On a Universal Failure Criterion for Brittle Materials

To date, there is no universally accepted comprehensive explanation of brittle fracture in compressive stress fields. Researchers have developed many theories for brittle fracture, each of which is only applicable to particular materials and stress states. Additionally, some of these theories are based on questionable assumptions. A generalized fracture-based criterion should rationally explain brittle material behaviour across all stress states, providing unity in a poorly understood field. Visible crack formation implies the existence of tension to separate the surfaces. In the literature, there is no consensus on the source of these tensile stresses in compressive stress fields. Various sources of tensile stresses in compression are surveyed, with voids being found to be the most critical. Having identified the key source of tension, a way of predicting crack propagation is sought. Previously unsuccessful treatments of void-induced compressive fracture are examined, then a highly simplified way of quantifying the stress intensity factor (KI) in compressive fracture is proposed. The simplification is validated against numerically calculated KI values for circular and rhomboidal voids of different sizes. In addition to the numerical efficiency of the simplified calculation, the simplification defines a function \(\sigma \left( a \right)\) which can be used to explain and predict various compressive fracture phenomena which are counter-intuitive from a typical Griffith-type explanation.