Mechanics of size effect on plane stress fracture toughness and R-curve development in thin sheet materials and consequent scaling laws

Abstract Fractures of thin sheet engineering materials occur under plane stress conditions with significant plasticity. For effective fracture prediction and control of structures, the mechanics of scaling of laboratory fracture toughness data from small specimens to large structures should be established. In this work, how and why plane stress fracture toughness depends on crack length and specimen size is investigated using a new net-section-mechanics approach. The approach evolves from Griffith's concept of strain energy increase owing to crack, which is formulated here for finite-sized specimens. The effects of material strength and specimen-size parameters on the nature of fracture resistance (R-curve) development in thin sheet materials are also investigated. Several interesting and unexpected findings are presented. For a given material, plane stress fracture toughness and R-curve development are strongly dependent on crack size and specimen width. The net-section theory accurately predicts these effects using the constancy of plastic collapse stress as the net-section fracture criterion. Extensive experimental data are used to demonstrate the validity of the net-section-mechanics approach for characterizing the fracture toughness and the development of fracture resistance with crack extension. This work is dedicated to Sir A. A. Griffith honouring the hundredth anniversary of his crack theory.