Analytical study of the elastic–plastic stress fields ahead of parabolic notches under antiplane shear loading

An analytical study is carried out on the elastic–plastic stress and strain distributions and on the shape of the plastic zone ahead of parabolic notches under antiplane shear loading and small scale yielding. The material is thought of as obeying an elastic-perfectly-plastic or a strain hardening law. When the notch root radius becomes zero, the analytical frame matches the solutions for the crack case due to Hult–McClintock (elastic-perfectly-plastic material) and Rice (strain hardening material). The analytical frame provides an explicit link between the plastic stress and the elastic stress at the notch tip. Neuber’solution for blunt notches under antiplane shear is also obtained and the conditions under which such a solution is valid are discussed in detail by using elastic and plastic notch stress intensity factors. Finally, revisiting Glinka and Molski’s equivalent strain energy density (ESED), these factors are used also to give, under antiplane shear loading, the increment of the strain energy at the notch tip with respect to the linear elastic case.