Universal scaling of the stress field at the vicinity of a wedge crack in two dimensions and oscillatory self-similar corrections to scaling

Abstract

We study the divergence of the stress field near the tip of a wedge crack of head angle between π and 2π. A new universal family of solutions is found, where the dominant singularity is characteristic of a pure tension on the external boundaries. Further from the tip, the first correction to this behavior is a power law characteristic of a pure shear on those boundaries. When the head angle of the wedge is inside a certain range, higher-order modifications to the field are found to be periodic in the logarithm of the distance from the tip. Inside this range, oscillatory solutions appear as more remote corrections to the power-law behavior. The relevance of these solutions to sidebranching and to self-similar pattern formation of cracks is discussed.