A Novel Micromechanics-Model-Based Probabilistic Analysis Method for the Elastic Properties of Unidirectional CFRP Composites

Abstract

Considerable uncertainties in the mechanical properties of composites not only prevent them from having efficient applications but also threaten the safety and reliability of structures. In order to determine the uncertainty in the elastic properties of unidirectional CFRP composites, this paper develops a probabilistic analysis method based on a micromechanics theoretical model and the Monte Carlo simulation. Firstly, four commonly used theoretical models are investigated by calculating the deterministic elastic parameters of three unidirectional CFRP composites, which are compared with experimental outcomes. According to error analyses, the bridging model is the most brilliant one, with errors lower than 6%, which suggests that it can be used in probabilistic analyses. Furthermore, constituent parameters are regarded as normally distributed random variables, and the Monte Carlo simulation was used to obtain samplings based on the statistics of constituent parameters. The predicted probabilistic elastic parameters of the T800/X850 composite coincide with those from experiments, which verified the effectiveness of the developed probabilistic analysis method. According to the probabilistic analysis results, the statistics of the elastic parameters, the correlations between the elastic parameters, and their sensitivity to the constituent’s properties are determined. The moduli E11, E22, and G12 of the T800/X850 composite follow the lognormal distribution, namely, ln(E11)~N[5.15, 0.0282], ln(E22)~N[2.15, 0.0242], and ln(G12)~N[1.48, 0.0382], whereas its Poisson’s ratio, v12, obeys the normal distribution, namely, v12~N(0.33, 0.0122). Additionally, the correlation coefficients between v12 and E11/E22/G12 are small and thus can be ignored, whereas the correlation coefficients between any two of E11, E22, and G12 are larger than 0.5 and should be considered in the reliability analyses of composite structures. The developed probabilistic analysis method based on the bridging model and the Monte Carlo simulation is fast and reliable and can be used to efficiently evaluate the probabilistic properties of the elastic parameters of any unidirectional composite in the reliability design of structures in engineering practice.