Supersonic cracks in lattice models

Abstract

We have studied cracks traveling along weak interfaces. We model them using harmonic and anharmonic forces between particles in a lattice, both in tension (Mode I) and antiplane shear (Mode III). One of our main objects has been to determine when supersonic cracks traveling faster than the shear wave speed can occur. In contrast to subsonic cracks, the speed of supersonic cracks is best expressed as a function of strain, not stress intensity factor. Nevertheless, we find that supersonic cracks are more common than has previously been realized. They occur both in Mode I and Mode III, with or without anharmonic changes of interparticle forces prior to breaking, and with or without dissipation. The extent and shape of the supersonic branch of solutions depends strongly on details such as lattice geometry, force law anharmonicity, and amount of dissipation. Particle forces that stiffen prior to breaking lead to larger supersonic branches. Increasing dissipation also tends to promote the existence of supersonic states. We include a number of other results, including analytical expressions for crack speeds in the high-strain limit, and numerical results for the spatial extent of regions where particles interact anharmonically. Finally, we note a curious phenomenon, where for forces that weaken with increasing strain, cracks can slow down when one pulls on them harder.

The dynamics of rapid fracture: instabilities, nonlinearities and length scales

“…When such enormous energy densities are reached, it is possible that an underlying premise of fracture mechanics, that energy must be transported from remote distances to enable fracture, should be re-examined. Work in this direction has, for example, demonstrated that in such circumstances supersonic tensile fracture can take place [102,126,197].…”

Microstructural effects in aqueous foam fracture

“…This is a striking illustration and confirmation of the finding Arif et al (2010Arif et al ( , 2012) that brittle cracks in foams are supersonic (cf. Guozden et al (2010)), outrunning relaxation of stress and pressure in the bulk of the foam and constantly reestablishing a localized stress distribution around their tips.…”

“…This understanding can then be used to elucidate the underlying mechanisms of fracture operating close to the crack tip and inform new microscopic models for failure of crystalline solids. The importance of microscopic structure details near crack tips has been the subject of many prominent studies (Buehler et al 2007;Livne et al 2010;Guozden et al 2010), but experimental data are hard to obtain. Foam experiments provide systems with relatively easily accessible length and time scales.…”

Dynamics of Simple Cracks

“…The analytical calculations are carried out in exactly solvable lattice models [106] and the experiments are carried out in rubber. The calculations in the figure are for a simple case of anti-plane shear (Mode III), but they have been extended to fracture in tension as well [107]. Rubber may seem an odd experimental setting for fracture mechanics, but the relation between force and displacement is nearly linear over wide range of displacements, showing that, depending upon how they are scaled and displayed, one focuses either upon conventional subsonic fractures or supersonic ruptures.…”