A crack in a linear-elastic material under mode II loading, revisited

A sharp crack in a two-dimensional infinite linear-elastic material, under pure shear (mode II) loading is re-examined. Several criteria have been proposed for the prediction of the onset and direction of crack extension along a path emanating from the tip of the initial crack. These criteria date back some three decades and are well documented in the literature. All the predictions from the different criteria are close and indicate that the crack extension takes a direction at an angle of ≈ ?70° measured counterclockwise from the positive x -axis, in the case of a remotely applied positive shear stress. However, the possibility seems to have been overlooked that the crack extension may initiate not from the crack tip itself, but instead may initiate on the free surface at an infinitesimal distance behind the crack tip. The effect of crack tip plasticity on the relevant stresses in the region of the crack tip is investigated by the application of an elastic–plastic finite element program.