Probability of fracture initiated by defects

Shortcomings of the existing weakest-link theories pertinent to the fracture of brittle materials are discussed. As an alternative, a general equation is derived, which predicts the probability of fracture in a stressed region varying from zero to the entire volume of the specimen. The equations derived regarding the fracture stress controlled by defects are verified by Monte Carlo simulations. An alternative mathematical formulation of the principle of the weakest link in the chain is proposed. It is also demonstrated that the equations related to probability of fracture are equivalent to equations describing coverage of space and phase transformation kinetics.