Energetic Size Effect in Quasibrittle Fracture

Abstract

Abstract The energetic size effect, transitioning from ductile behavior at small structure sizes to brittle behavior at large ones, is a quintessential feature of all quasibrittle fracture. Its analytical law, recently adopted for ACI Standard 318, is important for safe and efficient structural design. First it is explained that, in absence of any material characteristic length, which is the case for both elasticity and LEFM, the scaling of structural strength must be a power law of structure size. Its particular form is derived from dimensional analysis. After establishing the second-order asymptotic size effect of quasibritle structures at the small-size limit, the size effect law for geometrically scaled structure is derived by asymptotic matching to large-size asymptotic expansion of equivalent LEFM. The brittleness number is introduced as a geometry independent characteristic of failure behavior. Differences between the deterministic size effects of Type 1 and Type 2 are explained and their particular size effect laws are derived. It is also shown how to derive the R-curve from the observed size effect. Finally, the standardized use of the type 2 size effect law to obtain the fracture energy and characteristic FPZ size from the tests of maximum loads of similar notched specimens of sufficiently different sizes is derived and explained.