  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.
