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  • 1.
    Alfredsson, K. Svante
    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.
    Stability of beam-like fracture mechanics specimens2012In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 89, p. 98-113Article in journal (Refereed)
    Abstract [en]

    Test specimens used to determine the interlaminar strength of composites as well as the strength of adhesive layers are known to occasionally suffer from instability. Thus, even though the experiments are performed under controlled load-point displacement, the experiments are terminated prematurely by unstable crack propagation. Often there exists a critical crack length which must be exceeded in order to obtain stable crack propagation. In this paper, a general method to assess the stability of beam-like fracture mechanics specimens is developed. Both systems subjected to a single load and the more general situation with several independent loads are treated. A simple formula is derived for the critical crack length for one-parameter loading. The only parameter necessary as input is the compliance of the un-cracked specimen. For the case of non-proportional loading, stability is determined by studying the eigenvalues of a symmetric matrix. Other findings quantified in the paper are the effect of orthotropy, the influence of a flexible interphase layer and the influence of the compliance of the loading device.

  • 2.
    Alfredsson, Svante
    et al.
    University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    Continuum damage mechanics revised2004In: International Journal of Solids and Structures, ISSN 0020-7683, Vol. 41, no 15, p. 4025-4045Article in journal (Refereed)
    Abstract [en]

    A framework is derived for developing constitutive laws for engineering materials. The framework is based on physically motivated assumptions on the mechanical and thermal behaviour of plastically deformed and damaged materials. These assumptions are the starting point in a derivation of the relevant thermodynamic quantities. The procedure reveals important cross-dependencies that have to be considered while developing constitutive equations. A major result of this study is that both deterioration (increase of damage) and healing (decrease of damage) can be modelled in an integrated manner using the same constitutive law. For greater clarity the description is limited to small strain and isotropic behaviour

  • 3.
    Andersson, Tobias
    et al.
    University of Skövde, School of Engineering Science.
    Stigh, Ulf
    University of Skövde, School of Engineering Science.
    The stress-elongation relation for an adhesive layer loaded in peel using equilibrium of energetic forces2004In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 41, no 2, p. 413-434Article in journal (Refereed)
    Abstract [en]

    An experimental method to determine the stress–elongation relation for a thin adhesive layer loaded in peel is presented. The method is based on equilibrium of the energetic forces acting on a DCB-specimen. These energetic forces are identified to be associated with the geometrical positions of the acting loads and the start of the adhesive layer. The first energetic force is shown to be given by the product of the force and the rotation of the loading point. The second energetic force is shown to be given by the area under the stress–elongation curve for the adhesive layer. Using equilibrium of these energetic forces, the shape of the stress–elongation curve is determined. A test set-up is developed to facilitate the experiments. Special consideration is given to the accuracy of the measurement of the elongation of the adhesive. Results from two sets of experiments with slightly varying geometry are presented. The main result is that the stress–elongation relation can be described by a curve divided into three parts; initially the stress increases proportionally to the elongation. This corresponds to a linear elastic behaviour of the layer. The next part is given by a constant limiting stress. The curve ends with a parabolically softening part. After this point, a crack has been initiated in the adhesive. The experimental results are first compared to an asymptotic analysis using linear elastic fracture mechanics. This shows that the new method to evaluate the fracture energy gives consistent results. The experiments are also simulated using the measured stress–elongation law. Good agreement with the experiments is achieved which further validates the method. The fracture energy and the maximum peel stress are found to agree well within each set of experiments. Some variation is found between the two sets. This is accredited to differences in fracture initiation

  • 4.
    Biel, Anders
    et al.
    University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    An analysis of the evaluation of the fracture energy using the DCB-specimen2007In: Archives of Mechanics, ISSN 0373-2029, Vol. 59, no 4-5, p. 311-327Article in journal (Refereed)
    Abstract [en]

    The methods to estimate the fracture energy using DCB-specimens as advocated in common standards. For instance, ASTM D 3433 and BS 7991:2001 are based on a compliance method, i.e. on linear elastic fracture mechanics (LEFM). Since the mechanical properties of almost all adhesives are non-linear, errors are generated. In some of the standards, the non-linear behaviour is compensated for by the use of correction terms generated from the experiments. An analysis of the methods of evaluation the fracture energy from experiments is performed. This analysis is performed first by simulating an experiment using realistic data for an engineering adhesive and then, by analysing the results with different methods. In this way, the correct fracture energy is known beforehand and the error in the evaluated fracture energy can be determined. In the present work it is shown that the magnitude of this error depends on the length of the crack. The results show that some commonly  used methods generate substantial errors when a large region of non-linear deformation precedes the crack tip. It is also shown that methods based on nonlinear fracture methods do not produce this kind of error.

  • 5.
    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.

  • 6.
    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.

  • 7.
    Biel, Anders
    et al.
    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.
    Damage and plasticity of adhesive layers: an experimental study2011In: Procedia Engineering, ISSN 1877-7058, E-ISSN 1877-7058, Vol. 10, p. 2280-2285Article in journal (Refereed)
    Abstract [en]

    Time independent inelasticity is often modelled as due to plasticity and/or damage. The difference is manifested at reversed loading; plasticity reveals itself by a remaining strain in the unloaded state while damage is revealed by a decrease in the elastic stiffness during unloading. With thin adhesive layers, the deformation is inhomogeneously distributed along the layer. Large deformations occur at the ends of the layer. In the more central parts, the layer is virtually undeformed. This makes a direct measurement of the unloading properties virtually impossible. In the present paper, novel experiments are performed in order to evaluate the inelastic properties of epoxy adhesives. The load is first increased to a level corresponding to 50, 60, 70 or 80% of the fracture energy. The load is then reversed. The first step creates a zone of inelastically deformed adhesive at the start of the layer. During a final loading phase, the properties of this zone are analysed. Major differences due to the loading direction are observed. Some comparisons with simulation models are performed.

  • 8.
    Biel, Anders
    et al.
    University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    Effects of constitutive parameters on the accuracy of measured fracture energy using the DCB-specimen2008In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 75, no 10, p. 2968-2983Article in journal (Refereed)
    Abstract [en]

    Several methods exist to estimate the fracture energy for adhesive joints using the double cantilever beam specimen and linear elastic fracture mechanics. Since the mechanical properties of all adhesives are non-linear, errors are generated. By use of an exact solution experiments are simulated. These are evaluated with eight different methods. The influence of the constitutive parameters is systematically studied. This influence is small for most methods. The error due to the choice of evaluation method is considerably larger. One of the commonly used methods gives accurate results; the error is less than 3%. However, most methods yield substantial errors.

  • 9.
    Biel, Anders
    et al.
    Department of Wind Energy, Technical University of Denmark.
    Stigh, Ulf
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Measurement of tensile properties of fibres using a DCB-specimen2015In: 20th International Conference on Composite Materials: Copenhagen, 19-24th July 2015 / [ed] Ole Thybo Thomsen, Bent F. Sørensen, Christian Berggreen, 2015Conference paper (Refereed)
    Abstract [en]

    Constitutive data are needed at extreme strains to increase the understanding of fracture processes. Ordinary tensile tests ends prematurely due to localization and large amounts of elastic energy stored in the specimens prior to fracture. A novel method is proposed to perform tensile tests using a double cantilever beam specimen. To verify the method a large specimen is developed and tested. Similar results are achieved with the present method as with more standardized methods giving confidence in the method. The specimen should be possible to minimise to provide data with small specimens.

  • 10.
    Biel, Anders
    et al.
    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.
    Strength and toughness in shear of constrained layers2018In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 138, p. 50-63Article in journal (Refereed)
    Abstract [en]

    Confined layers may fracture in shear. This occurs, for example in adhesive joints and composite materials. A common mechanism for shear fracture is the formation of shear hackles associated with an expansion of the layer. This makes shear toughness and strength depend on the constraint of the expansion. By constraining the expansion using external loading in experiments, the expansion is reduced but not totally inhibited. The experiments are evaluated using the path independent properties of the J-integral. It is shown that the shear toughness increases for the more constrained case. Thus, from a strength analysis perspective, ignoring the expansion leads to a conservative estimate of the fracture properties. Extrapolation of the evaluated properties to totally inhibited expansions gives the traction separation relation and the fracture toughness for a layer in simple shear.

  • 11.
    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.
    Walander, Tomas
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Life Sciences.
    A Critical Study of an Alternative Method to Measure Cohesive Properties of Adhesive Layers2012In: Proceedings of the 19th European Conference on Fracture, Kazan Scientific Centre of the Russian Academy of Sciences , 2012Conference paper (Refereed)
    Abstract [en]

    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.

  • 12.
    Biel, Anders
    et al.
    University of Skövde, School of Technology and Society.
    Walander, Tomas
    University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    Influence of Edge-boundaries on the Cohesive Behaviour of an Adhesive Layer2012In: ASME 2012 International Mechanical Engineering Congress and Exposition, November 9–15, 2012, Houston, Texas, USA: Volume 8: Mechanics of Solids, Structures and Fluids, ASME Press, 2012, p. 507-511Conference paper (Refereed)
    Abstract [en]

    In comparison with other adhesives e.g. epoxies, polyurethane adhesives (PUR) are soft. In automotive applications, the thickness of PUR-adhesive layers is between about 2 to 5 mm. Since these adhesives cure by moisture, the width of the joints is limited. Often, the width is only marginally larger than the thickness of the layer. In numerical FE-simulations it is now common to represent epoxy adhesive layers by cohesive elements. With this model, both stress distribution and fracture can be modelled using mesh sizes that allows for large-scale analyses. Material properties are usually the result from experiments with coupon type specimens, e.g. the double cantilever beam specimen (DCB). With PUR-adhesives this approach is problematic. The adhesive is very flexible and effects from the edge-boundaries cannot be ignored. In order to study the influence of the edge-boundaries in peel loading, experiments with the DCB-specimens are performed. Specimens with a layer thickness of 3 mm and three different widths between 10.6 mm to 40.6 mm are studied. The PUR-adhesive SikaFlex-UHM is used. All the experiments are performed at a constant loading rate. The cohesive law is measured. The experimental results show that the maximum peel stress is increasing with an increasing width of the specimen, i.e. when the influences from the edges decrease. When the width increases from 10.6 mm to 40.6 mm, the maximum evaluated peak stress increases from about 5 MPa to about 7 MPa. From visual inspections during the experiments it is conjectured that crack growth starts with voids initiating inside the adhesive. At a critical point, the voids rapidly reach the surface and crack growth starts.

  • 13.
    Carlberger, Thomas
    et al.
    SAAB Automobile AB, Trollhättan, Sweden.
    Alfredsson, K. Svante
    University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    Explicit FE-formulation of interphase elements for adhesive joints2008In: International Journal for Computational Methods in Engineering Science & Mechanics, ISSN 1550-2287, E-ISSN 1550-2295, Vol. 9, no 5, p. 288-299Article in journal (Refereed)
    Abstract [en]

    The potential of adhesive bonding to improve the crashworthiness of cars is attracting the automotive industry. Large-scale simulations are time consuming when using the very small finite elements needed to model adhesive joints using conventional techniques. In the present work, a 2D-interphase element formulation is developed and implemented in an explicit FE-code. A simplified joint serves as a test example to compare the interphase element with a straightforward continuum approach. A comparison shows the time-saving potential of the present formulation as compared to the conventional approach. Moreover, the interphase element formulation shows fast convergence and computer efficiency.

  • 14.
    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.

  • 15.
    Carlberger, Thomas
    et al.
    SAAB Automobile, S-46180 Trollhättan, Sweden.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    An explicit FE-model of impact fracture in an adhesive joint2007In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 74, no 14, p. 2247-2262Article in journal (Refereed)
    Abstract [en]

    Dynamic fracture of an adhesive layer in a structure is analysed. The structure represents some specific properties of an automotive structure and is simple enough to allow for closed form solutions obtained by the method of characteristics. These solutions are compared to results of explicit FE-analyses. The FE-solutions agree with the closed form solutions. Damage is included in the FE-model. Three constitutive models of the adhesive layer are used. It is shown that an amplification of the strain rate is achieved in the adhesive layer. It is also shown that an artificially increased flexibility of the adhesive in an aluminium structure gives only minor influences of the general behaviour. In some load cases, the adhesive layer will experience repeated loading/unloading. It is shown that in these cases an explicit FE-analysis with a “large” time step is more prone to give immediate rupture. Thus, the method is conservative.

  • 16.
    Carlberger, Thomas
    et al.
    SAAB Automobile AB.
    Stigh, Ulf
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Dynamic testing and simulation of hybrid joined bi-material beam2010In: Thin-walled structures, ISSN 0263-8231, E-ISSN 1879-3223, Vol. 48, no 8, p. 609-619Article in journal (Refereed)
    Abstract [en]

    A specimen is developed for real-like low velocity impact testing of bi-material joint configurations. Six different joint configurations are analysed. Two engineering adhesives are evaluated with and without discrete mechanical fasteners, i.e. adhesive and hybrid joints. Experiments and simulations are performed. The simulations are performed using adhesive cohesive finite elements. Simulations show good agreement with experiments in impact energy and overall deformation mode. The histories of applied load vs. load-point deflection show reasonably good correlation. The results show that the impact energy consumption depends on the joint integrity. A threshold value for the fracture energy of the adhesive seems to exist. Beneath this value, adhesive and discrete fastener work together increasing the impact energy capacity. Above this value the discrete fastener has a negative effect, and may be regarded as a stress concentration.

  • 17.
    Carlberger, Thomas
    et al.
    SAAB Automobile AB.
    Stigh, Ulf
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Influence of Layer Thickness on Cohesive Properties of an Epoxy-Based Adhesive: An Experimental Study2010In: The journal of adhesion, ISSN 0021-8464, E-ISSN 1563-518X, Vol. 86, no 8, p. 814-833Article in journal (Refereed)
    Abstract [en]

    Cohesive laws are determined for different layer thicknesses of an engineering adhesive. The shape of the cohesive law depends on the adhesive layer thickness. Of  the  two  parameters  of  the  cohesive  law—the  fracture  energy  and  thestrength—the fracture energy is more sensitive to thickness variation than the strength. The fracture energy in peel mode (Mode I) increases monotonically as the thickness is increased from 0.1 to about 1.0 mm. At an adhesive thickness of 1.5 mm, the fracture energy is slightly lower than for a 1.0 mm adhesive thickness, indicating a maximum between 1.0 and 1.5 mm. In shear mode (Mode II), the thickness dependence is not as strong, but an increasing trend in fracture energy with increasing adhesive thickness is evident. A slight decrease in strength with increasing adhesive thickness is found in both loading modes.

  • 18.
    Carlberger, Thomas
    et al.
    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.
    Vilka hållfasthetsegenskaper har limfogen?: Simulering på Högskolan i Skövde ger svaren2014In: Fordonskomponenten, ISSN 2000-7299, no 3, p. 46-47Article, review/survey (Other (popular science, discussion, etc.))
    Abstract [sv]

    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.

  • 19.
    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.

  • 20.
    Högberg, J. Li
    et al.
    University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    Specimen proposals for mixed mode testing of adhesive layer2006In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 73, no 16, p. 2541-2556Article in journal (Refereed)
    Abstract [en]

    The experimental methods to determine the fracture properties for adhesives under mixed mode loading is not as well established as compared to such methods for adhesives under pure mode loading. Some controversies exist regarding the decomposition of the mode mixity. For a flexible linear elastic adhesive, the mode mixity of a single-layer adhesive joint is directly related to the deformation of the adhesive layer at the crack tip. The governing equations for linear elastic single-layer adhesive joints show that the mode mixity depends on the external loads, the properties of the adherends and often on the flexibility of the adhesive layer. This implies some fundamental problems that have to be addressed before an experimental method can be established. The purpose of this paper is to investigate different specimen configurations for mixed mode loading. Requirements for the design of a specimen configuration are given. A new specimen configuration is proposed based on the geometry of a semi-infinite symmetric DCB-specimen. According to this study, the proposed test specimen offers exceptional flexibility, variety and stability.

  • 21.
    Högberg, J. Li
    et al.
    University of Skövde, School of Technology and Society.
    Sørensen, B. F.
    Tech Univ Denmark, Mat Res Dept, Riso Natl Lab, DK-4000 Roskilde, Denmark.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    Constitutive behaviour of mixed mode loaded adhesive layer2007In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 44, no 25-26, p. 8335-8354Article in journal (Refereed)
    Abstract [en]

    Mixed mode testing of adhesive layer is performed with the Mixed mode double Cantilever Beam specimen. During the experiments, the specimens are loaded by transversal and/or shear forces; seven different mode mixities are tested. The J-integral is used to evaluate the energy dissipation in the failure process zone. The constitutive behaviour of the adhesive layer is obtained by a so called inverse method and fitting an existing mixed mode cohesive model, which uses a coupled formulation to describe a mode dependent constitutive behaviour. The cohesive parameters are determined by optimizing the parameters of the cohesive model to the experimental data. A comparison is made with the results of two fitting procedures. It is concluded that the constitutive properties are coupled, i.e. the peel and shear stress depend on both the peel and shear deformations. Moreover, the experiments show that the critical deformation in the peel direction is virtually independent of the mode mixity.

  • 22.
    Leffler, Karin
    et al.
    University of Skövde, School of Technology and Society.
    Alfredsson, K. Svante
    University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    Shear behaviour of adhesive layers2007In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 44, no 2, p. 530-545Article in journal (Refereed)
    Abstract [en]

    An experimental method to determine the complete stress versus deformation relation for a thin adhesive layer loaded in shear is presented. The method is based on a classic specimen geometry; the end-notch flexure specimen. The experiments are evaluated using an inverse method. First, the variation of the energy release rate with respect to the shear deformation at the crack tip is measured during an experiment. Then the traction–deformation relation is derived using an inverse method. The theory is based on the path-independence of the J-integral and considers the effects of a flexible adhesive layer.

    Quasi-static experiments on three different specimen geometries are performed using a servo-hydraulic testing machine. The experiments give consistent results. This shows that the traction–deformation relation can be taken as independent of the dimensions of the adherends. Thus, the constitutive relation can be considered as a property of the adhesive layer. The deformation process at the crack tip is also monitored during the experiments by the use of a digital camera attached to a microscope.

  • 23.
    Leffler, Karin
    et al.
    University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    On the existence of a unique stress-deformation relation for an adhesive layer loaded in shear2005In: 11th International Conference on Fracture (ICF11), Turin, Italy 20-25 March 2005: Volume 5, Curran Associates, Inc., 2005, p. 3763-3768Conference paper (Refereed)
    Abstract [en]

    An experimental method to determine the complete stress vs. deformation relation for a thin adhesive layer loaded in shear is presented. The experiments are performed by use of a classical specimen geometry, i.e. the end-notch flexure specimen, though the experiments are evaluated based on a novel inverse technique. With this  technique,  the  instantaneous  energy  release  rate  is  first  evaluated  by  use  of  a  theory  for  the  specimen based  on  the  Euler-Bernoulli  beam  theory.  Effects  of  a  flexible  adhesive  layer  are  considered  in  an approximate way. From the energy release rate, the stress-deformation relation is evaluated using an inverse method.  In  order  for  the  theory  to  be  valid,  the  adherends  of  the  specimen  are  only  allowed  to  deform elastically.  Quasi-static   experiments  are  performed  using  a  servo-hydraulic  testing  machine.  In  the experiments, the displacement of the loading point is gradually increased to obtain a constant velocity of the shear  deformation  at  the  crack  tip.  Formation  of  micro-cracks  and  the  propagation  of  a  macro-crack  are monitored during the experiments by use of a CCD-camera attached to a microscope. By varying the heights of the adherends, the size of the process zone in front of the crack tip changes from about 200 to 400 times the thickness of the adhesive layer. The results of the experiments give a fracture toughness of 2.5 kJ/m 2 , a critical  shear  deformation  of  0.13  mm,  and  a  maximal  strength  of  30  MPa  independent  of  the  specimen geometry.  The  experiments  show  consistent  results.  The  results  show  that  if  the  process  zone  is  large  as compared  to  the  thickness  of  the  adhesive layer,  the  shear  stress  –  shear  deformation  relation  can  be considered as a constitutive property of the adhesive layer.

  • 24.
    Marzi, Stephan
    et al.
    Fraunhofer IFAM, Wiener Str. 12, D-28359 Bremen, Germany.
    Biel, Anders
    University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    On experimental methods to investigate the effect of layer thickness on the fracture behavior of adhesively bonded joints2011In: International Journal of Adhesion and Adhesives, ISSN 0143-7496, E-ISSN 1879-0127, Vol. 31, no 8, p. 840-850Article in journal (Refereed)
    Abstract [en]

    A number of different experimental methods are used at two independent laboratories to evaluate the influence of layer thickness on the fracture properties atone batch of a crash resistant epoxy adhesive. Both mode I and II are considered. Novel, as well as state of the art methods are used. In mode I, the Double Cantilever Beam (DCB) and two versions of the Tapered Double Cantilever Beam (TDCB) specimens are utilized; in mode II, two versions of the End Notch Flexure (ENF) and the End-Loaded Shear Joint (ELSJ) specimens are used. Good agreement between the test results is achieved for thin layers in both fracture modes. For thicker layers the variation is larger. (C) 2011 Elsevier Ltd. All rights reserved.

  • 25.
    Marzi, Stephan
    et al.
    Fraunhofer IFAM, Bremen, Germany.
    Hesebeck, Olaf
    Fraunhofer IFAM, Bremen, Germany.
    Brede, Markus
    Fraunhofer IFAM, Bremen, Germany.
    Nagel, Christof
    Fraunhofer IFAM, Bremen, Germany.
    Biel, Anders
    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.
    Stigh, Ulf
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Effects of the bond line thickness on the fracture mechanical behaviour of structural adhesive joints2014In: Proceedings of the Annual Meeting of the Adhesion Society 2014, Adhesion Society , 2014, p. 189-192Conference paper (Refereed)
  • 26.
    Salomonsson, Kent
    et al.
    University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    An adhesive interphase element for structural analyses2008In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 76, no 4, p. 482-500Article in journal (Refereed)
    Abstract [en]

    A special purpose finite element is developed for structural simulations of complex adhesively bonded structures. In the interphase element, the adhesive is explicitly regarded as a material phase between two substrates. The element considers large rotations. Furthermore. it considers in-plane straining of the adhesive due to large curvatures of the bonded shells. This feature appears especially important when considering bonding of thin plastically deforming metallic shell structures. Simulations are made on specimens where the adherends deform both elastically and plastically. The results are in good agreement with previously performed experiments. Copyright (0 2008 John Wiley & Sons, Ltd.

  • 27.
    Salomonsson, Kent
    et al.
    Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, United States.
    Stigh, Ulf
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Influence of root curvature on the fracture energy of adhesive layers2009In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 76, no 13, p. 2025-2038Article in journal (Refereed)
    Abstract [en]

    Previously performed experiments to study the mode I behavior of an adhesive layer revealed an apparent increase in the fracture toughness when the adherends deformed plastically. Attempts to simulate the experiments are made; both with elastically and plastically deforming adherends. Thus, effects of the size of the process zone and the deformation of the adherends are revealed. The adhesive layer is modeled using finite elements with different approaches; cohesive elements and representative volume elements. The adherends are modeled with solid elements. With a long process zone, all models give good results as compared to the experiments. However, only the model with representative volume elements gives good agreement for large root curvatures and correspondingly short process zones. The results are interpreted by analyzing the deformation and mechanisms of crack propagation in the representative volume elements. It is shown that with large root curvature of the adherends, the in-plane stretching of the adhesive layer gives a substantial contribution to the fracture energy. A simple formula is derived and shown to give an accurate prediction of the effects of the root curvature. This result indicates the limits of conventional cohesive zone modeling of an adhesive layer of finite thickness.

  • 28.
    Salomonsson, Kent
    et al.
    University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    On the apparent influence of the adherends on the fracture toughness of adhesive layers2007In: Interface design of polymer matrix composites: mechanics, chemestry, modelling and manufacturing, 2007, p. 8 s.-Conference paper (Refereed)
    Abstract [en]

    A detailed model of experiments with the double cantilever beam specimen is set up. Analysis of the model shows that an experimentally deduced apparent increase of fracture energy with severely deforming adherends is due to contributions of in-plane straining of the adhesive layer to the fracture energy. An analysis with the J-integral confirms the result.

  • 29.
    Stigh, Ulf
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Applications of equilibrium of configurational forces for the measurement of cohesive laws2016In: Proceedings ECCM17: 17th European Conference on Composite Materials Munich, Germany, 26-30th June 2016, 2016Conference paper (Refereed)
    Abstract [en]

    A methodology to develop experimental methods to measure cohesive laws is introduced. This methodology is based on the property of all configurational forces equilibrium acting on a specimen to be in equilibrium. Two applications are given. The first shows a method to measure the cohesive law for shear representing the mechanical behaviour of an adhesive layer. The second application is a method to measure the cohesive law for the formation of a kink-band in a unidirectional composite. It is concluded that the methodology is critically dependent on the ability to associate a pseudopotential to the inelastic properties of the deforming material where the fracture process takes place. The importance to clearly identify the material that is modelled with the cohesive zone is also stressed.

  • 30.
    Stigh, Ulf
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Cohesive Laws for Delamination of CFRP: Experiments and Models2010In: ASME 2010 International Mechanical Engineering Congress and Exposition: Volume 9: Mechanics of Solids, Structures and Fluids, ASME Press, 2010, p. 45-50Conference paper (Refereed)
    Abstract [en]

    In the present paper, we study delamination of a carbon fibre reinforced composite at a small length scale, i.e. without consideration of crack bridging. The study is performed within the framework of cohesive modelling. We propose methods based on the applications of the path independent J-integral to measure the cohesive law for delamination. With a DCB-specimen, the cohesive law corresponding to mode I loading is measured and with an ENF-specimen, the law corresponding to mode II loading is measured. These laws are used to calibrate a mixed-mode cohesive law. It is argued that the most important parameters of a cohesive law are the ability to provide the correct fracture energy and strength. The cohesive law is developed using a minimum of adjustable parameters to provide a transparent calibration process.

  • 31.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    Continuum Damage Mechanics and the Life-Fraction rule2006In: Journal of applied mechanics, ISSN 0021-8936, E-ISSN 1528-9036, Vol. 73, no 4, p. 702-704Article in journal (Refereed)
    Abstract [en]

    This paper gives a short review of two different methods for life prediction at high temperature; namely continuum damage mechanics (CDM) and the linear life-fraction rule (LFR). It is well known that the class of CDM theories with a separable evolution law gives a life prediction in accordance with the LFR. However, it appears to be an open question if this is a necessary condition. It is here shown that in order for a CDM theory to comply with the LFR it must have a separable evolution law. That is, if we can assume that a material follows the LFR, it is necessary to chose a separable evolution law for this material. The reverse is also true, to get a life-fraction different from unity, we must chose a nonseparable evolution law.

  • 32.
    Stigh, Ulf
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Limning för hög hållfasthet2009In: Svetsen, ISSN 0039-7091, Vol. 68, no 3, p. 8-9Article in journal (Other academic)
  • 33.
    Stigh, Ulf
    et al.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Alfredsson, K. Svante
    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.
    Measurement of cohesive laws and related problems2009In: Proceedings of the ASME International Mechanical Engineering Congress and Exposition: IMECE2009, ASME Press, 2009, p. 293-298Conference paper (Refereed)
    Abstract [en]

    Cohesive modelling provides a simple method to introduce a process region in models of fracture. It is computationally attractive since it blends into the structure of finite element programmes for stress analysis. The development of computational methods and applications of cohesive modelling has accelerated during recent years. Methods to measure cohesive laws have also been developed. One class of such methods is based on the path-independence of the J-integral. By choosing a path encircling the cohesive zone, J can be shown to be given by the area under the traction-separation relation for the cohesive zone. Using an alternative path, J can in some cases be directly related to the applied load and deformation with relatively modest or no assumptions on the material behaviour. Thus, the cohesive law can be measured.

    Methods to measure cohesive laws for different specimen geometries are presented. The method are used to measure the cohesive law in peel, shear and mixed-mode for an adhesive layer. A new method to measure cohesive laws in shear is presented. The method is shown to give accurate data with a much smaller test pecimen than earlier methods.

  • 34.
    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.

  • 35.
    Stigh, Ulf
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Biel, Anders
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Effects of strain rate on the cohesive properties and fracture process of a pressure sensitive adhesive2018In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315Article in journal (Refereed)
    Abstract [en]

    Pressure sensitive adhesives provide high toughness at low stress and stiffness. These properties are beneficial for bimaterial bonding. In the present study the tape is modelled with a cohesive layer characterized by a cohesive law. This is suitable for FE-analysis of bonded structures. The cohesive law is measured using a method based on the path independent property of the J-integral. Complementing an earlier study, we here focus on influences of loading rate on the properties of the pressure sensitive adhesive. Transparent PMMA substrates are used with the transparent tape in Double Cantilever Beam specimens. The transparency of both the tape and the substrates provides the possibility of in-situ studies of the fracture process. The results indicate that the fracture energy levels off at about 1 kN/m for small loading rates. Moreover, the cohesive law also appears to level off below an engineering strain rate of about 2 s-1. The cohesive law contains two peak stresses. The first is associated with the nucleation of cavities in the tape. This occurs at a stress level comparable to the critical stress associated with an unbonded growth rate of a spherical cavity in rubber. The second peak stress is associated to the breaking down of walls formed between the fully developed cavities. This process precedes the final fracture of the tape. It also appears as nucleation of cavities is influenced by the strain rate where slower rates give more time for cavities to nucleate. This results in larger cavity density at smaller loading rates. The results also indicate a similarity of the effects of loading rate and ageing of the macroscopic properties of the present pressure sensitive adhesive.

  • 36.
    Stigh, Ulf
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Biel, Anders
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Shear properties of an adhesive layer exposed to a compressive load2014In: Procedia Materials Science, ISSN 2211-8128, Vol. 3, p. 1626-1631Article in journal (Refereed)
    Abstract [en]

    Adhesive joints are designed to transfer load in shear since both the fracture energy and the fracture stress are larger in shear than in peel. Shear deformation is isochoric, however, the fracture process involves nucleation and growth of a multitude of slanted microcracks. In order to grow, these microcracks open up. Thus, adhesive layers show a tendency to deform in peel during shear fracture. This opening is localized to the fracture process zone and the adherends have to separate locally over the process zone to allow for the adhesive to swell. Depending on the stiffness of the adherends, the opening mode is more or less prohibited. With stiffer adherends, the opening is obstructed more efficiently than with softer adherends. Micromechanical studies indicate that the constraints of the peel deformation during shear loading have a profound influence on the strength of the joint. In the present study, we compress the process zone during experiments. Repeated experiments with ENF-specimens are performed. A compressive force is applied on the first part of the adhesive layer by use of a pneumatic cylinder. The experiments are evaluated using the path independent J-integral. Together with measurements of the shear and peel deformation of the adhesive layer at the start of the layer, the complete shear stress vs shear deformation relations are evaluated. It is shown that the inhibited peel deformation gives a substantial increase of the fracture energy

  • 37.
    Stigh, Ulf
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Biel, Anders
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Studies of fracture in shear of a constrained layer2017In: Advanced Problems in Mechanics: Proceedings of the XLV Summer School Conference / [ed] Dmitri A. Indeitsev & Anton M. Krivtsov, St Petersburg: Institute for Problems in Mechanical Engineering RAS , 2017, p. 420-428Conference paper (Refereed)
    Abstract [en]

    Cracks normally propagate in the opening mode associated with a state of local symmetry at a crack tip. However, the micro- or macrostructure of a material or structure sometimes forces cracks to propagate in a shearing mode. Irrespective of the actual material studied, fracture in shear is frequently asso- ciated with the formation of a large number smaller sigmoidal-shaped cracks in the propagation direction of the major crack. Propagation of the major shear crack is accomplished by coalescing the sigmoidal-shaped cracks. Ex- periments show that the formation of sigmoidal cracks due to shear loading leads to a normal separation of the joined substrates. Theoretical studies show that constraining the local opening of the sigmoidal cracks increases the frac- ture resistance for the propagation of the major crack. In the present study, experiments with a ductile adhesive loaded in shear and where the normal sep- aration is constrained are presented. The experiments are evaluated using the path independent J-integral. The associated cohesive law shows that consid- erable normal compressive stress develops in the adhesive during macroscopic shear loading. It is also concluded that by ignoring the normal separation in the evaluation of the experiments, the strength of the adhesive is underesti- mated. Thus, the procedure developed in earlier studies is conservative from a strength analysis perspective. The present technique might be possible to extend to other materials to reveal their properties in shear fracture.

  • 38.
    Stigh, Ulf
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Biel, Anders
    Department of Wind Energy, Technical University of Denmark, DK-4000 Roskilde, Denmark.
    Svensson, Daniel
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Cohesive zone modelling and the fracture process of structural tape2016In: Proceedia Structural Integrity, ISSN 2452-3216, Vol. 2, p. 235-244Article in journal (Refereed)
    Abstract [en]

    Structural tapes provide comparable toughness as structural adhesives at orders of magnitude lower stresses. This is potentially useful to minimize the effects of differences in thermal expansion in the joining of mixed materials. The strength properties are modelled using the cohesive zone model. Thus, a cohesive zone represents the tape, i.e. stresses in the tape are transmitted to the substrates through tractions determined by the separations of the surfaces of substrates. This simplification allows for structural analysis of large complex structures. The relation between the traction and the separation is measured experimentally using methods based on the path independence of the J-integral. Repeated experiments are performed at quasi-static loading. A mixed mode cohesive law is adapted to the experimental data. The law is implemented as a UMAT in Abaqus. Simulations show minor thermal distortions due to thermal loading and substantial structural strength in mechanical loading of a mixed material structure.

  • 39.
    Stigh, Ulf
    et al.
    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.
    Walander, Tomas
    University of Skövde, The Virtual Systems Research Centre. University of Skövde, School of Technology and Society.
    Fracture of Adhesive Layers in Mode II2012In: Proceedings of the 19th European Conference on Fracture, Kazan Scientific Centre of the Russian Academy of Sciences , 2012Conference paper (Refereed)
    Abstract [en]

    Measuring fracture properties of adhesives in Mode II is often problematic. Indeed, no method can today be regarded as established by the community. In this paper a number of methods are presented. Experiments show that the evaluated properties of the same adhesive sometime vary considerably with the choice of specimen. Even just modest variations in loading conditions using the same specimen can yield considerable variation in the evaluated properties. Sources for these deficiencies are identified.

    It has long been understood that Mode II testing using the end-notched flexure specimen (ENF) is conditionally stable. That is, the length of the crack has to be large enough to achieve a stable experiment. This is also the case for other Mode II specimens. A condition for stability is derived leading to an easily evaluated equation. Moreover, careful studies of the crack tip area during Mode II experiments often reveal an expansion of the adhesive during the final phase of loading. That is, negative Mode I loading. Due to the stiffness of the adherends, this leads to a compressive transversal loading of the process zone. Experiments and simulations show that the evaluated fracture energy depends on this constraint. A more detailed analysis of Mode II loading considering large-scale process zones gives some insight into the problem. It is also clear that Mode II has to be more carefully defined than is necessary for Mode I. Due to the transversal expansion of the process zone associated with shear, we may choose to define Mode II as a state of pure shear deformation or a state of pure shear stress. In experiments, none of these states are easily achieved. Moreover, transversally loaded short specimens can result in a process zone extending under the loading point. The result is compression of the process zone and exaggerated evaluated fracture energy. This problem is especially important to consider when evaluating soft and tough adhesives. If better understood and modelled, these effects might also be used in design so that an adhesive joint is loaded in a more favourable way.

  • 40.
    Stigh, Ulf
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Biel, Anders
    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.
    Shear strength of adhesive layers – models and experiments2014In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 129, p. 67-76Article in journal (Refereed)
    Abstract [en]

    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.

  • 41.
    Stigh, Ulf
    et al.
    University of Skövde, School of Technology and Society.
    Svensson, Daniel
    University of Skövde, School of Technology and Society.
    On cohesive laws for delamination of composites2010In: 14th European conference on Composite materials, Budapest: University of Technology and Economics , 2010Conference paper (Refereed)
    Abstract [en]

    Analysis  of  delamination  of  carbon  fibre  reinforced  composite  using  cohesive  models  is studied. A method to measure the cohesive law associated with delamination is presented. The method  allows  for  identification  of  a  cohesive  law  fit  to  model  the  fracture  process  at  the crack tip, i.e. not considering fibre bridging. Due to the small size of the cohesive zone, an elaborated  method  involving  simulations  of  the  fracture  process  is  developed.  The  results show larger scatter in the parameters of the cohesive law than in the fracture energy.

  • 42.
    Svensson, Daniel
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Alfredsson, K. Svante
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Biel, Anders
    University of Skövde, School of Engineering Science.
    Stigh, Ulf
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Measurement of cohesive laws for interlaminar failure of CFRP2014In: Composites Science And Technology, ISSN 0266-3538, E-ISSN 1879-1050, Vol. 100, p. 53-62Article in journal (Refereed)
  • 43.
    Svensson, Daniel
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Alfredsson, K. Svante
    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.
    On the ability of coupled mixed mode cohesive laws to conform to LEFM for cracks in homogeneous orthotropic solids2016In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 163, p. 426-448Article in journal (Refereed)
    Abstract [en]

    The ability of coupled cohesive laws to conform to the predictions of linear elastic fracturemechanics (LEFM) in the case of small-scale-yielding (SSY) is explored. The study is concerned with cracks in homogeneous orthotropic solids and the results apply also for the case of isotropy. Both potential based and non-potential based cohesive laws are considered. It is shown that the initial stiffnesses of the cohesive law must be matched to the elastic moduli of the orthotropic solid in order to achieve a constant ratio of the cohesive stress components ahead of the crack tip. A simple condition for this is provided. For non potential based laws an additional apparently sufficient condition on the non-linear part of the cohesive law is identified: The traction vector must not change direction if the directionof the separation vector is constant. Fulfillment of this condition provides a uniform local mode mix in the cohesive zone with a value equal to the global mode mix. It is demonstrated that potential based cohesive laws display a varying local mode mix at the crack tip for cases with a mode dependent work of separation. This is identified as acomplicating feature in terms of calibrating the parameters of a cohesive law to experimental data.

  • 44.
    Svensson, Daniel
    et al.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Alfredsson, K. Svante
    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.
    Jansson, N. E.
    GKN Aerospace Engine Systems Sweden, Trollhättan, Sweden.
    An experimental method to determine the critical energy release rate associated with longitudinal compressive failure in CFRP2013In: Proceeding of the 19th international conference on composite materials (ICCM 19), 2013Conference paper (Refereed)
    Abstract [en]

    A test specimen for measurement of the critical energy release rate associated with longitudinal compressive failure is proposed. High strains are localized by decreasing the out-of-plane thickness towards the anticipated damage region which consists of a unidirectional (UD) laminate. Thus, the compressive fibre failure mode is isolated. Microscopic studies show that the UD-material fails in a kinking mode. A method based on a generalized form of the J-integral and full-field measurements of the strain field is developed to extract the fracture energy. The fracture energy in four experiments is measured to be 20-40 kN/m. Finite element simulations  are  performed  to  validate  the experimental results. The essential features of the response are captured by modelling the damage region with cohesive elements.

  • 45.
    Svensson, Daniel
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Alfredsson, K. Svante
    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.
    Jansson, Nicklas E.
    GKN Aerospace Engine Systems, Trollhättan, Sweden.
    Measurement of cohesive law for kink-band formation in unidirectional composite2016In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 151, p. 1-10Article in journal (Refereed)
    Abstract [en]

    Kink-band formation is an important mechanism limiting the compressive strength of high strength composites. A cohesive zone model is used to model the material in a unidirectional carbon fibre composite that forms the kink-band. Equilibrium of configurational forces is used to design and evaluate the experiments. Microscopic studies show that a kink-band is formed with the height of about 200 μm. The corresponding cohesive law has a peak stress of about 1.5 GPa, a compression at failure of about 50 μm and a fracture energy of about 25 kJ/m2.

  • 46.
    Walander, Tomas
    et al.
    University of Skövde, School of Technology and Society.
    Biel, Anders
    University of Skövde, School of Technology and Society.
    Stigh, Ulf
    University of Skövde, School of Technology and Society.
    An evaluation of the temperature dependence of cohesive properties for two structural epoxy adhesives2012In: 19th European Conference on Fracture, Kazan Scientific Centre of the Russian Academy of Sciences , 2012Conference paper (Refereed)
    Abstract [en]

    Cohesive modelling provides a more detailed understanding of the fracture properties of adhesivejoints than provided by linear elastic fracture mechanics. A cohesive model is characterized by astress-deformation relation of the adhesive layer. This relation can be measured experimentally.Two parameters of the stress-deformation relation are of special importance; the area under thecurve, which equals the fracture energy, and the peak stress. The influence of temperature of theseparameters is analyses experimentally and evaluated statistically for two structural epoxy adhesivesin the span from of -40°C to +80°C. The adhesives are used by the automotive industry and atemperature span below the glass transition temperature is considered. The results show that thattemperature has a modest influence on the adhesives Mode I fracture energy. For one of theadhesives, the fracture energy is independent of the temperature in the evaluated temperature span.In mode II, the influence of temperature is larger. The peak stresses decreases almost linearly withan increasing temperature in both loading cases and for both adhesives.

  • 47.
    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.

  • 48.
    Walander, Tomas
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Eklind, Alexander
    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.
    Fatigue damage of adhesive layers: experiments and models2014In: Procedia Materials Science, ISSN 2211-8128, Vol. 3, p. 829-834Article in journal (Refereed)
    Abstract [en]

    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.

  • 49.
    Walander, Tomas
    et al.
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Eklind, Alexander
    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.
    Rietz, Andreas
    Scania STC, Södertälje, Sweden.
    Prediction of mixed-mode cohesive fatigue strength of adhesively bonded structure using Mode I data2016In: International Journal of Adhesion and Adhesives, ISSN 0143-7496, E-ISSN 1879-0127, Vol. 66, p. 15-25Article in journal (Refereed)
    Abstract [en]

    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.

1 - 49 of 49
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