Mechanics of structural size effect in impact brittle fracture of steels and consequent scaling laws for fracture

A large structural size effect on brittle fracture energy was observed in studies of impact fracture of steels by Stanton, Batson and Docherty, nearly 100 years ago. The size effect was seen in macroscopically brittle fractures of geometrically similar specimens tested over a large size range. These historical findings have great significance in designing large-scale steel structures such as ships and bridges. However, there has been no physical principle or theory yet to explain the size effects observed by Stanton, Batson and Docherty. In the present work, a new approach based on net-section mechanics is used to explain the size effect. It is shown that the change in net-section strain energy predicts well the size effect on fracture energy, under the constant condition of cleavage crack initiation stress at the notch root. The spectacular decrease in specific fracture energy with increased specimen size is explained by noting the three-dimensional nature of stored strain energy and the two-dimensional nature of fracture energy dissipated in the crack layer. By scaling both energies to a reference cubic specimen volume and equating, an expression that describes the inverse size dependence of specific fracture energy has been formulated. The mechanics of the size effect is illustrated by assessing the theory with extensive experimental data. Further, scaling laws for fracture energy have been developed. This work honours the pioneering studies of Stanton, Batson and Docherty, which have been instrumental for the development of the present theory and analysis.