Morphological instabilities of dynamic fractures in brittle solids (original) (raw)
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Branching instabilities in rapid fracture: Dynamics and geometry
Physical Review E, 2005
We propose a theoretical model for branching instabilities in 2-dimensional fracture, offering predictions for when crack branching occurs, how multiple cracks develop, and what is the geometry of multiple branches. The model is based on equations of motion for crack tips which depend only on the time dependent stress intensity factors. The latter are obtained by invoking an approximate relation between static and dynamic stress intensity factors, together with an essentially exact calculation of the static ones. The results of this model are in good agreement with a sizeable quantity of experimental data.
Dynamic Instability of Brittle Fracture
Physical Review Letters, 1999
Using Eshelby's energy-momentum tensor, it is shown that the elastic configurational force acting on a moving crack tip does not necessarily point in the direction of crack propagation. A generalization of Griffith's approach that takes into account this fact is proposed to describe dynamic crack propagation in two dimensions. The model leads to a critical velocity below which motion proceeds in a pure opening mode, while above it, it does not. The possible relevance of this instability to recent experimental observations is discussed. [S0031-9007 08705-0] PACS numbers: 62.20.Mk, 46.05. + b, 46.50. + a, 81.40.Np
Theory of dynamic crack branching in brittle materials
International Journal of Fracture, 2007
The problem of dynamic symmetric branching of a tensile crack propagating in a brittle material is studied within Linear Elastic Fracture Mechanics theory. The Griffith energy criterion and the principle of local symmetry provide necessary conditions for the onset of dynamic branching instability and for the subsequent paths of the branches. The theory predicts a critical velocity for branching and a well defined shape described by a branching angle and a curvature of the side branches. The model rests on a scenario of crack branching based on reasonable assumptions and on exact dynamic results for the anti-plane branching problem. Our results reproduce within a simplified 2D continuum mechanics approach the main experimental features of the branching instability of fast cracks in brittle materials.
Dynamic Instabilities in Fracture
Physical Review Letters, 1996
We find that moving cracks are strongly unstable against deflection in essentially all conventional cohesive-zone models of fracture dynamics. This instability is governed by detailed mechanisms of deformation and decohesion at crack tips; it cannot be detected by quasistatic far-field theories that consider only energy balance and neglect relevant dynamic degrees of freedom. Our picture of intrinsic instability is consistent with a wide range of experimental observations.
Mechanics of crack curving and branching ? a dynamic fracture analysis
International Journal of Fracture, 1985
-On presente un c r i t e r e de courbure de f i s s u r e fond& sur sa s t a b i l i t i ! d i r e c t i o n n e l l e a i n s i qu'un c r i t e r e de r a m i f i c a t i o n necessi t a n t un f a c t e u r dynamique d ' i n t e n s i t@ de c o n t r a i n t e de r a m i f i c a t i o n e t l e c r i t e r e de courbure.
Universal Aspects of Dynamic Fracture in Brittle Materials
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.
Origin of crack tip instabilities
Journal of The Mechanics and Physics of Solids, 1995
This paper demonstrates that rapid fracture of ideal brittle lattices naturally mvolves phenomena long seen m expenment, but which have been hard to understand from a contmuum point of view. These Idealized models do not mimic realistic microstructure, but can be solved exactly and understood completely. First It IS shown that constant velocity crack solutions do not exist at all for a range of velocltles startmg at zero and rangmg up to about one quarter of the shear wave speed. Next It is shown that above this speed cracks are by and large linearly stable, but that at sufficiently high velocity they become unstable with respect to a nonlinear microcracking instablhty The way this instabllity works Itself out IS related to the scenario known as mtermittency, and the basic time scale which governs It is the inverse of the amount of disslpatlon m the model. Finally, we compare the theoretical framework with some new experiments in Plexiglas, and show that all qualitative features of the theory are mlrrored in our experlmental results.
Physical Review E, 1999
We use Eshelby's energy momentum tensor of dynamic elasticity to compute the forces acting on a moving crack front in a three-dimensional elastic solid ͓Philos. Mag. 42, 1401 ͑1951͔͒. The crack front is allowed to be any curve in three dimensions, but its curvature is assumed small enough so that near the front the dynamics is locally governed by two-dimensional physics. In this case the component of the elastic force on the crack front that is tangent to the front vanishes. However, both the other components, parallel and perpendicular to the direction of motion, do not vanish. We propose that the dynamics of cracks that are allowed to deviate from straight line motion is governed by a vector equation that reflects a balance of elastic forces with dissipative forces at the crack tip, and a phenomenological model for those dissipative forces is advanced. Under certain assumptions for the parameters that characterize the model for the dissipative forces, we find a second order dynamic instability for the crack trajectory. This is signaled by the existence of a critical velocity V c such that for velocities VϽV c the motion is governed by K II ϭ0, while for VϾV c it is governed by K II 0. This result provides a qualitative explanation for some experimental results associated with dynamic fracture instabilities in thin brittle plates. When deviations from straight line motion are suppressed, the usual equation of straight line crack motion based on a Griffiths-like criterion is recovered.