Dependence of crack tip singularity on loading functions

Under the theory of classical linear fracture mechanics, a finite crack sitting in an isotropic and homogeneous medium is considered. We find that the well-known crack tip singularity, the inverse square-root singularity 1 / sqrt(r), may disappear under certain type of loading traction functions. More specifically, depending on the crack-surface loading function, the behavior of the crack tip field may be shown to be as smooth as possible. The singular integral equation method is used to study the dependence of the crack tip singularity on the mode III loading traction functions. Exact crack opening displacements, stress fields, and their corresponding loading traction functions are provided. Although the method used is somewhat mathematically elementary, the outcome seems to be new and useful.