- taneously tracking tractions and sliding speeds on the rupturing interface, to disentangle its complex dependence on the slip, slip velocity, and on their history. In another application, we have uncovered new phenomena that could not be detected with previous methods, such as the formation of pressure shock fronts associated with “supersonic” propagation of shear ruptures in viscoelastic materials where the wave speeds are shown to depend strongly on the strain rate

Spatiotemporal Properties of Sub‐Rayleigh and Supershear Ruptures Inferred From Full‐Field Dynamic Imaging of Laboratory Experiments

Many earthquakes propagate at sub‐Rayleigh speeds. Earthquakes propagating at supershear speeds, though less common, are by far more destructive. Hence, it is important to quantify the motion characteristics associated with both types of earthquake ruptures. Here we report on the spatiotemporal properties of dynamic ruptures measured in our laboratory experiments using the dynamic digital image correlation technique. Earthquakes are mimicked by the frictional rupture propagating along the interface of two Homalite plates. Digital images of the propagating ruptures are captured by an ultrahigh‐speed camera and processed with digital image correlation in order to produce sequences of evolving displacement and velocity maps. Our measurements reveal the full‐field structure of the velocity components, bridge the gap between previous spatially sparse velocimeter measurements available only at two to three locations, and enable us to quantify the attenuation patterns away from the interface

Observations of transient high temperature vortical microstructures in solids during adiabatic shear banding

By using a unique infrared high-speed camera especially constructed for recording highly transient temperature fields at the microscale, we are able to reveal the spatial and temporal microstructure within dynamically growing shear bands in metals. It is found that this structure is highly nonuniform and possesses a transient, short range periodicity in the direction of shear band growth in the form of an array of intense "hot spots" reminiscent of the well-known, shear-induced hydrodynamic instabilities in fluids. This is contrary to the prevailing classical view that describes the deformations and the temperatures within shear bands as being essentially one-dimensional fields. These observations are also reminiscent of the nonuniform structure of localized shear regions believed to exist, at an entirely different length scale, in the earth's lower crust and upper mantle

Off-fault tensile cracks: A link between geological fault observations, lab experiments, and dynamic rupture models

We examine the local nature of the dynamic stress field in the vicinity of the tip of a semi-infinite sub-Rayleigh (slower than the Rayleigh wave speed, c_R) mode II crack with a velocity-weakening cohesive zone. We constrain the model using results from dynamic photoelastic experiments, in which shear ruptures were nucleated spontaneously in Homalite-100 plates along a bonded, precut, and inclined interface subject to a far-field uniaxial prestress. During the experiments, tensile cracks grew periodically along one side of the shear rupture interface at a roughly constant angle relative to the shear rupture interface. The occurrence and inclination of the tensile cracks are explained by our analytical model. With slight modifications, the model can be scaled to natural faults, providing diagnostic criteria for interpreting velocity, directivity, and static prestress state associated with past earthquakes on exhumed faults. Indirectly, this method also allows one to constrain the velocity-weakening nature of natural ruptures, providing an important link between field geology, laboratory experiments, and seismology

On the Scale of the Nonlinear Effect in a Crack Problem

When crack problems are analyzed on the basis of nonlinear theories, such as finite elasticity or deformation theory of plasticity, it is inevitable that nonlinear effects will predominate near a crack-tip, even if the loads are small. The most favorable circumstance in this regard occurs when the loads are so small that the zone of significant nonlinearity lies within the region of validity of the near-tip approximation to the global solution of the associated linearized crack problem. This situation - called small-scale yielding for crack problems in plasticity - permits simplifications in analysis which are often decisive; see, e.g., Knowles (1977) and Rice (1968). Insofar as we know, there are no analytical estimates available of the level of load below which nonlinear effects are guaranteed to be small-scale in the above sense. Indeed, even a precise version of the question seems to be lacking. In the present note we formulate and answer such a question for an especially cooperative crack problem; that corresponding to finite anti-plane shear of an infinite medium containing a crack of finite length for an elastic material of Neo-Hookean type. The associated boundary value problem is a linear one for Laplace's equation and thus can be solved globally. Nevertheless, there is a significant nonlinear effect of Kelvin type in the stress field. We give a condition under which this nonlinear response occurs on a small scale near the crack tips

Subsonic and intersonic shear rupture of weak planes with a velocity weakening cohesive zone

A substantial effort has been devoted in the past toward modeling earthquake source mechanisms as dynamically extending shear cracks. Most of the attention was focused on the subsonic crack speed regime. Recently, a number of reports have appeared in the seismological literature citing evidence of intersonic rupture speeds during shallow crustal earthquakes. In the first part of this paper, we discuss direct experimental observations of intersonic in-plane shear crack growth along a weak plane joining two homogeneous, isotropic, linear elastic plates. Associated with the primary intersonic crack and at locations behind the propagating shear crack tip, a series of secondary tensile cracks, at a steep angle to the shear crack plane, were also observed. Motivated by these observations, subsonic and intersonic mode II crack propagation with a velocity weakening cohesive zone is analyzed in the main body of the paper. A cohesive law is assumed wherein the cohesive shear traction is either a constant or decreases linearly with the local slip rate, the rate of decrease governed by a slip rate weakening parameter. The cohesive shear traction is assumed to vanish when the crack tip sliding displacement reaches a characteristic breakdown slip. It is shown that a positive energy flux into the rupture front is possible in the entire intersonic regime. The influence of shear strength and of the weakening parameter on the crack propagation behavior is investigated. Crack tip stability issues are also addressed, and favorable speed regimes are identified. Estimates of the slip rate weakening parameter are obtained by using the theoretical model to predict the angle of the secondary cracks. The rest of the parameters are subsequently estimated by comparing the isochromatic fringe patterns (contours of maximum in-plane shear stress) predicted by the solution with those recorded experimentally

Understanding dynamic friction through spontaneously evolving laboratory earthquakes

Friction plays a key role in how ruptures unzip faults in the Earth’s crust and release waves that cause destructive shaking. Yet dynamic friction evolution is one of the biggest uncertainties in earthquake science. Here we report on novel measurements of evolving local friction during spontaneously developing mini-earthquakes in the laboratory, enabled by our ultrahigh speed full-field imaging technique. The technique captures the evolution of displacements, velocities and stresses of dynamic ruptures, whose rupture speed range from sub-Rayleigh to supershear. The observed friction has complex evolution, featuring initial velocity strengthening followed by substantial velocity weakening. Our measurements are consistent with rate-and-state friction formulations supplemented with flash heating but not with widely used slip-weakening friction laws. This study develops a new approach for measuring local evolution of dynamic friction and has important implications for understanding earthquake hazard since laws governing frictional resistance of faults are vital ingredients in physically-based predictive models of the earthquake source

A three-dimensional numerical investigation of fracture initiation by ductile failure mechanisms in a 4340 steel

Fracture initiation in ductile metal plates occurs due to substantial tunneling of the crack in the interior of the specimen followed by final failure of side ligaments by shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. This phenomenon is clearly exhibited in a recent experimental investigation [8] performed on pre-notched plates of a ductile heat treatment of 4340 carbon steel. Experimental evidence obtained in [8] suggests that tunneling begins at an average value of J which is significantly lower than the J value at which gross initiation is observed on the free surface. In the present work, fracture initiation in the 4340 steel specimens used in [8] is analyzed by performing a 3-dimensional numerical simulation. A damage accumulation model that accounts for the ductile failure mechanisms of void nucleation, growth, and void coalescence is employed. Results indicate that incipient Cmaterial failure at the center-plane of the 3-dimensional specimen is predicted quite accurately by this computation. Also, good agreement between results obtained at the center-plane of the 3-dimensional specimen and a plane strain analysis, suggests that a local definition of J can be used to characterize fracture initiation in the center-plane of the specimen. Finally, radial and thickness variations of the stress and porosity fields are examined with view of understanding the subsequent propagation of the failure zone

Experimental investigation of dynamic mixed-mode fracture initiation

The use of a coherent gradient sensing (CGS) apparatus is explored in dynamic fracture mechanics investigations. The ability of the method to accurately quantify mixed-mode crack tip deformation fields is tested under dynamic loading conditions. The specimen geometry and loading follow that of Lee and Freund who give the theoretical and numerical mixed mode K values as a function of time for the testing conditions. The CGS system’s measurements of KI and KII are compared with the predicted results, and good agreement is found