Linear elastic fracture mechanics as a limit-case of strain-softening instability

Abstract

Size-scale, slenderness and degree of redundancy are shown to have a fundamental impact on the global structural behaviour, which can range from ductile to brittle when strain softening and localization are taken into account. The brittle behaviour involves an internal instability in the load-deflection path, which shows a positive slope in the softening branch. This virtual branch is revealed only if the loading process is controlled by a monotonically increasing time function (e.g., the crack opening displacement). Otherwise, the loading capacity shows discontinuity with a negative jump. When the post-peak behaviour is kept under control up to the complete structure separation, the area bounded by the load-deflection curve and the deflection axis represents the energy dissipated in the fracture process. A general explanation of the well-known decrease in apparent strength and increase in fracture toughness by increasing the specimen size is given in terms of dimensional analysis. Due to the different physical dimensions of strength [FL−2] and toughness [FL−1], the actual values of these two intrinsic material properties may be found exactly only with comparatively large specimens.