Entwicklung eines probabilistischen Ersatzmodells für Faserverbundwerkstoffe zur Berücksichtigung mikromechanischer Materialunsicherheiten auf Lamina-Ebene

Kurzfassung

Nowadays fibre-reinforced plastics are used for a wide variety of engineering applications, especially for highly loaded parts and structures. In those cases, fibre-reinforced plastics are often the only lightweight material fulfilling the desired mechanical properties. But the effects of manufacturing laws and material uncertainties are far less predictable as they are for metals, thus leading to unnecessarily high safety margins and the postprocessing of unimportant manufacturing flaws. These downsides are limiting the further dissemination and exploitation in fields of engineering, in which manufacturing reliability is a predominant factor. Therefore, despite those outstanding mechanical properties, composite materials are rarely used within these fields. Within the AFP process these flaws are gaps and overlaps, which reduce the overall stiffness of the multi-layered composite and are simulated with a finite element model. Uncertainties of the components on the micromechanical level are not taken into account. A new analytical homogenization method based on three existing models is developed, describing the mechanical properties of the laminae as a function of up to seventeen micromechanical parameters. The method shows superb accuracy for a wide variety of possible applications and even holds in comparison to similar periodic homogenization methods. Furthermore, a multi-scale approach is described to propagate these uncertainties from the micromechanical to the composite level, using the newly developed homogenization method for the laminae and the classical laminate theory for the composite level. For each level, a metamodel based on the polynomial chaos expansion is developed to reduce the computing cost of the probabilistic simulations. Additionally, the scientific standard of using independent random variables to model the uncertainties is challenged. A probabilistic stability criterion is formulated for transversal-isotropic fibres. In some cases, this leads to a necessary correlation structure in-between the transversal Young’s modulus and the out-of-plane shear modulus. Finally a practical application is presented, transferring the approach onto a kriging-based metamodel of the existing finite element model to evaluate the influence of gaps in a multi-layered composite with micromechanical uncertainties. The usefulness of the approach is shown by the evaluation of the maximum gap width according to a predefined safety margin and an acceptable probability of failure. In conclusion, the overall methodology can be used to make the manufacturing process of fibrereinforced plastics more predictable and is therefore reducing its costs by removing the necessity for the correction of all manufacturing flaws.