A criterion study for non-singular stress concentrations in brittle or quasi-brittle materials

In engineering applications, it is difficult to avoid the non-singular stress concentrations that often play an important role in structure designs. The simplest engineering strength criteria are in general not appropriate due to their incapacity in dealing with important size effect induced by stress gradients. In this paper, we present first a simple experimentation, which consists of plates with a central hole under uniaxial tensile loading, showing important size effect. Second, numerous criteria, including commonly used engineering criteria, crack initiation criteria based on the finite fracture mechanics, or cohesive criteria, were adapted to fit the experimental results. We found that most of these criteria, including criteria with a single material parameter and those with two material parameters, are not suitable for fracture prediction of materials under non-singular stress concentrations. It seems that three material parameters would be the minimum to establish an adequate fracture criterion for arbitrary stress concentrations. By analysing the energy dissipation of micro-crack bands under different stress concentrations, we proposed a new fracture criterion with three material parameters based on the finite fracture mechanics. It is shown that this criterion can provide accurate critical remote loads comparing with experimental data. We believe that the three parameter concept is physically reasonable and can be used in establishing fracture criteria in both the cases of singular and non-singular stress concentrations.