Comparison of methods for obtaining crack-tip stress distributions in an elastic-plastic material

Under linear elastic and elastic-plastic conditions the K field and the HRR (Hutchinson-Rice-Rosengren) field respectively are expected to provide an accurate representation of the stress field close to the crack tip in an elastic-plastic material. It has recently been proposed in French and UK defect assessment procedures that the Neuber method, originally developed for sharply curved notches, provides an alternative approach to estimate both notch and crack-tip stress fields, for use in conjunction with the sigma- d (σd) method to predict creep crack initiation times. In this work, the crack-tip stress fields under plane strain conditions, predicted from the Neuber approach, are compared with the HRR and K fields as well as those obtained from full-field finite element calculations. A compact tension and a single edge notched tension specimen have been examined; the material model used is the Ramberg-Osgood, power law plasticity model. As expected, the K field and HRR field have been found to provide a good representation of the near-tip fields at low and high loads respectively. Satisfactory solutions have also been obtained through the use of the reference stress to estimate the amplitude of the crack-tip stress in conjunction with the HRR field. The Neuber approach provides a good estimate of the equivalent (von Mises) stresses over the full range of load levels. However, but the use of the Neuber approach directly to predict the maximum principal stress in the plane of the crack provides a non-conservative prediction. A modified Neuber method, using an appropriate scaling function, has been proposed to determine the maximum principal stress in the plane of the crack from the equivalent (von Mises) stress predicted by the Neuber approach. Using the proposed method, a significantly improved estimate of the crack-tip stresses is obtained.