Crack Size Limit and its Effects on the Shape of Local Yielding Zone at the Crack Tip

The validity range of one single parameter or K-characterization for the entire crack-tip stress and deformation fields under small-scale yielding conditions is shown to be surprisingly small. As a vehicle for demonstration purposes, an inclined crack buried in an infinite plane plate subjected to biaxial remote loadings is first analysed. The standard singular fields are found to be inadequate in characterizing, to within some reasonable accuracy, such important parameters in controlling such fracture phenomena as the hydrostatic stress, the maximum shear stress and the Mises equivalent stress or the size of the plastic zone at a crack tip. They also fail to describe, even roughly, the experimentally observed shape changes of the plastic zone under both plane stress and plane strain conditions. If, however, the non-singular term in Williams' eigenfunction series expansion is retained instead of being omitted arbitrarily, it is then found that such shape changes can be predicted quite adequately. Comparison with previous results based on elasto-plastic FEM analysis and inelastic modelling is favourable. Influences of specimen geometry configuration on the plastic zone shape are illustrated. Related topics such as the crack initiation angle prediction and fatigue crack propagation description are also discussed.