Dynamic Instability of Brittle Fracture

Philosophical Magazine B, 1998

The classical theory of fracture mechanics states that a crack propagating in an unbounded body should smoothly accelerate until it reaches the Rayleigh wave speed. We introduce here a general approach for solving the equation of motion of the crack tip. We show that the loading conditions and the geometry of the con® guration do not produce inertial e ects. The equation of motion of a propagating crack is always a ® rst-order di erential equation.

Physical Review E, 2004

We address the interaction of fast moving cracks in stressed materials with microcracks on their way, considering it as one possible mechanism for fluctuations in the velocity of the main crack (irrespective whether the microcracks are existing material defects or they form during the crack evolution). We analyze carefully the dynamics (in two space dimensions) of one macrocrack and one microcrack, and demonstrate that their interaction results in a large and rapid velocity fluctuation, in qualitative correspondence with typical velocity fluctuations observed in experiments. In developing the theory of the dynamical interaction we invoke an approximation that affords a reduction in mathematical complexity to a simple set of ordinary differential equations for the positions of the crack tips; we propose that this kind of approximation has a range of usefulness that exceeds the present context.

Physical Review Letters, 2010

Experimental Chaos, 2004

We present an experimental study of the dynamics of rapid tensile fracture in brittle amorphous materials. We first compare the dynamic behavior of "standard" brittle materials (e.g. glass) with the corresponding features observed in "model" materials, polyacrylamide gels, in which the relevant sound speeds can be reduced by 2-3 orders of magnitude. The results of this comparison indicate universality in many aspects of dynamic fracture in which these highly different types of materials exhibit identical behavior. Observed characteristic features include the existence of a critical velocity beyond which frustrated crack branching occurs 1, 2 and the profile of the micro-branches formed. We then go on to examine the behavior of the leading edge of the propagating crack, when this 1D "crack front" is locally perturbed by either an externally introduced inclusion or, dynamically, by the generation of a micro-branch. Comparison of the behavior of the excited fronts in both gels and in soda-lime glass reveals that, once again, many aspects of the dynamics of these excited fronts in both materials are identical. These include both the appearance and character of crack front inertia and the generation of "Front Waves", which are coherent localized waves 3-6 which propagate along the crack front. Crack front inertia is embodied by the appearance of a "memory" of the crack front 7,8 , which is absent in standard 2D descriptions of fracture. The universality of these unexpected inertial effects suggests that a qualitatively new 3D description of the fracture process is needed, when the translational invariance of an unperturbed crack front is broken.

Physical Review Letters, 2014

The temporal evolution of mechanical energy and spatially-averaged crack speed are both monitored in slowly fracturing articial rocks. Both signals display an irregular burst-like dynamics, with power-law distributed uctuations spanning a broad range of scales. Yet, the elastic power released at each time step is proportional to the global velocity all along the process, which enables dening a material-constant fracture energy. We characterize the intermittent dynamics by computing the burst statistics. This latter displays the scale-free features signature of crackling dynamics, in qualitative but not quantitative agreement with the depinning interface models derived for fracture problems. The possible sources of discrepancies are pointed out and discussed.

Physical Review Letters, 1996

Measurements in PMMA of both the energy flux into the tip of a moving crack and the total surface area created via the microbranching instability indicate that the instability is the main mechanism for energy dissipation by a moving crack in brittle, amorphous material. Beyond the instability onset, the rate of fracture surface creation is proportional to the energy flux into the crack. At high velocities microbranches create nearly an order of magnitude larger fracture surface than smooth cracks. This mechanism provides an explanation for why the theoretical limiting velocity of a crack is never realized.

Journal of the Mechanics and Physics of Solids, 1998

MRS Bulletin, 2001

Arxiv preprint arXiv:0911.0173, 2009

Cracks are the major vehicle for material failure and often exhibit rather complex dynamics. The laws that govern their motion have remained an object of constant study for nearly a century. The simplest kind of dynamic crack is a single crack that moves along a straight line. We first briefly review the current understanding of this "simple" object. We then critically examine the assumptions of the classic, scale-free theory of dynamic fracture and note when it works and how it may fail if certain assumptions are relaxed. Several examples are provided in which the introduction of physical scales into this scale-free theory profoundly affects both a crack's structure and the resulting dynamics.

Nature, 1996

What drives physicists to study cracks? There is certainly some attraction in being able to tell the children one is getting paid to break things. There is also a perverse pleasure in learning the physical laws underlying irreversible change, decay, and destruction. A paper of Eran Sharon, Steven Gross, and Jay Fineberg, "Energy Dissipation in Dynamic Fracture" which appeared on 18 March in Physical Review Letters contains an answer to an old and deceptively simple question, "How fast do things break, and why?" The first scientific attempts to answer this question go back to research of Hubert Schardin and Wolfgang Struth in 1937[1], who used sparks to take photographs of cracks in less than one ten-millionth of a second. They concluded that "the maximum velocity of propagation of glass fractures is to be considered a physical constant," and they measured crack speeds that were approximately one quarter the speed of sound in many different glasses. Some time after these experiments came theories of crack motion, which firmly insisted that cracks should move at about twice the speed observed. The classic theory[2], developed by B. V. Kostrov, J. D. Eshelby, and L. B. Freund, left little room for uncertainty. Cracks leave two new surfaces behind them. The speed at which vibrations travel across a free surface is the Rayleigh wave speed, a speed governing the motion of sound when one raps one's knuckles on the top of a table, or the speed at which earthquakes travel on the surface of the earth. Cracks, said the theory, should move at this Rayleigh wave speed too-but it does not happen. In Plexiglas, for example, the Rayleigh wave speed is around 1000 metres per second, but cracks never exceed 600 metres per second. This descrepancy was widely acknowledged to