Two-level finite element study of axisymmetric cracks

Abstract

We extend the two-level finite element method (2LFEM) to the accurate analysis of axisymmetric cracks, where both the crack geometry and applied loads are symmetrical about the axis of rotation. The complete eigenfunction expansion series for axisymmetric cracks developed by us are employed as the global interpolation function such that the stress intensity factors are primary unknowns. The coupled coefficients in the series are solved iteratively. The stress intensity factors are computed directly from the coefficients for any arbitrary axisymmetric loading on the boundary. Engineering applications of 2LFEM to numerical fracture mechanics analysis for stress intensity factors include several examples: Penny-shaped and circumferential cracks in round bars; and internal and edge circumferential cracks in thick wall pipes.