Estimation of Composite Laminate Design Allowables based on the Statistical Characteristics of Lamina Level Test Data

Abstract

In this study, the method is proposed to obtain the design allowables of composite laminate with analysis, which are currently obtained by tests. The design allowable for a material property computed based on the statistical characteristics of that property, so several tests are required for same laminate configuration and environmental condition. But since the deterministic analysis method only gives averaged values for the analysis result, the Monte Carlo simulation method is adopted for the statistical values for the result. It is one of the main purposes to generate suitable samples which reflect the characteristics of the material for the Monte Carlo simulation. To do that, estimation of statistical distribution of the material properties, the correlations between the properties, and efficient sampling method by the Latin hypercube sampling method are considered. For the composite material lamina level test data, which is performed to obtain the material's basic properties, The estimation of distribution results gives that each of the 13 basic properties obeys some distribution functions such and Weibull, normal or lognormal distribution. But some properties did not obey any of the pre-determined statistical distributions. To contrast the effects of applying different statistical distribution for each properties, tensile strength analyses for some laminate configuration were performed with classical laminated plate theory. The valid differences were found among the proposed method, the method assuming normal distribution for all properties, and the method assuming Weibull distribution for all properties. From the correlation analysis for the lamina level test data, it was found that correlations exist between some properties such as tensile strength and tensile modulus. For the random sampling method, no correlation exists between the property samples, the rank order correlation method was applied to reflect the correlation characteristics of real test data. Comparing analysis results between the samples with no correlation and samples modified by test data's correlation characteristics, the mean value of analysis results gives the negligible difference, but the standard deviation shows meaningful difference. The standard deviation values are not important in the deterministic analysis. But since the standard deviation value has large effect for the process to compute the design allowables, the correlation characteristics should be considered in the input sample generation. To simulate the failure behavior of composite laminates properly, the progressive failure analysis method was applied. IPSAP which is in-house code developed in the Aerospace Structure Laboratory in Seoul National University, was used for the progressive failure analysis. The analysis was performed for the 1,000 sample sets that reflect the statistical characteristic of the material test data and the correlations between the properties. Then the 1,000 analysis results were regarded as the population of the results, as the specimen sampling process in the real tests, the subsets were collected from the analysis results. The B-basis value were computed from the subset. By repeating this subset collecting for 100 times, 100 B-basis values are computed and 99% confidence interval of B-basis values can be presented. The B-basis estimation results are compared with the design allowable values from the laminate tests such as open-hole tensile tests for Hexcel 8552 IM7 and Hexcel 8552 AS4, most basis values were predicted well by this method based on the lamina level test data and the progressive failure analysis.