Fracture initiation at sharp notches: Correlation using critical stress intensities

In the context of linear elasticity, a stress singularity of the type Knrδ (δ < 0) may exist at sharp re-entrant corners, with an intensity Kn. The magnitude of the intensity fully characterizes the stress state in the region of the corner. A critical value of Kn 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 Kn 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 Kn to correlate failure with a series of notched polymethyl methacrylate (PMMA) three-point flexure specimens with notch angles of 60°, 90°, and 120°. Using the measured failure loads and the finite element solutions for Kn, we infer the critical notch stress intensity Kcrn, for sharp-notched PMMA. The data show that excellent failure correlation is obtained through the use of the single parameter Kcrn, 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 Kn can be used to correlate fracture initiation.