Modelling the threshold conditions for propagation of stage I fatigue cracks

Under near threshold conditions fatigue cracks often propagate along crystallographic slip planes with a marked mode II contribution to the loading, particularly when the crack is short. We present here a model for this stage I fatigue crack in which a mode II crack generates dislocations either through activation of a source ahead of the crack or through direct emission from the tip, and the motion and interaction of these dislocations are then simulated dynamically throughout the load–unload cycle. The crack is assumed to grow when cyclic displacement occurs at the crack tip, so that the condition that at least one emitted dislocation per cycle must return to the crack tip, allows the threshold cyclic stress intensity (Δ K th) to be calculated. In accord with experimental data we find that Δ K th increases with decreasing load ratio. At high load ratio the fatigue threshold is best defined by the need for the cyclic stress intensity to exceed some critical value, while at low load ratio, the requirement is that the maximum stress intensity exceeds a second critical value.