Evaluation of stress concentration factors and stress intensity factors from remote boundary data

Usually, the stress concentration factors (SCFs) for holes and the stress intensity factors (SIFs) for cracks are evaluated by using the data near holes or cracks. However, the abrupt change of the stresses near holes, especially near crack tips, may lead to an unavoidable error. Thus, it is always interesting to ®nd an equivalent formulation for SCF and SIF by using only remote boundary responses (displacements, stresses and strains) cooperating with the necessary geometric data. Through a special boundary element formulation of which the fundamental solution was derived using Strohʹs formalism for two-dimensional anisotropic elasticity, all the internal stresses and strains can be expressed in terms of the boundary (not including the hole and crack boundaries) displacements and tractions. By proper mathematical manipulation, a closed form solution for SIF of the internal crack and SCF of the internal hole, expressed by using only remote boundary displacements and tractions, is derived in this paper. To show that the proposed formula is accurate and ecient, several numerical examples are presented