Models of localized and delocalized fracture of fibre reinforced composite materials have been considered from the viewpoint of the theory of branching processes. The analysis has shown that, in spite of apparent differences, both types of models can be reduced to generally the same Markov chain. As a result, a new fracture criterion has been proposed that is valid for any model. The use of the new criterion allowed for the revelation of a new structural effect, i.e. the dependence of the fracture stress of the composite upon the size of the cross-section of the composite sample. In the case of a fracture of an infinitely large composite sample, the criterion yields the same fracture stress as calculated on the basis of earlier models. In the case of the fracture of a sample of a finite size, the predicted fracture stress is lower than calculated according to previous models. The effect can be explained as a non-linear fracture phenomenon arising out of the non-linear dependence of microfracture probabilities upon overstressing caused by other microfractures. The effect is essential for evaluating the strength of a structured composite with several levels of ordering and constriction elements of a small size.