Molecular dynamics (MD) simulations are performed to study the onset of fracture at the free edges of bi-material interfaces. The objective is to see whether a unified criterion could be formulated for crack initiation at interface edges with different angles or not. The simulations are facilitated with model bi-material systems interacting with Morse pair potentials. Three simulation models are considered, i.e. the interface edges with angles 45°, 90° and 135°, respectively. The simulation results show that, at the instant of crack initiation, the maximum stresses along the interfaces reach the ideal strength of the interface; also, the interface energies just decrease to below the value of the intrinsic cohesive energy of the interface. These findings revealed that the onset of fracture at the interface edges with different geometries could be controlled by the maximum stresses or the cohesive interfacial energy.