Nonlocal and Gradient Fracture Criteria for Quasi-Brittle Materials under Compression

The paper analyzes the applicability of available nonlocal and gradient fracture criteria to brittle, quasi-brittle, and ductile fracture in notched materials. All chosen criteria use an internal size parameter as a material structure characteristic, which makes it possible to describe the scale effect under stress concentration and to extend the range of their application compared to conventional ones. However, this range is limited to brittle or quasi-brittle fracture with a small prefracture zone. For extending the criteria to quasi-brittle fracture with a developed prefracture zone, we should dismiss the hypothesis on the prefracture zone size as a constant related solely to the structure of materials. In this paper, a new physically substantiated approach is proposed which modifies the criteria of average stress, point stress, fictitious crack, and stress gradient such that their modified versions contain a complex parameter allowing for the size of a prefracture zone, structure of a material, its plastic properties, geometry, and loading conditions. Their experimental verification as applied to tensile cracking in compressed geomaterials with a round hole shows that all modified criteria provide a good description of quasi-brittle fracture and allow one to explain the experimentally observed transition from brittle to ductile fracture with increasing hole sizes.