A probabilistic theory on the time to fracture of amorphous crosslinked polymers

The energy probability theory of fracture proposed by Valanis has been extended to apply to the global fracture of a large material region and has been generalized to take into account the probabilistic distribution among bonds of the free energy of the region. In contrast to the theory of fracture initiation of the first author, it is assumed, in the present paper, that global fracture is brought about by the fracture of a critical number N_cr of primary bonds. Whereas this condition alleviates some of the problems encountered in the application of the theory to fracture initiation and propagation—such as determination of the local energy field at the root of a developed crack—it introduces the difficulty that N_cr may, in general, depend on the geometry of the specimen and the directionality of the stress field, though it was found to be relatively insensitive to the rate of deformation, as corroborated in this paper. The theory is used in this work to predict the time of global fracture, under conditions of constant load, constant strain, and constant strain rate.