Mechanics of Crack and Specimen Size Effects on Fracture Toughness Determined Using Compact Tension Specimens: Analysis by Net-Section Stress Modeling

Abstract The effects of crack size and specimen size on plane strain fracture toughness values of materials, measured using compact tension C(T) specimens, are examined through the analysis of elastic strain energy stored in the net-section at fracture. A large body of experimental data shows that there is a strong crack (or ligament) size effect on plane strain fracture toughness data that were experimentally obtained using compact tension C(T) specimens. The size effect is significant at relatively small crack sizes, but it gets stronger as a/W approaches unity. This dependence exists in both brittle and ductile materials, ruling out any effect of ligament plasticity. In this work, the net-section-based analysis of fracture behavior, enforcing constancy of crack tip fracture stress at all crack lengths, reveals that the measured fracture toughness should vary with crack size and specimen width. It is indeed found that in most materials, fracture occurs at a constant crack tip fracture stress, which is nearly equal to the tensile strength. A few exceptional cases have been noted, but even in these cases, fractures, at all crack lengths, still occurred at constant crack tip fracture stresses that are lower than tensile or bend strengths. Experimental fracture toughness data from ceramics, metals, and biomaterials have been used to demonstrate the crack and specimen size effects on toughness. It is shown that the expressions developed by the net-section stress analysis can predict the fracture toughness variations with crack/specimen size, quite accurately, with constant crack tip fracture stress as the fracture criterion. The results suggest that fracture toughness, measured using the C(T) specimen, is not a material property.