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 (SIF) at the crack tip. Indeed, there are significant numerical data showing the effect of specimen aspect-ratio on 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 SIF expressions for center and edge cracks in tension plates of various aspect ratios. Expressions have been derived for both uniform stress as well as uniform displacement boundary conditions. Comparisons are made with the available numerical stress intensity factor data. A 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 SIF for a semi-infinite crack in an infinitely wide strip, validating the analysis. Additionally, the SIF expressions developed here also highlight some 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 values of stress intensity factors for cracks in materials and structures under tension loading.