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  • 1.
    Alfredsson, K. Svante
    University of Skövde, School of Engineering Science.
    On the determination of constitutive properties of adhesive layers loaded in shear - an inverse solution2003In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 123, no 1-2, p. 49-62Article in journal (Refereed)
    Abstract [en]

    A method to determine constitutive properties of thin adhesive layers loaded in shear is presented. The test specimen consists of two adherends joined by the adhesive layer. By loading the specimen antisymmetrically with respect to the adhesive layer a state of pure shear is ensured. To avoid instability the test specimen is designed to give a non-uniform stress distribution in the adhesive layer. This is achieved by using a long specimen loaded at one side. The method is based on an exact inverse solution which is derived utilizing the balance of the energetic forces of the applied loads and of the adhesive at the start of the adhesive layer. The method is intended for determination of both hardening and softening behaviour of adhesives but is confined to monotonic loading

  • 2.
    Alfredsson, Svante
    et al.
    University of Skövde, School of Technology and Society.
    Högberg, J. Li
    University of Skövde, School of Humanities and Informatics.
    Energy release rate and mode-mixity of adhesive joint specimens2007In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 144, no 4, p. 267-283Article in journal (Refereed)
    Abstract [en]

    Fracture behaviour of adhesive joints under mixed mode loading is analysed by using the beam/adhesive-layer (b/a) model, in which, the adherends are beamlike and the adhesive is constrained to a thin flexible layer between the adherends. The adhesive layer deforms in peel (mode I), in shear (mode II) or in a combination of peel and shear (mixed mode). Macroscopically, the ends of the bonded part of the joints can be considered as crack tips. The energy release rate of a single-layer adhesive joint is then formulated as a function of the crack tip deformation and the mode-mixity is defined by the shear portion of the total energy release rate. The effects of transversal forces and the flexibility of the adhesive layer are included in the b/a-model, which can be applied to joints with short crack length as well as short bonding length. The commonly used end-loaded unsymmetric semi-infinite joints are examined and closed-form solutions are given. In comparison to the singular-field model in the context of linear elastic fracture mechanics, the b/a-model replaces the singularity at the crack tip with a stress concentration zone. It is shown that the b/a-model and the singular-field model yield fundamentally different mode-mixities for unsymmetric systems. The presented closed-form b/a-model solutions facilitates parametric studies of the influence of unbalance in loading, unsymmetry of the adherends, as well as the flexibility of the adhesive layer, on the mode mixity of an adhesive joint.

  • 3.
    Andersson, Tobias
    et al.
    University of Skövde, School of Technology and Society.
    Biel, Anders
    University of Skövde, School of Technology and Society.
    On the effective constitutive properties of a thin adhesive layer loaded in peel2006In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 141, no 1-2, p. 227-246Article in journal (Refereed)
    Abstract [en]

    An experimental method to determine the complete stress-elongation relation for a structural adhesive loaded in peel is presented. Experiments are performed on the double cantilever beam specimen, which facilitates a more stable experimental set-up as compared with conventional methods like the butt-joint test. The method is based on the concept of equilibrium of the energetic forces acting on the specimen. Two sources of energetic forces are identified: the start of the adhesive layer and the positions of the two acting loads. By use of the concept of equilibrium of energetic forces, it is possible to measure the energy release rate of the adhesive layer instantaneously during an experiment. The complete stress-elongation relation is found to be the derivative of the energy release rate with respect to the elongation of the adhesive layer at its start. By this procedure, an effective property of the adhesive layer is measured. That is, the fields are assumed to be constant through the thickness of the layer and only vary along the layer. To investigate the validity of this approach, experiments are performed on five different groups of specimens with different dimensions. This leads to large variations in the length of the damage zone at the start of the adhesive layer. Four of the experimental groups are used to determine the stress-elongation relation. This is found to be independent of the geometry. For the remaining experimental group, the adherends deform plastically and simulations are performed with the stress-elongation relation determined from the four elastic groups. It is found that the relation cannot be used to accurately predict the behaviour of the experiments where the adherends deform plastically. This indicates that the stress-elongation relation has limited applicability.

  • 4.
    Biel, Anders
    et al.
    Department of Wind Energy, Technical University of Denmark, Roskilde, Denmark.
    Stigh, Ulf
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Cohesive zone modelling of nucleation, growth and coalesce of cavities2017In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 204, no 2, p. 159-174Article in journal (Refereed)
    Abstract [en]

    The stress-deformation relation i.e. cohesive law representing the fracture process in an almost incompressible adhesive tape is measured using the double cantilever beam specimen. As in many ductile materials, the fracture process of the tape involves nucleation, growth and coalesce of cavities. This process is studied carefully by exploiting the transparency of the used materials and the inherent stability of the specimen configuration. Utilising the path independence of the J -integral, the cohesive law is measured. The law is compared to the results of butt-joint tests. The law contains two stress peaks—the first is associated with nucleation of cavities at a stress level conforming to predictions of void nucleation in rubber elasticity. The second stress peak is associated with fracture of stretched walls between fully-grown cavities. After this second peak, a macroscopic crack is formed. The tape suffers at this stage an engineering strain of about 800%. A numerical analysis with the determined cohesive law recreates the global specimen behaviour.

  • 5.
    Biel, Anders
    et al.
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Damage and plasticity in adhesive layer: an experimental study2010In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 165, no 1, p. 93-103Article in journal (Refereed)
    Abstract [en]

    An experimental method is developed to identify a suitable model of in-elastic behaviour of an adhesive layer. Two prototype models are considered: an elastic-plastic model where the in-elasticity is considered due to permanent straining of the adhesive and an elastic-damage model where the in-elasticity is due to a reduction in elastic stiffness. Simulations show that the evaluated property is sensitive to the choice of model. In the experimental study of an engineering epoxy adhesive, the elastic-damage model fits the experiments. The study also reveals that plasticity and damage accumulated at the crack tip influences the evaluated fracture properties.

  • 6.
    Carlberger, Thomas
    et al.
    SAAB Automobile AB, Trollhättan, Sweden.
    Biel, Anders
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Influence of temperature and strain rate on cohesive properties of a structural epoxy adhesive2009In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 155, no 2, p. 155-166Article in journal (Refereed)
    Abstract [en]

    Effects of temperature and strain rate on the cohesive relation for an engineering epoxy adhesive are studied experimentally. Two parameters of the cohesive laws are given special attention: the fracture energy and the peak stress. Temperature experiments are performed in peel mode using the double cantilever beam specimen. The temperature varies from −40 to + 80°C. The temperature experiments show monotonically decreasing peak stress with increasing temperature from about 50 MPa at −40°C to about 10 MPa at + 80°C. The fracture energy is shown to be relatively insensitive to the variation in temperature. Strain rate experiments are performed in peel mode using the double cantilever beam specimen and in shear mode, using the end notch flexure specimen. The strain rates vary; for peel loading from about 10−4 to 10 s−1 and for shear loading from 10−3 to 1 s−1. In the peel mode, the fracture energy increases slightly with increasing strain rate; in shear mode, the fracture energy decreases. The peak stresses in the peel and shear mode both increase with increasing strain rate. In peel mode, only minor effects of plasticity are expected while in shear mode, the adhesive experiences large dissipation through plasticity. Rate dependent plasticity, may explain the differences in influence of strain rate on fracture energy between the peel mode and the shear mode.

  • 7.
    Eklind, Alexander
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Walander, Tomas
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Carlberger, Thomas
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Stigh, Ulf
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    High cycle fatigue crack growth in Mode I of adhesive layers: modelling, simulation and experiments2014In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 190, no 1-2, p. 125-146Article in journal (Refereed)
    Abstract [en]

    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.

  • 8.
    Högberg, J. Li
    University of Skövde, School of Technology and Society.
    Mixed mode cohesive law2006In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 141, no 3-4, p. 549-559Article in journal (Refereed)
    Abstract [en]

    A traction-separation relation to model the fracture process is presented. The cohesive law captures the linear elastic and softening behaviour prior to fracture. It also allows for different fracture parameters, such as fracture energy, strength and critical separation in different mode mixities. Thus, the fracture process in mode I (peel), in mode II (shear) or in mixed mode (a combination of peel and shear) can be modelled without the limitation of a common fracture energy in peel and shear. Examples are given in form of FE- implementations of the normalised cohesive law, namely for the Unsymmetrical Double Cantilever Beam (UDCB) specimen and the Mixed-mode double Cantilever Beam (MCB) specimen. Both specimens are adhesively bonded and loaded in mixed-mode

  • 9.
    Stigh, Ulf
    et al.
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Alfredsson, Svante K.
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Andersson, Tobias
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Biel, Anders
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Carlberger, Thomas
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Salomonsson, Kent
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Some aspects of cohesive models and modelling with special application to strength of adhesive layers2010In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 165, no 2, p. 149-162Article in journal (Refereed)
    Abstract [en]

    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.

  • 10.
    Walander, Tomas
    et al.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Biel, Anders
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Stigh, Ulf
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Temperature dependence of cohesive laws for an epoxy adhesive in Mode I and Mode II loading2013In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 183, no 2, p. 203-221Article in journal (Refereed)
    Abstract [en]

    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.

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