Analysis of the non-singular stress terms for the sharp notches under anti-plane loading

Abstract

It is the singular term dominating the stress field near the vertex of a sharp notch, while the non-singular terms also play a non-ignorable role on the complete stress field. The non-singular stresses near the apex of anti-plane sharp notches are calculated and their roles on the fracture mechanics are analyzed in this paper. By coupling the singular characteristic analysis with the finite element method, the amplitude coefficients together with the singular orders and angular functions in the Williams expansion are solved. Then, different singular stress and higher-order non-singular stress terms can be determined from the asymptotic expansion according to the requirement. It is found that the solution merely considering the singular stress term can approximately reflect the stress field very close to the vertex, while it is invalid far from the notch vertex. The computational error is still greater than 5% in the solution containing the singular stress term together with the first non-singular stress term. However, the solution taking the singular stress term and the first two non-singular stress terms into account can accurately characterize the stress field far from the notch tip and its maximum error is less than 2%.