R.D.S.G. Campilho

Advances in Numerical Modelling of Adhesive Joints

The analysis of adhesively bonded joints started in 1938 with the closed-form model of Volkersen. The equilibrium equation of a single lap joint led to a simple governing differential equation with a simple algebraic equation. However, if there is yielding of the adhesive and/or the adherends and substantial peeling is present, a more complex model is necessary. The more complete is an analysis, the more complicated it becomes and the more difficult it is to obtain a simple and effective solution. The finite element (FE) method, the boundary element (BE) method and the finite difference (FD) method are the three major numerical methods for solving differential equations in science and engineering. These methods have also been applied to adhesive joints, especially the FE method. This book deals with the most recent numerical modelling of adhesive joints. Advances in damage mechanics and extended finite element method are described in the context of the FE method with examples of application. The classical continuum mechanics and fracture mechanics approach are also introduced. The BE method and the FD method are also discussed with indication of the cases they are most adapted to. There is not at the moment a numerical technique that can solve any problem and the analyst needs to be aware of the limitations involved in each case.

Modelling of Single-Lap Joints Using Cohesive Zone Models: Effect of the Cohesive Parameters on the Output of the Simulations

The available techniques for strength prediction of bonded joints have improved over the years. Cohesive zone models (CZM) coupled to finite element method (FEM) analyses surpass the limitations of stress/strain and fracture criteria, and simulate damage growth. CZMs require the instantaneous energy release rates in tension (G n) and shear (G s) along the fracture paths and respective fracture energies in tension (G n c) and shear (G s c), and crack growth is ruled by traction-separation laws that are established at the failure paths. Additionally, the cohesive strengths must be defined (t n 0 for tension and t s 0 for shear) relating to the onset of damage. A few techniques are available for the estimation of these parameters (e.g., the property identification technique, the direct method and the inverse method) that differ in complexity and expected accuracy of the results. In this work, the influence of the cohesive law parameters of a triangular CZM used to model a thin adhesive layer in bonded joints is studied, to estimate their effect on the predictions. Some conclusions were established to provide important data for the proper selection of the estimation technique and expected accuracy of the simulation results.

Stress and failure analyses of scarf repaired CFRP laminates using a cohesive damage model

This study describes stress and failure analyses of tensile loaded repaired Carbon Fibre Reinforced Composite (CFRP) laminates, using scarf configuration. A numerical model including interface finite elements was used to obtain peel and shear-stress distributions in the directions tangent and normal to the scarf. These stresses were evaluated at several locations in the repair, namely in the middle of the adhesive, at interfaces between adhesive and patch, and between adhesive and parent material. Several scarf angle values were considered in the analysis. A cohesive mixed-mode damage model was also used to carry out the failure analysis, in order to assess the efficiency of the repairs, for different stacking sequences. A study was performed to evaluate the influence of the mechanical properties of the adhesive and parent laminate/adhesive and adhesive/patch interfaces on the strength and failure modes of the joint. It was concluded that the strengths of the adhesive and interfaces are more important than the fracture properties in the failure process of the repair. It was also verified that the strength of the repair increased exponentially with the scarf angle reduction.

Strength Improvement of Adhesively-Bonded Joints Using a Reverse-Bent Geometry

Adhesive bonding of components has become more efficient in recent years due to the developments in adhesive technology, which has resulted in higher peel and shear strengths, and also in allowable ductility up to failure. As a result, fastening and riveting methods are being progressively replaced by adhesive bonding, allowing a big step towards stronger and lighter unions. However, single-lap bonded joints still generate substantial peel and shear stress concentrations at the overlap edges that can be harmful to the structure, especially when using brittle adhesives that do not allow plasticization in these regions. In this work, a numerical and experimental study is performed to evaluate the feasibility of bending the adherends at the ends of the overlap for the strength improvement of single-lap aluminium joints bonded with a brittle and a ductile adhesive. Different combinations of joint eccentricity were tested, including absence of eccentricity, allowing the optimization of the joint. A Finite Element stress and failure analysis in ABAQUS® was also carried out to provide a better understanding of the bent configuration. Results showed a major advantage of using the proposed modification for the brittle adhesive, but the joints with the ductile adhesive were not much affected by the bending technique.

Temperature Dependence of the Fracture Toughness of Adhesively Bonded Joints

Adhesives used in structural high temperature space and aerospace applications must operate in extreme environments. They need to exhibit high-temperature capabilities in order to maintain their mechanical properties and their structural integrity at the intended service temperature. One class of the adhesives which are able to withstand the temperature extremes that are experienced in the space environment and are able to maintain a good degree of flexibility at very low temperatures are the room temperature vulcanizing (RTV) silicone adhesives. As is known, adhesive strength generally shows temperature dependence. Similarly, the fracture toughness is expected to show temperature dependence. In this study, the pure mode I fracture toughness for adhesive joints bonded with a high temperature RTV silicone adhesive was measured over a wide range of temperatures. Double cantilever beam (DCB) tests were performed on specimens at room temperature (RT), 100 and 200°C. Mode I traction–separation laws were obtained as a function of temperature, directly from the experiments, by differentiation of simultaneously measured data (the J-integral and the end-opening displacement). Results showed that the fracture toughness, the peak cohesive stress and the respective end-opening displacement all decreased with the temperature rise.

Effects of temperature and loading rate on the mechanical properties of a high temperature epoxy adhesive

The variation of the mechanical properties of adhesives with temperature and strain rate is one of the most important factors to consider when designing a bonded joint due to the polymeric nature of adhesives. It is well known that adhesive strength generally shows temperature dependence. Moreover, in many structural applications, the applied loads can be dynamic and the design of the joint requires the knowledge of the high loading rate mechanical behaviour of the adhesive. In this study, the combined effect of the temperature and test speed on the tensile properties of a high temperature epoxy adhesive was investigated. Tensile tests were performed at three different test speeds and various temperatures (room temperature (RT) and high temperatures (100, 125 and 150°C)). The glass transition temperature (T g) of the epoxy adhesive investigated is approximately 155°C. The ultimate tensile stress decreased linearly with temperature (T) while increased logarithmically with the loading rate, which is in the accord with the Airings molecular activation model.

The Effect of Adhesive Thickness on the Mechanical Behavior of a Structural Polyurethane Adhesive

One parameter that influences the adhesively bonded joints performance is the adhesive layer thickness. Hence, its effect has to be investigated experimentally and should be taken into consideration in the design of adhesive joints. Most of the results from literature are for typical structural epoxy adhesives which are generally formulated to perform in thin sections. However, polyurethane adhesives are designed to perform in thicker sections and might have a different behavior as a function of adhesive thickness. In this study, the effect of adhesive thickness on the mechanical behavior of a structural polyurethane adhesive was investigated. The mode I fracture toughness of the adhesive was measured using double-cantilever beam (DCB) tests with various thicknesses of the adhesive layer ranging from 0.2 to 2 mm. In addition, single lap joints (SLJs) were fabricated and tested to assess the influence of adhesive thickness on the lap-shear strength of the adhesive. An increasing fracture toughness with increasing adhesive thickness was found. The lap-shear strength decreases as the adhesive layer gets thicker, but in contrast to joints with brittle adhesives the decrease trend was less pronounced.

Single-Lap Joints of Similar and Dissimilar Adherends Bonded with an Acrylic Adhesive

In this study, the tensile strength of single-lap joints (SLJs) between similar and dissimilar adherends bonded with an acrylic adhesive was evaluated experimentally and numerically. The adherend materials included polyethylene (PE), polypropylene (PP), carbon-epoxy (CFRP), and glass-polyester (GFRP) composites. The following adherend combinations were tested: PE/PE, PE/PP, PE/CFRP, PE/GFRP, PP/PP, CFRP/CFRP, and GFRP/GFRP. One of the objectives of this work was to assess the influence of the adherends stiffness on the strength of the joints since it significantly affects the peel stresses magnitude in the adhesive layer. The experimental results were also used to validate a new mixed-mode cohesive damage model developed to simulate the adhesive layer. Thus, the experimental results were compared with numerical simulations performed in ABAQUS®, including a developed mixed-mode (I+II) cohesive damage model, based on the indirect use of fracture mechanics and implemented within interface finite elements. The cohesive laws present a trapezoidal shape with an increasing stress plateau, to reproduce the behaviour of the ductile adhesive used. A good agreement was found between the experimental and numerical results.

Computational Modelling of the Residual Strength of Repaired Composite Laminates Using a Cohesive Damage Model

This work reports on a three-dimensional numerical analysis to assess the residual strength of single and double-strap repaired CFRP composite laminates, under tensile, compressive and bending loads. Interface finite elements including a triangular cohesive mixed-mode damage model are used in order to simulate damage onset and growth. The influences of several geometric changes on damage onset as well as growth and on the repair residual strength are addressed. The geometric changes include chamfering the outer and inner patch faces, filling the drilled hole with adhesive (plug filling), use of fillets of different shapes and dimensions at the outer edge of the overlap, chamfering the outer and inner parent laminate faces and combinations thereof. This work showed that with the correct repair geometry, a significant strength improvement could be achieved for all the loads considered and for both single and double-strap geometries.

Adhesive Selection for Single Lap Bonded Joints: Experimentation and Advanced Techniques for Strength Prediction

The integrity of multi-component structures is usually determined by their unions. Adhesive-bonding is often used over traditional methods because of the reduction of stress concentrations, reduced weight penalty, and easy manufacturing. Commercial adhesives range from strong and brittle (e.g., Araldite® AV138) to less strong and ductile (e.g., Araldite® 2015). A new family of polyurethane adhesives combines high strength and ductility (e.g., Sikaforce® 7888). In this work, the performance of the three above-mentioned adhesives was tested in single lap joints with varying values of overlap length (LO). The experimental work carried out is accompanied by a detailed numerical analysis by finite elements, either based on cohesive zone models (CZM) or the extended finite element method (XFEM). This procedure enabled detailing the performance of these predictive techniques applied to bonded joints. Moreover, it was possible to evaluate which family of adhesives is more suited for each joint geometry. CZM revealed to be highly accurate, except for largely ductile adhesives, although this could be circumvented with a different cohesive law. XFEM is not the most suited technique for mixed-mode damage growth, but a rough prediction was achieved.