On stress singularity at crack tip in elasticity

Abstract

In order to gain a better understanding of the stress singularity at the crack tip in elasticity, the relevant solutions are investigated. Based on the rigorous solution of a plate containing a crack and its corresponding asymptotic expression, the stress singularity at the crack tip was described in details. The stress singularity at the crack tip is identified as: the infinite stress exists at the crack tip, and the stress components at the crack tip are multivalued. Besides, the rigorous solution of the infinite plate containing a crack may be derived from the rigorous solution of the infinite plate containing an elliptical hole, which is solved from Mushelishvili’s approach. As half minor-axial length approaches zero, the stress concentration field of a plate with an elliptical hole evolves into the stress singularity field of a plate with a crack. Thus, the stress intensity factor characterizing the stress singularity field near the crack tip may also be read as characterizing the infinite stress concentration field near the crack tip. Therefore, the mechanical concept of stress intensity factor can be identified as follows: stress intensity factor is a parameter characterizing the strength of infinite stress concentration field at the crack tip. Keywords: Fracture mechanics, Stress singularity, Crack tip, Stress concentration