A new singular element for evaluating stress intensity factors of V-shaped notches under mixed-mode load

In this paper, a new singular element is presented to evaluate stress intensity factors of V-shaped notches subjected to mixed-mode load. The proposed element takes into account special variation of displacements in the vicinity of the notch tip. The singularity at notch tip is variable unlike the crack problem where the displacements around the crack tip have variation of square root of r. In the proposed method, special basis functions considering the singularity order at notch tip are incorporated into the shape functions of the new element, and the singularity order is determined by the included angle of the notch. With the new element, more accurate displacement and stress fields in the neighborhood of the notch tip can be obtained, thus the stress intensity factors are computed more accurately. Accurate stress intensity factors are important for the V-notched structures to develop a fracture criterion. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.