Statistical correlation between elastic properties of plain-weave composite and its influence on structure reliability

Statistical correlation between in-plane elastic properties of plain-weave composite (E-glass fabric/epoxy and carbon fabric/epoxy) is studied by probabilistic finite element method. The in-plane elastic properties including Young's moduli, shear moduli and Poisson's ratios are derived from finite element model on a composite unit-cell subjected periodic boundary constraint. It is shown that significant statistical correlation exists between the in-plane elastic properties and it depends on the variations of both the constituent properties and the unit-cell geometry. Two numerical examples are present on the reliability evaluation of unidirectional and multi-layer laminated plates bearing multi-axial in-plane loads, and this is conducted at two scenarios: considering and neglecting the statistical correlation. Monte-carlo (MC) method is employed to conduct the reliability calculation and Gibbs sampling is used for drawing samples where there is statistical correlation between random variables. For the multi-layer laminated plates, it is observed that neglecting the statistical correlation would result an 15-20% overestimation on the laminate failure probability, which indicates the importance of consideration of the statistical correlation in the process of reliability evaluation or reliability based design of plain-weave composite structures.