Plane-stress fields for sharp notches in pressure-sensitive materials

The effect of pressure sensitive yield on materials toughness can be determined by investigating stress fields around cracks and notches. In this work, fully-developed plastic stress fields around sharp wedge-shaped notches of perfectly-plastic pressure-sensitive materials are investigated for plane-stress case and Mode 1 loading condition. The pressure-sensitive yielding behavior is represented using the Drucker-Prager criterion. Using equilibrium equations, boundary conditions, and the yield criterion, closed-form expressions for stress fields are derived. The analysis covers the gradual change in the notch angle and compares it with the limiting case of a pure horizontal crack. Effects of notch geometry and pressure sensitivity on stress fields are examined by considering different specimen geometries, as well as different levels of pressure sensitivity. Results indicate that while the stress values directly ahead of the notch-tip are not affected, the extent of stress sector at notch front is reduced, thereby causing increase in the radial stress value around the notch. As the pressure sensitivity increases the reduction of the stress sector directly ahead of the notch tip is more evident. Also, for high pressure sensitivity values, introduction of the notch angle reduces the variation of the stress levels. Results are useful for design of structural components. (author)