Dynamics and Instabilities of Planar Tensile Cracks in Heterogeneous Media

Abstract

The dynamics of tensile crack fronts restricted to advance in a plane are studied. In an ideal linear elastic medium, a propagating mode along the crack front with a velocity slightly less than the Rayleigh wave velocity, is found to exist. But the dependence of the effective fracture toughness $\Gamma (v)$ on the crack velocity is shown to destabilize the crack front if $(d\Gamma )/(dv)<0$. Short wavelength radiation due to weak random heterogeneities leads to this instability at low velocities. The implications of these results for the crack dynamics are discussed.

12 pages

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