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  • 1.
    Alfredsson, K. Svante
    et al.
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Biel, Anders
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Salimi, Saeed
    Högskolan i Skövde.
    Shear testing of thick adhesive layers using the ENF-specimen2015Ingår i: International Journal of Adhesion and Adhesives, ISSN 0143-7496, E-ISSN 1879-0127, Vol. 62, s. 130-138Artikel i tidskrift (Refereegranskat)
  • 2.
    Alfredsson, Svante
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Biel, Anders
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Leffler, K.
    An experimental method to determine the complete stress-deformation relatioin for a structural adhesive layer loaded in shear2003Ingår i: The 9th International Conference on The Mechanical Behaviour of Materials, 2003Konferensbidrag (Övrigt vetenskapligt)
  • 3.
    Andersson, Tobias
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Biel, Anders
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Effects of the length of the damage zone on the effective constitutive properties of an adhesive layer loaded in peel2004Ingår i: The 15th European Conference on Fracture: ECF 15, 2004Konferensbidrag (Övrigt vetenskapligt)
  • 4.
    Andersson, Tobias
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Biel, Anders
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    On the effective constitutive properties of a thin adhesive layer loaded in peel2006Ingår i: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 141, nr 1-2, s. 227-246Artikel i tidskrift (Refereegranskat)
    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.

  • 5.
    Andre, A.
    et al.
    Swerea Sicomp AB, Composite Struct, Molndal, Sweden / Chalmers, Div Struct Engn, S-41296 Gothenburg, Sweden .
    Haghani, Reza
    Chalmers, Div Struct Engn, S-41296 Gothenburg, Sweden .
    Biel, Anders
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Application of fracture mechanics to predict the failure load of adhesive joints used to bond CFRP laminates to steel members2012Ingår i: Construction and Building Materials, ISSN 0950-0618, E-ISSN 1879-0526, Vol. 27, nr 1, s. 331-340Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The use of bolted or welded elements to upgrade metallic structures has been a common practice for many years. Moreover, the use of adhesively bonded carbon fiber reinforced polymer (CFRP) laminates, as an alternative method, has attracted a great deal of attention in recent years. One important aspect of the design of adhesive joints used to bond CFRP laminates to steel substrates is the determination of the properties of the CFRP/adhesive/steel interfaces, which have not yet been established in codes or standards. The purpose of this paper is experimentally to determine the fracture properties of the adhesive material and to evaluate the accuracy of numerical methods using this information, in order to predict the strength of adhesive joints in steel members bonded with CFRP laminates. The results from four series of experimental tests are compared with numerical results and discussed in terms of load-bearing capacity and failure modes. (C) 2011 Elsevier Ltd. All rights reserved.

  • 6.
    Biel, Anders
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Constitutive behaviour and fracture toughness of an adhesive layer2005Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    This report presents the fracture energy and the complete stress – elongation relation for a structural adhesive loaded in modus I. The experiments are performed on the Double Cantilever Beam (DCB) specimen and the method to analyse the experiments is based on the J-integral approach which means that the energy release rate, i.e. J, is measured continuously during an experiment. Since J is given by the area under the stress – elongation relation for the adhesive layer, both the fracture energy and the stress – elongation relation can be measured in the experiments. The geometry of the specimens is varied in order to examine if the evaluated stress – elongation relation is a unique constitutive relation for the adhesive layer. No dependence on the specimen geometry has been detected provided that the adherends only deform elastically. If the adherends are allowed to deform plastically the fracture energy increases and the stress – elongation relation from the elastically deforming tests cannot be used to simulate the structural behaviour. This is interpreted as an effect of a substantially shorter damage zone with the plastically deforming adherends. An evaluation of effects of the loading rate is also performed. This shows that the fracture energy increases with the loading rate. A number of standardized methods are available to evaluate the fracture properties of adhesives from experiments on the DCB-specimen. Furthermore, alternative methods have recently been suggested by Tamuzs et al. (2003). In an effort to examine the accuracy of the alternative methods, FE-simulations are performed and evaluated according to the alternative methods. The simulations are based on the stress – elongation relation evaluated from the present experiments. Large differences between the correct and the evaluated fracture energies are found for most of the methods. Two of the methods show good accuracy and appear particularly promising. Stress whitening is used to evaluate the length of the damage zone. This length compares reasonably well with the length evaluated from FE-simulations of the experiments.

  • 7.
    Biel, Anders
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Mechanical behaviour of adhesive layers: experimental methods, cohesive laws, and fracture mechanics2008Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Adhesive joining is today viewed as one of the key technologies to achieve decreased emissions in the automobile industry. To decrease weight, optimal material selection often results in different materials for different parts. This leads to the necessity to join mixed material. Here, the use of adhesives is the most promising joining technology. For a rational design process, good models for strength analysis of adhesively joined structures are essential. With cohesive modelling, fracture of the adhesive layer is modelled with a stress-deformation law. This law - often denoted a cohesive law - gives the traction exerted on the adherends due to the deformation of the adhesive layer. This thesis is concerned with experimental methods to measure cohesive properties of engineering adhesives and standardized methods to measure the fracture energy of adhesives. A new method to measure cohesive laws is developed. With this method, the cohesive law of an epoxy adhesive is measured in shear. In peel loading, with elastically deforming adherends, the cohesive law is shown to be independent of the geometry of the specimen. If the adherends deform plastically the fracture energy increases. Experiments are performed in order to determine the temperature dependence of the cohesive layer for an epoxy adhesive. It is shown that the peak stress is strongly dependent on the temperature while the fracture energy shows only small temperature dependence. Experiments are also performed to study the influence of strain rate in peel and shear loading. The experiments show that the peak stress increases with an increasing strain rate and that the fracture energy increase in peel loading and decreases in shear with increasing strain rate. A new method to experimentally determine the relation between damage and plasticity in the adhesive during the fracture process is developed. For the present adhesive, it is shown that only minor plasticity occurs during the fracture process in peel loading. For peel, several commonly used methods to evaluate the fracture energy using the double cantilever beam specimen are critically studied. For some methods the error in evaluated fracture energy is larger than 40 %. It is shown that the evaluated fracture energy is more dependent on the choice of method than on the cohesive properties of the adhesive layer.

  • 8.
    Biel, Anders
    et al.
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Alfredsson, K. Svante
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Carlberger, Thomas
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Adhesive Tapes; Cohesive Laws for a Soft Layer2014Ingår i: Procedia Materials Science, ISSN 2211-8128, Vol. 3, s. 1389-1393Artikel i tidskrift (Refereegranskat)
    Abstract [en]

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

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

  • 9.
    Biel, Anders
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Carlberger, Thomas
    SAAB Automobile AB, SE-461 80 Trollhättan, SWEDEN .
    Influence of temperature on cohesive parameters for adhesives2007Ingår i: Interface design of polymer matrix composites: mechanics, chemistry, modelling and manufacturing / [ed] B. F. Sørensen, L. P. Mikkelsen, H. Lilholt, S. Goutianos, F. S. Abdul-Mahdi, 2007, s. 143-148Konferensbidrag (Refereegranskat)
    Abstract [en]

    Experiments are performed to evaluate the temperature dependence of the stress-elongation relation for an engineering epoxy adhesive. Seven temperatures from -40ºC to 80ºC are considered. At each temperature, about seven experiments are performed with a double cantilever beam specimen. The experiments are evaluated using an inverse solution. The results show that the peak stress decreases monotonically with temperature, from about 55 MPa at -40ºC to about 11 MPa at 80ºC. Thus, the shape of the stress-elongation relation varies with the temperature. At higher temperatures, the fracture energy decreases slightly.

  • 10.
    Biel, Anders
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Carlberger, Thomas
    Influences of temperature on cohesive parameters for adhesives2007Ingår i: Proceedings of the 28th Risø International Symposium on Materials Science, Risö national laboratory , 2007Konferensbidrag (Refereegranskat)
    Abstract [en]

    Experiments are performed to evaluate the temperature dependence of the stress-elongation relation for an engineering epoxy adhesive. Seven temperatures from -40ºC to 80ºC are considered. At each temperature, about seven experiments are performed with a double cantilever beam specimen. The experiments are evaluated using an inverse solution. The results show that the peak stress decreases monotonically with temperature, from about 55 MPa at -40ºC to about 11 MPa at 80ºC. Thus, the shape of the stress-elongation relation varies with the temperature. At higher temperatures, the fracture energy decreases slightly.

  • 11.
    Biel, Anders
    et al.
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Chaudhry, Mobina
    Institute of Biomedicine, University of Gothenburg, Göteborg, Sweden.
    Gustafsson, Stefan
    Department of Applied Physics, Chalmers University of Technology, Göteborg, Sweden.
    Nygren, Håkan
    Institute of Biomedicine, University of Gothenburg, Göteborg, Sweden.
    The use of MgO-paste as a biodegradeable bone cement2016Ingår i: Materials Today: Proceedings, E-ISSN 2214-7853, Vol. 3, nr 2, s. 556-561Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The use of MgO-paste as bone cement was tested on titanium cylinders implanted into rat tibia. The evaluation of bone healingwas made with the retention force (pull-out) test, light microscopy and ESEM/ EDX. Preimplantation of the MgO-paste into drillperforations of rat tibia increased the retention of the titanium implant 6-fold. The error was expressed as the 95% confidenceinterval of means (n=10 bones in each group). The observed difference between 3.46+/-0.71 N/mm2 for Ti-cylinders implantedwith MgO-paste and 0.56+/-0.26 N/mm2 for Ti-cylinders implanted directly into the bone, is statistically significant (p<0.01).The increase of retention force, caused by MgO is parallel to an increased thickness of the compact bone surrounding the implantand closer contact between bone and implant.Histological examination of the implant-related bone showed that the MgO-induced bone growth is mediated by the formation ofa bone-inducing matrix. The matrix contains organic substance, most likely proteins.

  • 12.
    Biel, Anders
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    An analysis of the evaluation of the fracture energy using the DCB-specimen2007Ingår i: Archives of Mechanics, ISSN 0373-2029, Vol. 59, nr 4-5, s. 311-327Artikel i tidskrift (Refereegranskat)
    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.

  • 13.
    Biel, Anders
    et al.
    Department of Wind Energy, Technical University of Denmark, Roskilde, Denmark.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Cohesive zone modelling of nucleation, growth and coalesce of cavities2017Ingår i: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 204, nr 2, s. 159-174Artikel i tidskrift (Refereegranskat)
    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.

  • 14.
    Biel, Anders
    et al.
    Karlstad University.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Comparison of J-integral methods to experimentally determine cohesive laws in shear for adhesives2019Ingår i: International Journal of Adhesion and Adhesives, ISSN 0143-7496, E-ISSN 1879-0127, Vol. 94, s. 64-75Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    High-quality simulation methods demand accurate material models. In simulations an adhesive can be represented by a cohesive layer. A cohesive layer model utilizes a cohesive law to represent the homogenized mechanical behaviour of a layer with a thickness. In the current paper we use three experimental methods to measure the cohesive law in shear using the ENF-specimen; one of the methods is novel and is also useful for evaluation of experiments with the ELS-specimen. Two sets of experiments are performed, one with elastic substrates and one with plastically deforming substrates. Each experiment is evaluated using all three methods. The evaluation shows that all methods provide reasonable data; the results are similar if the substrates are elastic. With smaller specimens, the substrates deform plastically and one of the methods is identified as the most accurate.

  • 15.
    Biel, Anders
    et al.
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Stigh, Ulf
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Damage and plasticity in adhesive layer: an experimental study2010Ingår i: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 165, nr 1, s. 93-103Artikel i tidskrift (Refereegranskat)
    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.

  • 16.
    Biel, Anders
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för teknik och samhälle. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Damage and plasticity of adhesive layers: an experimental study2011Ingår i: Procedia Engineering, ISSN 1877-7058, E-ISSN 1877-7058, Vol. 10, s. 2280-2285Artikel i tidskrift (Refereegranskat)
    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.

  • 17.
    Biel, Anders
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Effects of constitutive parameters on the accuracy of measured fracture energy using the DCB-specimen2008Ingår i: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 75, nr 10, s. 2968-2983Artikel i tidskrift (Refereegranskat)
    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.

  • 18.
    Biel, Anders
    et al.
    Department of Wind Energy, Technical University of Denmark.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Measurement of tensile properties of fibres using a DCB-specimen2015Ingår i: 20th International Conference on Composite Materials: Copenhagen, 19-24th July 2015 / [ed] Ole Thybo Thomsen, Bent F. Sørensen, Christian Berggreen, 2015Konferensbidrag (Refereegranskat)
    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.

  • 19.
    Biel, Anders
    et al.
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Strength and toughness in shear of constrained layers2018Ingår i: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 138, s. 50-63Artikel i tidskrift (Refereegranskat)
    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.

  • 20.
    Biel, Anders
    et al.
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Stigh, Ulf
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Walander, Tomas
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för vård och natur.
    A Critical Study of an Alternative Method to Measure Cohesive Properties of Adhesive Layers2012Ingår i: Proceedings of the 19th European Conference on Fracture, Kazan Scientific Centre of the Russian Academy of Sciences , 2012Konferensbidrag (Refereegranskat)
    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.

  • 21.
    Biel, Anders
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Walander, Tomas
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Influence of Edge-boundaries on the Cohesive Behaviour of an Adhesive Layer2012Ingår i: 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, s. 507-511Konferensbidrag (Refereegranskat)
    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.

  • 22.
    Carlberger, Thomas
    et al.
    SAAB Automobile AB, Trollhättan, Sweden.
    Biel, Anders
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Stigh, Ulf
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Influence of temperature and strain rate on cohesive properties of a structural epoxy adhesive2009Ingår i: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 155, nr 2, s. 155-166Artikel i tidskrift (Refereegranskat)
    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.

  • 23.
    Marzi, Stephan
    et al.
    Fraunhofer IFAM, Bremen, Germany.
    Biel, Anders
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Hesebeck, Olaf
    Fraunhofer IFAM, Bremen, Germany.
    3D optical displacement measurements on dynamically loaded adhesively bonded T-peel specimens2015Ingår i: International Journal of Adhesion and Adhesives, ISSN 0143-7496, E-ISSN 1879-0127, Vol. 56, s. 41-45Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Adhesively bonded T-Peel specimens are loaded in a rotary impact device to investigate the behaviour of adhesive joints under high-strain rates. To gain a better understanding of that kind of tests and their results, the deformation of the samples as well as the movement of specimen support during the test is analyzed. A three-dimensional optical measurement system is used in combination with two synchronized high-speed cameras to obtain the deformations. The paper explains the experimental challenges and discusses the results of the analyses with respect to a planned usage of the experimental results in a finite element crash simulation. As main results of the investigations it can be summarized that the compliant clamping leads to an inadvertent out-of-plane-movement of the load introduction point. Based on finite element calculations it can be concluded that the measured out-of-plane-movement possesses a negligible influence on the obtained force signal, which is of primary interest in a T-Peel test.

  • 24.
    Marzi, Stephan
    et al.
    Fraunhofer IFAM, Wiener Str. 12, D-28359 Bremen, Germany.
    Biel, Anders
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    On experimental methods to investigate the effect of layer thickness on the fracture behavior of adhesively bonded joints2011Ingår i: International Journal of Adhesion and Adhesives, ISSN 0143-7496, E-ISSN 1879-0127, Vol. 31, nr 8, s. 840-850Artikel i tidskrift (Refereegranskat)
    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
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Walander, Tomas
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Effects of the bond line thickness on the fracture mechanical behaviour of structural adhesive joints2014Ingår i: Proceedings of the Annual Meeting of the Adhesion Society 2014, Adhesion Society , 2014, s. 189-192Konferensbidrag (Refereegranskat)
  • 26.
    Stigh, Ulf
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Alfredsson, K. Svante
    Högskolan i Skövde, Institutionen för teknik och samhälle. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Biel, Anders
    Högskolan i Skövde, Institutionen för teknik och samhälle. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Measurement of cohesive laws and related problems2009Ingår i: Proceedings of the ASME International Mechanical Engineering Congress and Exposition: IMECE2009, ASME Press, 2009, s. 293-298Konferensbidrag (Refereegranskat)
    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.

  • 27.
    Stigh, Ulf
    et al.
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Alfredsson, Svante K.
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Andersson, Tobias
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Biel, Anders
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Carlberger, Thomas
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Salomonsson, Kent
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Some aspects of cohesive models and modelling with special application to strength of adhesive layers2010Ingår i: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 165, nr 2, s. 149-162Artikel i tidskrift (Refereegranskat)
    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.

  • 28.
    Stigh, Ulf
    et al.
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Biel, Anders
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Effects of strain rate on the cohesive properties and fracture process of a pressure sensitive adhesive2018Ingår i: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 203, s. 266-275Artikel i tidskrift (Refereegranskat)
    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.

  • 29.
    Stigh, Ulf
    et al.
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Biel, Anders
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Shear properties of an adhesive layer exposed to a compressive load2014Ingår i: Procedia Materials Science, ISSN 2211-8128, Vol. 3, s. 1626-1631Artikel i tidskrift (Refereegranskat)
    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

  • 30.
    Stigh, Ulf
    et al.
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Biel, Anders
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Studies of fracture in shear of a constrained layer2017Ingår i: 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, s. 420-428Konferensbidrag (Refereegranskat)
    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.

  • 31.
    Stigh, Ulf
    et al.
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Biel, Anders
    Department of Wind Energy, Technical University of Denmark, DK-4000 Roskilde, Denmark.
    Svensson, Daniel
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Cohesive zone modelling and the fracture process of structural tape2016Ingår i: Proceedia Structural Integrity, ISSN 2452-3216, Vol. 2, s. 235-244Artikel i tidskrift (Refereegranskat)
    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.

  • 32.
    Stigh, Ulf
    et al.
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Biel, Anders
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Walander, Tomas
    Högskolan i Skövde, Forskningscentrum för Virtuella system. Högskolan i Skövde, Institutionen för teknik och samhälle.
    Fracture of Adhesive Layers in Mode II2012Ingår i: Proceedings of the 19th European Conference on Fracture, Kazan Scientific Centre of the Russian Academy of Sciences , 2012Konferensbidrag (Refereegranskat)
    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.

  • 33.
    Stigh, Ulf
    et al.
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Biel, Anders
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Walander, Tomas
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Shear strength of adhesive layers – models and experiments2014Ingår i: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 129, s. 67-76Artikel i tidskrift (Refereegranskat)
    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.

  • 34.
    Svensson, Daniel
    et al.
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Alfredsson, K. Svante
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Biel, Anders
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för ingenjörsvetenskap. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Measurement of cohesive laws for interlaminar failure of CFRP2014Ingår i: Composites Science And Technology, ISSN 0266-3538, E-ISSN 1879-1050, Vol. 100, s. 53-62Artikel i tidskrift (Refereegranskat)
  • 35.
    Walander, Tomas
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Biel, Anders
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    An evaluation of the temperature dependence of cohesive properties for two structural epoxy adhesives2012Ingår i: 19th European Conference on Fracture, Kazan Scientific Centre of the Russian Academy of Sciences , 2012Konferensbidrag (Refereegranskat)
    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.

  • 36.
    Walander, Tomas
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Biel, Anders
    Högskolan i Skövde, Institutionen för teknik och samhälle. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för teknik och samhälle. Högskolan i Skövde, Forskningscentrum för Virtuella system.
    Temperature dependence of cohesive laws for an epoxy adhesive in Mode I and Mode II loading2013Ingår i: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 183, nr 2, s. 203-221Artikel i tidskrift (Refereegranskat)
    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.

1 - 36 av 36
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