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FRACTFRICT Report Summary

Project ID: 267256
Funded under: FP7-IDEAS-ERC
Country: Israel

Final Report Summary - FRACTFRICT (Fracture and Friction: Rapid Dynamics of Material Failure)

The research culminated in establishing and validating a new paradigm for understanding the onset of frictional sliding (or "how things slide"), and, by extension, earthquake dynamics. We have basically shown that the onset of friction is purely a dynamic fracture process. These ideas and experiments have opened a new window into the hitherto "hidden" dynamics that take place within the microscopic plane of contact that holds two bodies together by frictional forces.
In addition, this project has provided a fundamental explanation for "how things break" - or how and why instabilities take place in cracks during brittle fracture. The origin of these instabilities has been an open question for decades. Our work has provided a detailed explanation of these important processes. In the following, a more detailed description is provided.

The Dynamics of Friction
Our work performed on frictional interfaces has introduced a new paradigm for both frictional processes and earthquakes. We first identified a variety of different modes of “Laboratory Earthquakes” and demonstrated that the traditional way of characterizing friction, via a static friction coefficient, is basically wrong; values of the friction coefficient and consequent stress changes along a slipping interface are tightly linked to changes in the dynamics of how rough interface separating the two sliding bodies rupture.
We then demonstrated that that theoretical framework that best describes interface dynamics (either earthquake or frictional rupture) is provided by fracture mechanics; the classical theory first derived to describe shear cracks in a homogeneous material provides an excellent quantitative description interface rupture. These results provide the key to a number of important questions in both earthquake dynamics and the general dynamics of frictional motion. First, they demonstrate that the transition to sliding is a well-defined fracture problem – and is not described by standard ideas of a “static” friction coefficient. This new framework now provides a new quantitative tool for the following:
1. Measuring the amount of energy dissipation that takes place at the tip of a frictional rupture moving earthquake.
2. A fundamental explanation for puzzling observations in “ice-quakes” observed in glacier movement and some earthquake sequences.
3. Quantitatively successful predictions of the magnitudes of precursory slip sequences that are the laboratory analog of natural earthquakes.
4. The first measurements and consequent validation of the equation of motion for frictional cracks (and, by extension, earthquakes)
We have also shown that the framework of fracture mechanics quantitatively describes the dynamics of lubricated interfaces; surprisingly demonstrating that rupture of lubricated interfaces actually dissipates considerably more energy than dry frictional interfaces. Recent experimental work has also delved into how “bimaterial” interfaces separated by elastically different materials lose their frictional stability. Coupling between slip and normal stress variations is unique to bimaterial interfaces. When a frictional interface is formed by even slightly different materials, we found that rupture modes unique to bimaterial interfaces dominate frictional motion. These results, anticipated for over 50 years, were the first to both characterize these modes and explicitly demonstrate the mechanism for their formation. With our collaborators, we have also shown, experimentally and theoretically that geometrically dissimilar interfaces also behave as effective bi-materials.
All in all, this body of work has revealed a new paradigm for the description of both frictional sliding and earthquake dynamics, establishing the proper fundamental conceptual framework with which to view these important processes.

The Dynamics of Fracture
In addition our above work on Friction, my group has made a number of notable contributions to our fundamental understanding of brittle fracture. These results both contribute to our understanding of the structure of the singular fields that drive fracture and show how this structure is linked to two different crack instabilities that have, until now, eluded our understanding. These contributions have been in three areas.
1. A fundamental understanding of the structure of the nonlinear singular zone surrounding the tip of moving cracks. Together with my collaborator, Prof. Eran Bouchbinder, we extended the theory of fracture mechanics to encompass the nonlinear elastic deformations that must take place at the tip of a moving crack and experimentally validated this theory. We then studied and experimentally validated how the nonlinear zone defined by this theory is modified by the existence of large external strains, which characterize the fracture of soft and tough materials.
2. We demonstrated how the nonlinear zone essentially determines the existence of the oscillatory instability of cracks that approach their asymptotic velocity. We showed how the scale of the nonlinear zone determines the wavelength of this instability. This was the first demonstration of the importance of nonlinear elasticity to crack dynamics.
3. We demonstrated how that the micro-branching instability of rapid cracks is intimately related to the above oscillatory instability. We found that both micro-branching and the oscillatory instabilities are driven by out of plane (shear) perturbations, where micro-branching necessitates a velocity-dependent finite amplitude perturbation. The critical amplitude of the perturbation goes to zero at the onset of the oscillatory instability. This work is the first explanation of dynamic crack instabilities.
4. We performed the first real-time measurements of crack front dynamics. We demonstrated the spontaneous formation of cusps along moving crack fronts, once the micro-branching instability is excited. We showed that the time scale for cusp formation corresponds to micro-branch lifetimes; while the micro-branching instability is turned on by a localized shear perturbation, these results suggest that the instability is “turned off” by the development of cusps along the crack front.

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