A multiplicative damage model for strength of fibrous composite materials

Knowledge of the tensile strength properties of a fibrous composite material is essential in the design of reliable structures from that material. Determination of statistical models for the tensile strength of a composite material which provide good fits to experimental data from tensile tests on material specimens is therefore important for engineering design. Perhaps the most commonly used statistical model is the Weibull distribution, based on 'weakest link of a chain' arguments. However, in many cases the usual Weibull distribution does not adequately fit experimental data on tensile strength for composite materials made from brittle fibers such as carbon. Here, an alternative model is developed for tensile strength of carbon composites, which is based on a multiplicative cumulative-damage approach. This approach results in a 3-parameter extension of the Birnbaum-Saunders fatigue model and incorporates the material specimen size (size effect) as a known variable. This new distribution can also be written as an inverse Gaussian-type distribution, which can be interpreted as the first passage of the accumulated damage past a damage threshold, resulting in material failure. The new model fits experimental tensile-strength data, for carbon micro-composites better than existing models, providing more accurate estimates of material strength.