Dynamics and Instabilities of Planar Tensile Cracks in Heterogeneous Media

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 γ(v) on the crack velocity is shown to destabilize the crack front if dγdv<0. Short wavelength radiation due to weak random heterogeneities tends to lead to this instability at low velocities. The implications of these results for the crack dynamics are discussed.