Direct bonded copper (DBC) alumina (Al2O3) substrates are used in power electronic devices in order to transfer the heat from semiconductor devices to the heat sink and to carry high electric currents. Fatigue-induced cracks in the ceramic result in a diminished heat dissipation, leading to failure of a power device. Hence, a lifetime model concerning this failure mode is necessary. In this paper, a new lifetime model including crack initiation as well as crack propagation for the fatigue fracture of Al2O3-based DBC substrates is presented. It is based on experimental crack detection techniques and finite element method (FEM) simulations including fracture mechanics. For the validation of the lifetime model, experiments are presented which show that by appropriate design of the copper edge, the lifetime of the substrates is increased substantially.