Analytical study on the mode III stress fields due to blunt notches with cracks

This work presents an analytical study on the stress fields induced by cracks nucleated at the tip of radiused notches under antiplane shear and torsion loadings. Closed-form solutions for both shallow and deep notches are derived leveraging a combination of proper curvilinear coordinate systems and the complex potential method for antiplane elasticity. Based on the exact stress field solutions, convenient expressions for the stress intensity factors are derived. The accuracy of all the analytical formulations is verified by comparison with the results from a bulk of numerical analyses