R-curve and size effect in quasibrittle fractures: Case of notched structures

Abstract

Within the framework of Bažant’s theory, the size effect on nominal strength of notched structures deduced from a size-dependent R-curve is proposed. It is shown that the expected size effect is more complicated than the one proposed in Bažant’s Size Effect Law (SEL) and especially in the crossover regime. As a function of the fracture parameters describing the R-curve, two kinds of size effect on the resistance at peak load are possible and lead to three different scalings on the nominal strength. We argue that these expected size effects are mainly driven by the value of the scaling exponent characterizing the size effect on the critical crack length increment and on the critical resistance assumed in the R-curve behavior. The three resulting size effects on the nominal strength are compared to Bažant’s SEL. It appears that, if Bažant’s SEL always underestimates nominal strength and consequently provides a safety design of structures, an optimal design should take into account the size effect on the R-curve and their consequences on the size effect on the nominal strength especially for large structures sizes.