On the stochastic first-ply failure analysis of laminated composite plates under in-plane tensile loading

This paper highlights the amount of risk taken when a deterministic approach is used in designing composite structures without consideration of stochastic effects. The study treats all material and geometric parameters of the composite laminated plates under investigation as stochastic. Monte Carlo simulation is employed to investigate the stochastic effects of material properties, ply thickness, and ply orientation on the failure of laminated composite plates under static loads. Classical lamination theory is used to calculate the strength ratios using maximum stress, Tsai-Hill, and Tsai-Wu failure criteria for plates of three different materials in various stacking sequences. Variation in the failure ply distributions are shown to increase with coefficient of variation of the input variables. A positive linear trend between the coefficients of variation of the strength ratio and input variables is found, whose slope increases as randomness is considered for more input variables. Probability of failure and failure ply distributions are shown to be heavily dependent on the combination of laminate stacking sequence, material, and failure probability. In particular, while the empirical failure probability for cross-ply laminates is highest for the ply predicted by a deterministic analysis, this probability decreases rapidly with increasing variation in input parameters. Further, the failure of unexpected plies for cross-ply laminates is shown to be related to the stiffness ratios of the plies. The general significance of considering ply thickness and ultimate strength as random variables is also demonstrated, as well as the significance of randomness in ply orientation for balanced and angle ply laminates.