Size-effect on the apparent tensile strength of brittle materials with spherical cavities

The decrease of the apparent uniaxial tensile strength resulting from a single flawless spherical cavity in an infinite linear elastic continuum under uniaxial tension is investigated. To this end, a new generalized semianalytical expression for the stress intensity factor of an annular crack surrounding the spherical cavity under different loading conditions is proposed and validated. The apparent tensile strength is then estimated by four different approaches: two criteria implement a single condition, either on the stress field (Theory of Critical Distances) or on the energy release rate (equivalent Linear Elastic Fracture Mechanics), whereas the other two are stress-energy coupled criteria, namely the Finite Fracture Mechanics and the Cohesive Zone Model. Finally, theoretical predictions are discussed and compared with experimental data and atomistic simulations available in the literature, showing good correlation.