Multi-Domain Semi-Analytical Cohesive Zone Approach

Abstract

With the progressively more widespread exploitation of post-buckled skin-stiffened structures in the aerospace industry, aimed at making them more weight efficient, assessing the failure of such structures is of utmost importance. Additionally with the trend of moving towards fastener free connections, one of the potential failure modes of skin-stiffened structures is the skin-stiffener separation that leads to a sudden and drastic reduction in the load carrying capacity of the structure. Hence, it is imperative that structures are designed against such failure modes, being crucial to have predictive models for the initiation and propagation of delaminations at the connection interface.

Given this motivation, the present thesis investigates the development of a novel multi-domain semi-analytical cohesive zone approach to predict the initiation and propagation of damage along a two-dimensional interface. In the multi-domain method the main structure being analyzed is decomposed into multiple smaller domains for computational advantage, with each domain having its own set of continuous approximation functions based on the Ritz method. A penalty formulation governs the inter-connection of domains. To extend the multi-domain framework to model damage, the interface connection is modelled as a cohesive zone with the traction-separation law governing its response. The area connection from the multi-domain method is modified to include a damage-dependent penalty stiffness term, whose degradation is controlled by the traction-separation law of the cohesive zone model. Lastly, the energy dissipated to create a crack is included in the formulation. Since the framework is based on the Ritz approach, the appropriate choice of continuous approximations to model damage is investigated, presenting their limitations and the proposed methods to overcome them.

Finally, the results obtained from the multi-domain framework were verified against finite elements for a multitude of cases, which in turn had been validated by experimental data. The results were subsequently followed by discussions and the caveats of the developed framework. Results indicate that the developed multi-domain semi-analytical cohesive zone method predicts the results within 4.3% of finite element results, while taking 75% less time on average.

Finally, having somewhat successfully modelled the initiation and propagation of damage along a two-dimensional interface, this thesis establishes a robust basis for future research involving the use mixed-mode behaviours with multi-linear cohesive laws, whose formulations can just be slotted into the current framework. All of this forms a solid foundation to efficiently model damage initiation in larger structures and, more concretely, skin-stiffener separation.