Supersonic cracks in lattice models

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.