Introducing a novel LLD-CMOD equivalence fracture model for quasi-brittle materials exposed to three-point bending

Abstract

Effective crack models have been preferred in the fracture of concrete thanks to their analytical solution for equivalent effective crack length. Nevertheless, the main hypothesis in the effective crack models, the Load-LLD or Load-CMOD equivalence between a real cohesive material and a corresponding virtual specimen, is controversial. The present study aims to offer a distinct perspective on the effective crack approach. To this end, the Load-LLD or the Load-CMOD equivalence was replaced by the LLD-CMOD equivalence in the proposed fracture model for the notched beams under three-point bending. In the proposed LLD-CMOD equivalence fracture model, three fracture toughness parameters are used, two of them depend on the evolution of the fracture process zone (FPZ) and the other is for the peak load measured. That is, KICin and KICde define the limit of the nonexistent FPZ and the fully developed FPZ, respectively, but KICun corresponds to the peak load only. The test results of the notched beams revealed that KICin and KICun show size independence, but this was not the case for KICde. The proposed fracture model was also compared with the Double-K model through the experimental results from the literature. Accordingly, a good agreement between both models was achieved in terms of the effective crack length and fracture toughness at the peak load.