Parametric study of bonded composite joints under mixed-mode

Abstract

Composite aircraft structures have been thoroughly investigated with regard to various loading combinations, which are capable of inducing different failure modes. The failure modes, particularly the fracture energies associated with modes I and II, are influenced by geometric and material variations, contributing to both epistemic and intrinsic uncertainties. The present work introduces a numerical-experimental methodology to simulate the Mixed Mode Bending (MMB) test conducted on specimens manufactured with carbon fibre and epoxy resin adherents and a ductile-based epoxy adhesive. The methodology employs a two-dimensional finite element model developed in Abaqus^® software aided by a Python^® routine. The Design of Experiments (DoE) technique, based on the Plackett-Burman Design (PBD) method, is applied to reduce the number of simulations needed. To assess the impact of mechanical and geometric variables on fracture strength responses in various mixed-mode ratios, the Compliance-Based Beam Method (CBBM) adapted for the MMB test is used, following the ASTM D6671 standard. The numerical model uses 4-node cohesive elements (COH2D4) for the adhesive layer and 4-node plane strain elements (CPE4R) for the composite adherents, with the loading system modelled through two-node linear rigid links (R2D2). A triangular traction-separation law (TSL) is adopted to simulate adhesive behaviour, allowing validation against experimental results from the literature. The methodology, considering the investigated materials, was applied to mixed-mode ratios of 25%, 50%, 60%, and 75%, and results showed that at 25%, the influence of mode I fracture energy (G _Ic ) was only 8% lower than that of mode II (G _IIc ), whereas at higher ratios the difference exceeded 270%, highlighting the increasing dominance of mode II mechanisms. The numerical model consistently predicted fracture loads conservatively compared to experimental values, and the statistical analysis identified that mode II fracture energy and adhesive modulus are key parameters influencing bonded joint strength. The total mixed-mode fracture energy (G_Tc,MMB) resulting from CBBM was used to determine the Main Effect (ME), clearly ranking the parameters that most affect the mechanical behaviour of the bonded joint. These results demonstrate the effectiveness and robustness of the proposed methodology for assessing bonded composite joints under complex mixed-mode conditions.