Fracture initiation at sharp notches: Correlation using critical stress intensities

the context of linear elasticity, a stress singularity of the type K(n)r(delta) (delta --> 0) may exist al sharp re-entrant corners, with an intensity K-n. The magnitude of the intensity fully characterizes the stress state in the region of the corner. A critical value of K-n may be appropriate as a failure criterion in situations where the region around the corner dominated by the singular field is large; compared to intrinsic flaw sizes, inelastic zones, and process zone sizes. We determined K-n for notched mode I three-point flexure specimens using a combination of the Williams (Williams, M. L. (1952) Stress singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics 74, 526-528) asymptotic method, dimensional considerations, and detailed finite element analysis. We carried out an experimental study of the feasibility of using a critical value of K-n to correlate failure with a series of notched polymethyl methacrylate (PMMA) three-point flexure specimens with notch angles of 60 degrees, 90 degrees, and 120 degrees. Using the measured failure loads and the finite element solutions for K-n, we infer the critical notch stress' intensity K-cr(n) for sharp-notched PMMA. The data show that excellent failure correlation is obtained through the use of the single parameter K-cr(n). Furthermore, simple estimates of the size of the inelastic zone for the notched PMMA specimens show it to be small relative to the singularity-dominated zone. This supports the applicability of linear elastic notch mechanics (LENM), and the idea that a critical value of K-n can be used to correlate fracture initiation. (C) 1997 Elsevier Science Ltd.