Multiaxial criterion for failure of brittle materials

Most brittle materials show little straining at failure and an ultimate strength that depends upon loading geometry. The surface that defines failure in stress space has a characteristic shape that may be defined by an appropriate mathematical criterion. In this paper, the authors present a simple multiaxial criterion formulated from two quadric functions. Under conventional triaxial compression, the MSDP criterion reduces to the Mises-Schleicher criterion at low mean stress and it takes the shape of the conical Nadai-Drucker-Prager criterion at higher mean stress. The MSDP criterion can be expressed from the three principal stresses or from the usual invariants I-1, J(2), and J(3). It includes four characteristic parameters, each having a particular significance regarding material properties. The validity of the criterion is shown using experimental results taken from the literature on rock, concrete, and grey cast iron.