Collision of Stress Pulses with Obstacles and Dynamics of Fracture

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Abstract
The interaction of stress pulses with obstacles is considered not from the aspect of ``wave stability'' (scattering), but from the aspect of ``obstacle stability'' (fracture). For this purpose the equation of motion for a penny-shaped crack which is subjected to stress pulses is derived directly from Hamilton's principle of least action. This way was chosen in order to make an important result of this work, the least-action theorem for crack stability, directly traceable to this first principle of mechanics. The indicated quantum interpretation can be made plausible in this way. It is also shown that crack stability can be treated as an eigen-value problem. A cross section for material-wave interaction is derived. From the law that the action density of the pulse σ2τ/E has to be at least approximately πγ/a to fracture materials, a few applications are drawn. The conditions for supersonic fracture are indicated.

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