A Novel Analysis of the Size Effect on Stress Intensity Factor for Center and Edge Cracks in Tension by the Net-Section Mechanics

Abstract

An unresolved question in fracture mechanics is whether the variations in the size or aspect-ratio of cracked plates or structures have a significant effect on the stress intensity factor at the crack tip. Indeed, there are significant numerical data showing the effect specimen aspect ratio on stress intensity factor (SIF). There is also experimental evidence supporting the existence of the size effect on fatigue and fracture behavior. However, there is no analytical formula to capture such a size effect on the stress intensity factor for standard fracture mechanics crack configurations. In this study, a novel net-section based approach is used to develop simple and approximate stress intensity factor expressions for center- and edge-cracks in tension plates of various aspect ratios. Expressions were determined for both uniform-stress as well as unform-displacement boundary conditions. Comparisons are made with the available numerical stress intensity factor data. A very remarkable agreement of the net-section based SIF expressions with the numerical data (complex potential, finite element, and variational approaches), is found. For the clamped-end condition the net-section approach leads to Rice’s limiting stress intensity factor for a semi-infinite crack in an infinitely wide strip, validating the analysis. Additionally, the SIF expressions developed also highlight the discrepancies in numerical data. The study provides simple SIF expressions that can be readily used to analyze specimen size or aspect ratio effects on critical stress intensity factors for cracks in materials and structures under tension loading.