The growth of a short edge crack during more than 14000 cycles of fatigue loading was investigated in detail. An edge crack, in a semi-infinite body with no pre-existing obstacles present, was modelled in a boundary element approach by a distribution of dislocation dipoles. The fatigue cycles were fully reversed (R = -1), and the load range was well below the threshold for long fatigue cracks. The developing local plasticity consisted of discrete edge dislocations that were emitted from the crack tip. The movements of discrete dislocations were restricted to slip along preferred slip planes. The present model was restricted to a 2-dimensional plane strain problem with a through-thickness crack, assuming no 3-dimensional irregularities. A remote load was applied perpendicular to the crack extension line, and the material parameters were those of a body-centered cubic crystal structure. The competition between influence of the global loading on and local shielding of the crack tip governs the crack growth. The growth rate increased in discrete steps with short periods of retardation, from approximately the size of Burgers vector, b, up to 25b per cycle as the length of the crack was tripled. The plastic zone changed from having an elongated, slender form to include a low angle grain boundary, which, eventually, divides into two parts. The crack growth was found to change from constant acceleration to constant growth rate as the event of the low-angle grain boundary split was approached. The results were compared to long crack characteristics, for which linear elastic fracture mechanics and Paris law could be used to predict fatigue crack growth. The exponent in Paris law varies between 1 and 0 in the present study, i.e. smaller than typical values for ductile body-centered cubic materials. The ratio between static and cyclic plastic zone sizes was found to increase during crack growth, and the angle of the general plastic zone direction increased, showing a tendency towards long crack values. The characteristics of the simulated crack growth, found in the present study, were typical for belowthreshold growth, with slow acceleration, constant growth rate, and, eventually, either arrest or transition to long crack growth behaviour, as reported in the literature.

Growth of a Short Fatigue Crack – a Long Term Simulation using a Dislocation Technique. C.Bjerkén, S.Melin: International Journal of Solids and Structures, 2009, 46[5], 1196-204