A THEORY OF FATIGUE-CRACK INITIATION

Consider two adjacent planes where positive and negative dislocations are accumulated by a ratcheting mechanism. The dislocation dipoles are increased by each cycle of loading. The total free energy of the system increases with the fatigue cycle number owing to the increase in elastic strain energy. It is shown that there exists a critical fatigue cycle number beyond which the initial state of dislocation dipole accumulation becomes energetically unstable. The dislocation dipoles are annihilated to form a crack (microvoid). The analysis provides the S-N curves for the crack initiation. The theory is applied to the fatigue microvoid formation at the interface between a thin film and a substrate. Then the theory is compared with the plane bending fatigue tests to specimens of carbon steel coated by Au in plating. The theory agrees with the experiments qualitatively very well. However, experimental data show 10(18) times higher crack initiation cycle than the theory. This quantitative disagreement is discussed in terms of the irreversibility of dislocation accumulation.