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.

This thesis concerns some aspects that have influence on the strength of adhesive layers. The strength is determined by the stress deformation-relation of the layer. This relation is also referred to as cohesive law. The aspects having influence on the cohesive laws that are studied in this work are temperature, fatigue, multi-axial fatigue and mixed mode loading.

For each aspect, a model is developed that can be used to describe the influence of the aspects on the cohesive laws numerically, e.g. by using the finite element method. These models are shown to give good agreement with the experimental results when performing simulations that aims at reproducing the experiments. For the aspect of temperature, a FE-model is suggested that can be used to simulate the mechanical behaviour in pure mode loadings at any temperature within the evaluated temperature span. Also, a damage law for modelling high cycle fatigue in a bonded structure in multi-axial loading is presented. Lastly, a new experimental set-up is presented for evaluating strength of adhesives during mixed mode loading. The set-up enables loading with a constant mode-mix ratio and by the experimental results, a potential model for describing the mechanical behaviour of the evaluated adhesive is presented.

A so called Controlled Mixed-Mode Bending (CMMB) test is presented, which has been developed toinvestigate the fracture of crash-optimized, elastic-plastic adhesives loaded in mixed-mode. While mostcommon mixed-mode tests, like e.g. the MMB test, work fine with brittle adhesives, the controlled MMBtakes into account the large crack opening displacements at the crack tip and ensures a constant mode mixat the crack tip by the regulation of two actuators. Consequently, the definition of mode mixity is asignificant difference to state-of-the-art experiments, which define the mode mixity in terms of the ratio ofdissipated energy in the single modes and which are therefore based on analytical models or assumptionsconcerning the energy dissipation during the test. A further target of the presented CMMB test is to obtain information on the complete shape of the socalled traction separation law, which describes the relation between stress and displacement inside theadhesive layer. Such traction separation law is often used to define the failure behaviour of an adhesivejoint within a numerical analysis, using cohesive elements in a finite element code or similar approaches. Beside the theory and the idea of the CMMB test, experimental results for the adhesive SikaPower 498 arepresented and deeply discussed with respect to difficulties and limitations of the proposed method and therealized experimental setup.

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.

The mode II properties of adhesives joints are of special interest since these joints are strongest if loaded in shear. Today no standardized method is available to measure shear properties. After a brief discussion of different models used to analyse adhesive joints, we identify some of the reasons for problems that arise in some of the more frequently used experimental methods. It is shown that transversally loaded specimens with elastically deforming adherends can lead to unstable crack growth provided the un-cracked specimen is flexible. With tough adhesives, a substantial process zone develops at the crack tip. That is, most specimens are in a state of large scale yielding. If not properly taken into account, the evaluated properties will be in error. Moreover, the process zone may grow in under the loading point which hinders its evolution and yield errors in the evaluated properties. Modest variations in loading conditions using the same specimen can yield considerable variation in the evaluated properties. However, properly designed and used, both the thick-adherend lap-shear joint and the end-notched flexure specimen provide useful results.

In this work, the influence of the temperature on the cohesive laws for two epoxy adhesives is studied at temperatures below the glass transition temperature for both Mode I and Mode II loading. Cohesive laws are measured experimentally under quasi-static loading conditions in the temperature range -30≤T≤80"C" . Three parameters of the cohesive laws are studied in detail: the elastic stiffness, the peak stress and the fracture energy. Methods for determining the elastic stiffness in Mode I and Mode II are derived and evaluated. With these methods, the results in this work show that it is possible to measure all three parameters for each pure mode loading case by the use of only the DCB- and the ENF-test specimens. Even though the measures tend to spread in values, this can significantly reduce the cost for performing experiments. It is shown that most of the cohesive parameters are decreasing with an increasing temperature in both loading modes and for both adhesives. An exception is the Mode I fracture energy for one of the adhesives. This is shown to be independent of the temperature in the studied temperature range. For the same adhesive, the Mode II fracture energy is shown to be continuously decreasing with an increasing temperature. The experimental results are verified by finite element analyses. The simulations only consider uncoupled cohesive behaviours. By use of the experimental results, simplified bi-linear cohesive laws to be used at any temperature within the studied temperature range are derived for one adhesive in both loading modes. This is desired in order to simulate adhesively bonded structures that suffer a wide range in temperature.

The influence of the temperature on the cohesive laws for an epoxy adhesive is studied in the glassy region, i.e. below the glass transition temperature. Cohesive laws are derived in both Mode I and Mode II under quasi-static loading conditions in the temperature range C. Three parameters of the cohesive laws are studied in detail: the elastic stiffness, the peak stress and the fracture energy. Methods for determining the elastic stiffness in Mode I and Mode II are derived and evaluated. Simplified bi-linear cohesive laws to be used at any temperature within the studied temperature range are derived for each loading mode. All parameters of the cohesive laws are measured experimentally using only two types of specimens. The adhesive has a nominal layer thickness of 0.3 mm and the crack tip opening displacement is measured over the adhesive thickness. The derived cohesive laws thus represent the entire adhesive layer as having the present layer thickness. It is shown that all parameters, except the Mode I fracture energy, decrease with an increasing temperature in both loading modes. The Mode I fracture energy is shown to be independent of the temperature within the evaluated temperature span. At C the Mode II fracture energy is decreased to about 2/3 of the fracture energy at C. The experimental results are verified by finite element analyses.

A perfect experiment is only sensitive to the properties to be analysed. However, evaluation of experimental results is always based on assumptions. Depending on the assumptions, the derived results are more or less correct. In this paper a method based on linear elastic fracture mechanics is compared to a method based on the path independence of the J-integral and the assumptions of the existence of a cohesive zone. Contrary to the other methods, the J-integral method only rests on the assumption that the material of the specimen has a strain energy density that not explicitly depends on the position in the direction of crack propagation. That is, the conditions for J to be path independent. Evaluation of simulated experiments gives the exact value of the fracture energy. The alternative method is based on linear elastic fracture mechanics. Contrary to the conventional methods we use an expression where the crack length is eliminated in favour of the flexibility of the specimen.

Influences of assumptions are studied both experimentally and numerically. Differences in stiffness are achieved by changing the type of adhesive and the layer thickness. Two different adhesives are studied. One is a modern crash resistant epoxy adhesive, SikaPower-498. This is a relatively stiff and tough adhesive. The other adhesive is a soft and extremely tough polyurethane based adhesive, Sikaflex-UHM. Two layer thicknesses are tested; 1.0 mm for the epoxy and 3.0 mm for the polyurethane based adhesive. The results show that the two methods give similar results for the thinner and stiffer epoxy adhesive but differences are recorded for the soft polyurethane based adhesive. This analysis gives a better understanding of the evaluation methods and their limitations and possibilities to extract cohesive laws.