Size effect in quasibrittle fracture: derivation of the energetic Size Effect Law from equivalent LEFM and asymptotic analysis

Abstract

Within the framework of Bažant’s theory, the size effect on the ultimate fracture properties of notched structures is studied from an energy based asymptotic analysis in which the resistance curve behavior is considered through an analytic expression. The scaling on the relative crack length at peak load as well as the size effect on the corresponding resistance to crack growth are investigated. It is shown that, for intermediate structure sizes, the relative crack length at peak load decreases with respect to the structure size while the resistance grows. These scalings lead to a size effect on nominal strength which is in agreement with Bažant’s Size Effect Law (SEL) for small and large structures sizes, but for intermediate sizes, an additional asymptotic regime occurs instead of a simple crossover regime as expected in SEL. The slope and the extent in size of the additional asymptotic regime depend only on the exponent characterizing the curvature of the R-curve. The comparison between the resulting size effect and Bažant’s SEL shows that SEL provides an approximate size effect which is in agreement with the expected asymptotic behaviors, with the exception of the extreme cases corresponding to very strong and slight R-curve’s curvatures. On this basis, the safety design of large structures is discussed.