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Monte Carlo simulations are compared with strength data from carbon fibers and composites made from similar fibers, in order to investigate several issues concerning the failure of fibrous composite materials under tensile load. Failure of,"bundles" consisting of up to 1000 fibers under several different localized load-sharing rules and two different models for fiber strength is simulated, and the chain-of-bundles model is used to simulate tows of varying gauge lengths. The relationships of composite strength, Weibull shape inflation and ineffective length are investigated for the new models. The issues of volume effects and critical crack growth are also discussed.

Consider a family of distributions with survival distributions that are log concave and stochastically increasing in a parameter over which it will be mixed. It is shown that a necessary and sufficient condition for a mixture over any such family to have an increasing failure rate is that the mixing distribution have an increasing failure rate. Some observations are given on generalizing this result as well as weakening the conditions on Prekopa's Theorem.

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The maximum-entropy formalism developed by E. T. Jaynes is applied to the breaking strain of a bundle of fibers of various cross-sectional areas. When the bundle is subjected to a tensile load, and it is assumed that Hooke's law applies up to the breaking strain of the fibers, it is proved that the survival strain distribution for a fiber in the bundle is restricted to a certain class consisting of generalizations of the log-logistic distribution. Since Jaynes's formalism is a generalization of statistical thermodynamics, parallels are drawn between concepts in thermodynamics and in the theory of inhomogeneous bundles of fibers. In particular, heat transfer corresponds to damage to the bundle in the form of broken fibers, and the negative reciprocal of the parameter corresponding to thermodynamic temperature is the resistance of the bundle to damage.