Discriminating between volume and surface integral theories for brittle materials

Many theories have been proposed for the failure of brittle materials. Most of these are based on the Weibull weakest link theory and require an evaluation of an integral of the stress state either over the volume or surface of the stressed component. In this paper, the predictions using volume and surface integrals are compared and it is shown that to distinguish between them it is best to obtain material data from a test state which is essentially bending and predict tests in which the stress is relatively constant throughout the volume. Using these tests the failure theories based on volume and surface integrals can be separated, as the spread is considerably greater than the probable experimental error. The relative size of the specimens is also examined and it is found that the "bending specimen" should be thin and the "constant stress specimen" thick.