On self-sustaining fracture waves

The breakage of a tiny tail on a head of solid glass just removed from a glass bath and treated by fluoric acid (a "Batavian tear") makes the tear explode into a cloud of dust with the sound like that of a shot. This explosion reminds that of TNT but TNT disintegrates into molecules of the order of 10^-9 m while the glass particles of dust are of the order of 10^-6 m and have the same chemical composition as the solid glass. Rock bursts in deep mines of South Africa and Russia represent another example of the sudden, explosive self-destruction. To explain this phenomenon the theory of self-sustaining fracture waves was suggested earlier by Galin and Cherepanov (1966). This theory was based on the analogy with detonation waves later criticized as insufficiently substantiated. The approach presented below is based only on the conservation laws and does not use any analogies. It proves that the self-sustaining fracture wave can propagate only in compressed structures at the speed of longitudinal elastic waves.