On the Δ Concept: An Investigation by Means of a Discrete Dislocation Model
SourceSome results of discrete dislocation mechanics concerning fatigue crack growth are discussed in two parts. The first part deals with the plasticity-induced crack closure under plane strain conditions. The equations describing the deformation of crack flanks induced by edge dislocations are derived. These equations predict crack face contact for an edge dislocation in the wake of a sharp crack. The principle of superposition then immediately shows that the crack flanks even may contact at blunted cracks. This is visualized first by a suitable choice of the dislocation arrangement and afterwards also by the results of simulations of the dislocation motion at a growing fatigue crack.
In the second part these simulations are investigated more closely. During the initial period of a constant-amplitude test the crack growth increment per loading cycle and the closure stress intensity are monitored. By applying Elber's ΔKeff concept a conceptual crack growth rate is calculated and is compared with the real crack growth increment per loading cycle.