Size effect on flexural strength of fiber-composite laminates

The size effect on the flexural strength (or modulus of rupture) of fiber-polymer laminate beams failing at fracture initiation is analyzed. A generalized energetic-statistical size effect law recently developed on the basis of a probabilistic nonlocal theory is introduced. This law represents asymptotic matching of three limits: (1) the power-law size effect of the classical Weibull theory, approached for infinite structure size; (2) the deterministic-energetic size effect law based on the deterministic nonlocal theory, approached for vanishing structure size; and (3) approach to the same law at any structure size when the Weibull modulus tends to infinity. The limited test data that exist are used to verify this formula and examine the closeness of fit. The results show that the new energetic-statistical size effect theory can match the existing flexural strength data better than the classical statistical Weibull theory, and that the optimum size effect fits with Weibull theory are incompatible with a realistic coefficient of variation of scatter in strength tests of various types of laminates. As for the energetic-statistical theory, its support remains entirely theoretical because the existing test data do not reveal any improvement of fit over its special case, the purely energetic theory-probably because the size range of the data is not broad enough or the scatter is too high, or both.