Strength Prediction of Adhesively-bonded Scarf Repairs in Composite Structures under Bending

This work reports on the experimental and numerical study of the bending behaviour of two-dimensional adhesively-bonded scarf repairs of carbon-epoxy laminates, bonded with the ductile adhesive Araldite 2015. Scarf angles varying from 2 to 45o were tested. The experimental work performed was used to validate a numerical Finite Element analysis using ABAQUS and a methodology developed by the authors to predict the strength of bonded assemblies. This methodology consists on replacing the adhesive layer by cohesive elements, including mixed-mode criteria to deal with the mixed-mode behaviour usually observed in structures. Trapezoidal laws in pure modes I and II were used to account for the ductility of the adhesive used. The cohesive laws in pure modes I and II were determined with Double Cantilever Beam and End-Notched Flexure tests, respectively, using an inverse method. Since in the experiments interlaminar and transverse intralaminar failures of the carbon-epoxy components also occurred in some regions, cohesive laws to simulate these failure modes were also obtained experimentally with a similar procedure. A good correlation with the experiments was found on the elastic stiffness, maximum load and failure mode of the repairs, showing that this methodology simulates accurately the mechanical behaviour of bonded assemblies. Introduction Carbon-Fibre Reinforced Plastic (CFRP) composites are often used in structures requiring high specific strength and stiffness. However, these materials are highly susceptible to suffer delamination damage, due to their low interlaminar strength. Adhesively-bonded repairs of structures with these materials are increasing in engineering applications, compared to the traditional repair techniques, such as riveting or mechanical fastening. Adhesively-bonded repairs benefit from a reduction of weight, easy conformance to complex shapes, less stress concentrations, preservation of the fibres continuity, amongst other advantages. There are mainly two repair techniques for composite structures: strap (single or double) and scarf repairs. The larger bond areas and the reduction of stress concentrations at the bond edges due to the adherend tapering effect justify the higher efficiency of the scarf repairs, compared to the easy-execution strap repairs. The majority of the works on the strength of scarf joints or repairs focus on their tensile behaviour. Li et al. [1] proposed a technique based on relative strain measurements, using Bragg grating sensors, to identify debonding onset in scarf joints under tension. Debonding onset was detected by a differential strain approach, using two sensors whose strain differential increased with the debond length. A two-dimensional stress and failure Finite Element Method (FEM) numerical analysis of tensile loaded CFRP scarf repairs was carried out by Odi and Friend [2], for scarf angles varying from 1.1 to 9.2o. The repairs strength was predicted using the Tsai-Wu and maximum stress failure criteria for the adherend and the average shear stress failure criterion for the adhesive. Kumar et al. [3] presented an experimental and FEM study regarding the tensile strength of CFRP scarf joints. The numerical failure loads as a function of the scarf angle were obtained using the FEM and the Hashin-Lee criterion for the adherends, and agreed with the experimental ones. This work addresses an experimental and numerical study of CFRP adhesively-bonded scarf repairs under bending. Scarf angles (α) varying from 2 to 45o are considered. The experimental results were used to validate a developed numerical methodology using the FEM and a mixed-mode cohesive damage model implemented in ABAQUS. The behaviour of the adhesive layer was modelled using cohesive elements with trapezoidal traction-separation laws in pure modes I and II. This shape was selected to account for the ductility of the adhesive used in this work (Araldite 2015). The respective cohesive laws in pure modes I and II were determined with Double Cantilever Beam (DCB) and End-Notched Flexure (ENF) tests, respectively, using an inverse method. Since in the experiments interlaminar and transverse intralaminar failures also occurred, cohesive laws to simulate these failure modes were also obtained experimentally with an identical procedure. Cohesive Damage Model Model Description. A mixed-mode (I+II) cohesive damage model implemented within zero thickness interface finite elements was used to simulate a thin adhesive layer of Araldite 2015. A trapezoidal law between stresses (σ) and relative displacements (δr) between homologous points of the interface finite elements was used (Fig. 1). Fig. 1 – Trapezoidal softening law in pure mode and mixed mode. It is thus necessary to know the local strength at the crack tip (σu,i, i=I, II) and the fracture toughness (Jic, i=I, II) in each mode. Damage initiation is predicted using the following quadratic stress criterion