Analysis of the fracture of fiber composites on the basis of the statistical theory of branching processes

Abstract

A statistical theory of branching processes is used to examine models of the localized and delocalized fracture of fiber composites. It is shown that despite the differences between the two types of models, both can be reduced to the same generalized Markov process. A new fracture criterion to be used for all types of models is proposed. The use of this criterion makes it possible to theoretically describe a new structural effect — the dependence of the breaking stress of a composite specimen on its cross-sectional area. In the limiting case of an infinitely large cross-sectional area, the breaking stress calculated on the basis of the proposed approach turns out to be equal to that calculated using previous models. The breaking stress for specimens of finite dimensions turns out to be lower than for specimens of infinite size. This result is due to the nonlinear dependence of the probability of fiber rupture on the additional overstresses that develop in the composite during local microscopic fractures. The results that are obtained should be taken into account in the calculation of the strength of structurally reinforced composites and small structural elements made of composite materials.