Fracture initiation at sharp notches under mode I, mode II, and mild mixed mode loading

Abstract

In the context of linear elasticity, a stress singularity of the type Kⁿr^δ(δ<0) may exist at sharp re-entrant corners, with an intensity Kⁿ. In general the order of the stress singularity δ and the stress intensity differ for symmetric (mode I) and antisymmetric (mode II) loading. Under general mixed-mode loadings, the magnitudes of the mode I and II intensities fully characterize the stress state in the region of the corner. A failure criterion based on critical values of these intensities may be appropriate in situations where the region around the corner dominated by the singular fields is large compared to intrinsic flaw sizes, inelastic zones, and fracture process zone sizes. We determined the mode I and II stress intensities for notched mode I tensile specimens and notched mode II flexure specimens using a combination of the Williams (1952) asymptotic method, dimensional considerations, and detailed finite element analysis. We carried out a companion experimental study to extract critical values of the mode I and II stress intensities for a series of notched polymethyl methacrylate (PMMA) tensile and flexure specimens with notch angles of 90-. The data show that excellent failure correlation is obtained, in both mode I and II loading, through the use of a single parameter, the critical stress intensity. We then analyzed and tested a series of T-shaped structures containing 90- corners. The applied tensile loading results in mixed-mode loading of the 90- corners. Failure of the specimens is brittle and can be well-correlated with a critical mode I stress intensity criterion using the results of the notched mode I tensile tests. This is attributed to large difference in the strength of the stress singularities in modes I and II: δ= -0.4555 and -0.0915 for modes I and II for a 90- notch. As a result, the mode I loading dominates the failure process for the 90- corner in the T-structure.