Högskolan i Skövde

A cohesive zone model is presented for analyzing the fatigue life of an adhesive joint in the range of 10⁴–10⁶ load cycles. The parameters of the model are derived from Mode I double cantilever beam experiments. Fatigue experiments with adhesively joined components from the automotive industry are performed, and the results from the experiments are compared to the results of simulations. The error in the predicted fatigue strength is of the same order as the statistical deviation of the fatigue experiments, indicating that the simulation method produces acceptable predictions of the fatigue strength for applications in e.g. early product development.

For adhesive tapes, the strain before fracture often exceeds 500%. Although the maximum stresses are quite modest the high strains to fracture result in impressive fracture energy. Due to hydrostatic stress the fracture process often starts by nucleation of microscopic cracks inside the layer. The final crack path is usually close to one of the adherends.

Repeated experiments are performed both with DCB-specimens and butt-joints. The used adhesive tape is an acrylic foam tape with a thickness of 1.1 mm and a width of 19 mm. The geometry of the specimen is adapted to the properties of the soft layer. For the DCB-specimen this implies that the length of the specimen is about 1 m. The evaluated cohesive laws from the DCB- specimens give a fracture energy of 2 kN/m and a maximum stress about 0.5 MPa. For the butt-joints, the evaluated cohesive law corresponds well to the results from the DCB-experiments. However, the strain to fracture is slightly smaller. The stress in these specimens is distributed over a larger area and a nucleated crack rapidly crosses the load bearing area and fails the joint prematurely. For both kinds of experiments the evaluated cohesive laws show a small linear part. After this part there is an almost linear strain-hardening phase until fracture.

Mode I fatigue crack growth at load levels close to the threshold is studied with the aim of improving the understanding of the fatigue properties. We also aim at identifying a suitable damage evolution law for large-scale simulation of built-up structures. A fatigue test rig is designed where up to six specimens are tested simultaneously. Each specimen is evaluated separately indicating the specimen-to-specimen variation in fatigue properties. A rubber-based and a PUR-based adhesive are tested. The two adhesives represent adhesives with very different material properties; the rubber adhesive is a stiff structural adhesive and the PUR adhesive is a soft modular adhesive. The experiments are first evaluated using a traditional Paris’ law approach. Inspired by an existing damage evolution law, a modified damage evolution law is developed based on only three parameters. The law is implemented as a user material in Abaqus and the parameters are identified. The results from simulations show a very good ability to reproduce the experimental data. With this model of fatigue damage, a zone of damage evolves at the crack tip. The extension of this zone depends on the stiffness of the adherends; stiffer adherends leads to a larger damage zone. This means that the rate of crack growth depends on the stiffness of the adherends. Thus, not only the state at the crack tip governs the rate of crack growth. This is in contrast to the results of a model based on Paris’ law where only the state at the crack tip, through the energy release rate, governs the rate of crack growth. This indicates that the threshold value of the energy release rate may depend on the stiffness of the adherends.

The capability to predict high cycle fatigue properties of adhesive joints is important for cost-efficient and rapid product development in the modern automotive industry. Here, the adaptability of adhesives facilitates green technology through the widening of options of choosing and joining optimal materials. In the present paper a continuum damage mechanics model is developed based on the adhesive layer theory. In this theory, through-thickness averaged variables for the adhesive layer are used to characterise the deformation, damage and local loading on the adhesive layer. In FE-simulations, cohesive elements can thereby be used to model the adhesive layer. This simplifies simulations of large scale complex built-up structures. The model is adapted to experimental results for two very different adhesive systems; one relatively stiff rubber based adhesive and one soft polyurethane based adhesive. The model is able to reproduce the experimental results with good accuracy except for the early stage of crack propagation when the loads are relatively large. The model also predicts a threshold value for fatigue crack growth below which no crack growth occurs. The properties of the model are also compared with the properties of Paris’ law. The relations between the parameters of the continuum damage mechanics law and the parameters of Paris’ law are used to adapt the new law. It also shows that the properties of a joined structure influence the Paris’ law properties of the adhesive layer. Thus, the Paris’ law properties of an adhesive layer are not expected to be transferable to joints with adherends having different mechanical properties.

Att beräkna limfogars hållfasthet är inte helt enkelt, vilket beror på spänningskoncentrationens inflytande vid limfogens kanter.

Materialmekanik vid Högskolan i Skövde har specialiserat sig på hållfasthetssimulering av limfogar genom kohesiv modellering.

An overview of recent development of cohesive modelling is given. Cohesive models are discussed in general and specifically for the modelling of adhesive layers. It is argued that most cohesive models model a material volume and not a surface. Detailed microscopic and mesomechanical studies of the fracture process of an engineering epoxy are discussed. These studies show how plasticity on the mesomechanical length scale contributes to the fracture energy in shear dominated load cases. Methods to measure cohesive laws are presented in a general setting. Conclusions and conjectures based on experimental and mesomechanical studies are presented. The influence of temperature and strain rate on the peak stress and fracture energy of cohesive laws indicates fundamentally different mechanisms responsible for these properties. Experiments and mesomechanical studies show that in-plane straining of an adhesive layer can give large contributions to the registered fracture energy. Finite element formulations including a method to incorporate this influence are discussed.

Today, crash simulations replace crash testing in the product development phase in theautomotive industry. High quality simulations enable shorter product development time andhigher competitiveness. However, increasing requirements regarding emissions andcrashworthiness are demanding optimised material choice in the parts constituting the carbody structure. Lightweight materials are becoming frequently used. Joining dissimilarmaterials is difficult using common joining techniques like spot welding. To this end,adhesive joining is currently gaining popularity not only due to the ability to join dissimilarmaterials, joint integrity and structural stiffness both increase by the use of adhesive joining.Moreover, the number of spot welds may be reduced in hybrid joints.In this thesis, adhesive joints are studied with respect to crashworthiness of automotivestructures. The main task for the adhesive is not to dissipate the impact energy, but to keep thejoint integrity so that the impact energy can be consumed by plastic work of the basematerials. Fracture of adhesives can be accurately modelled by cohesive zones. The dynamicbehaviour of finite element structures containing cohesive zones is studied using a simplifiedstructure. An amplified strain rate is found in the adhesive as compared to the base material.The cohesive zone concept is used in the development of a 2D interphase element. Theaccuracy and time step influence of the interphase element is compared to solutions based oncontinuum element representation of the adhesive. The interphase element is found to predictfracture of the adhesive joint with engineering accuracy and has a small effect on the timestep of the explicit FE method.The cohesive laws for use in the material models of the adhesive have been determined usingdedicated test methods. The double cantilever beam specimen and the end notched flexurespecimen are used with inverse methods to determine cohesive laws in peel and shear,respectively. The cohesive laws are determined for varying temperature, strain rate andadhesive layer thickness. A built up bimaterial beam is designed for testing and simulation ofjoints consisting of bolts, adhesives and combinations of bolts and adhesives, i.e. hybridjoints. The model of the hybrid beam developed was found to be able to predict results fromimpact tests, quantified as maximum load and deformed shape of the beam.

The development of competitive and crashworthy automotive car bodies has reached so far that the manufacturers no longer rely on mono-material steel structures. Improved strength/weight performance may be achieved by using optimal material in each part of the car structure, leading to bi-material joints and ruling out spot welding; the common joining method during the past half century of automotive history. Adhesive bonding is an attractive joining method, not only capable of managing dissimilar materials, but also capable of improving stiffness and strength in monomaterial structures. Moreover, the joints do not need additional sealing and there may be cost savings using adhesive bonding. Impact simulation of car structures is mostly performed using an explicit FE-method. This method has an inherent stability criterion: the time step used may not exceed the stable time step, or critical time step, Δtc. In this thesis, a simplified cohesive zone model is studied. It is implemented into an explicit FE-code and compared to a closed form solution. The FE-solutions agree with the closed form solutions. It is found that the evolution of damage in the adhesive layer may stop under certain conditions that are likely to occur in a real structure. It is shown that an explicit FE-analysis with a “large” time step is more prone to give immediate rupture. Thus, the method is conservative. An interphase element formulation is derived for a 2D-adhesive joint model, joining beam adherends. It is shown that the mass matrix of the interphase element gives a small contribution to the mass matrix of the structure. However, this contribution is positive for the numerical stability of the explicit FE-method and it is recommended to keep this matrix in the analysis. Moreover, it is concluded that the contribution of material damping of the adhesive layer can be neglected as compared to the effects of plasticity of the adherends. The interphase element formulation is used to analyse the Double Cantilever Beam specimen. The results are compared to an alternative model using continuum elements. The comparison shows substantially faster convergence and shorter execution time for the interphase formulation. A rough estimate indicates fifteen times shorter execution time using the interphase elements in a realistic structure.