Cylindrical specimens of polycrystalline alumina and sodium glass with a deep circumferential notch were loaded cyclically under compression, and the fatigue crack-propagation processes in the notch root were studied. The studies showed that debris and a fatigue crack are formed in the notch root of alumina, but not in glass. There, only fragmentation takes place at the crack tip; glass chips are formed which surround the notch. The influence of microstructural inhomogeneities on fatigue crack formation and propagation as well as the consequences for material scientists and engineers are discussed on the basis of a simple model.