A molecular-dynamics model for crack propagation under steady-state conditions is used to study dynamic instabilities along a grain boundary in aluminum that occur when the crack speed approaches 1/3 of the material's Rayleigh wave speed. Instead of crack branching, as is characteristic for a crack propagating in a homogeneous environment, the instability of an intergranular crack results in a periodic series of dislocation bursts. These bursts limit the crack speed and produce velocity oscillations with a large increase in energy dissipation that increases the grain boundary toughness.