Generalization of the Kitagawa Diagram to V-Notched Members

Abstract

From a mechanical analysis of plastic yielding in V-notch stress singularities and the experimental result that the driving force of a short crack is minimum at the end of the notch cyclic plastic zone, a general formulation of the endurance limit of V-notched members as a function of the length of a precrack is derived. Kitagawa-type diagrams which depend on the notch angle ψ and the material threshold and cyclic yield stress are obtained. The results are coherent in the limit case of a crack (ψ = 0) and the classical Kitagawa diagram is shown to be the particular case when ψ tends to 180°. This suggests that a general theory should govern short crack behavior in both smooth and severe geometries. As the notch angle increases from 0 to 180°, the uncracked notch endurance limit increases progressively from a full dependence on the threshold to a full dependence on the cyclic yield stress. The critical crack length of the endurance diagram also corresponds for severe notches to the maximum length of a non-propagating crack and to the minimum amount of notch plasticity for fracture. The slope of the decrease beyond this length decreases with decreasing notch angle and vanishes in the case of a crack. While the critical crack length only depends on notch angle, the uncracked notch endurance limit decreases with increasing notch size. The lower the notch angle, the larger the size effect. On the other hand, “short” notches, for which the minimum amount of notch plasticity is not reached before general yielding, do not affect the endurance limit.