Correlation model for composite elastic properties using only measurements from a single specimen

In probabilistic design, composite material properties are often treated as independent random variables since correlation coefficients are not widely available. This is due to the paucity of experiments where correlation is measured. However, high material correlations are expected from common physical characteristics, such as variability in fiber volume fraction. Therefore, the focus of this paper is to translate known variability in composition into a correlation model for elastic constants. The dependence of the elastic constants on fiber volume fraction was estimated from simple mixture rules. The correlated material variability was applied to a glass/epoxy material system. The material variability was combined with the measurement error to obtain the total covariance of the elastic constants. The measurement error for the glass/epoxy laminate was from correlated data from a single vibration testing experiment. In this case of a single test, the variability between specimens was not captured in the measurement error, and the proposed correlation model provides a physical basis for approximating the specimen variability. The uncertainty in elastic properties was propagated to strain under mechanical loading in a pressure vessel problem using the classical lamination theory. The results were interpreted as a failure probability according to the maximum strain criterion. It was found that neglecting correlations can lead to an inefficient or unsafe design.

► Correlated material variability in composite properties was based on volume fraction.
► Measurement error included correlation data from vibration tests on a laminated plate.
► Material variability was used to approximate specimen variability for a single test.
► Neglecting correlation in composite properties overestimated the failure probability.