Effects of pressure sensitivity and notch geometry on notch‐tip fields

Abstract

Plane‐strain stress and slip‐line fields near the sharp and round tips of wedge‐shaped notches in perfectly plastic pressure‐sensitive materials are investigated to illustrate the effects of pressure sensitivity and notch geometry on notch‐tip fields. The Drucker‐Prager yield criterion is adopted to describe the material yielding behavior. Notch‐tip stress and slip‐line fields are first established for a sharp notch. Then the notch‐tip stress and slip‐line fields for a round notch tip are obtained. The results indicate that for sharp wedge‐shaped notches, as the pressure sensitivity increases, the opening stress and hydrostatic tension ahead of the tip decrease. As the wedge angle increases, the opening stress and hydrostatic tension ahead of the tip decrease. For round wedge‐shaped notches, as the pressure sensitivity increases, the extent of the exponential spiral zone ahead of the tip increases. As the wedge angle increases, the extent of the exponential spiral zone ahead of the tip decreases and the maximum opening stress and hydrostatic tension ahead of the tip decrease. The closed‐form notch‐tip stress solutions are useful for design of plastic structural components.