Three-dimensional aspects of plasticity-induced fatigue crack closure

Abstract A three-dimensional elastic-plastic finite element analysis of fatigue crack growth and closure in a middle-crack tension specimen was performed in order to investigate the crack-opening stress as a function of specimen thickness under constant amplitude loading conditions. Elastic-perfectly plastic conditions were assumed and cyclic loading was kept at R = σ min / σ max = 0.1 . Firstly, by imposing proper boundary conditions on the three-dimensional model, a plane strain analysis was carried out. The ratio of stabilized opening stress over the maximum applied stress under plane strain conditions was found to be 0.28. Secondly, the model thickness was varied under fully 3D conditions and crack-opening stresses were determined for each specimen thickness. The crack-opening stress is found to vary through the thickness for a middle-crack tension specimen. On the specimen surface and in the mid-plane the crack-opening stress levels tend to two-dimensional solutions for plane stress and plane strain conditions, respectively. A weighted average crack-opening stress was calculated for each specimen. Such weighted crack-opening stresses of a three-dimensional body lie somewhere inbetween the limiting conditions of plane stress and plane strain depending upon the specimen thickness.