A dislocation model for the two critical stress intensities required for threshold fatigue crack propagation

We have examined the variations, with decreasing load ratio, of threshold peak and cyclic stress intensities required for fatigue crack growth in stage I (mainly mode II loading) using a simple model simulating dislocation motion near a crack tip. In this model the crack grows by dislocations running into the crack during loading and unloading phases. Initially we have studied the behaviour of a crack with a dislocation source relatively far away from the crack tip. Crack propagation rates showed a Paris regime at high ΔK, and an abrupt threshold value ΔK_th below which no crack growth occurred. The variation with load ratio of the peak (K_th) and cyclic (ΔK_th) stress intensities at the fatigue threshold showed that two different processes controlled the behaviour. At high load ratios dislocations are generated readily during loading and the threshold is controlled by the need for sufficient unloading to allow dislocations to run back into the crack, so that the criterion ΔK ≥ ΔK∗ results. At negative load ratios it is the generation of dislocations during the loading phase that controls the threshold condition, since once generated, the large unloading and reversed loading easily forces dislocations back to the crack. Under these conditions the threshold criterion becomes K_max ≥ K∗.