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

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

  • 2.
    Alfredsson, K. Svante
    University of Skövde, School of Technology and Society.
    On the instantaneous energy release rate of the end-notch flexure adhesive joint specimen2004In: International Journal of Solids and Structures, ISSN 0020-7683, Vol. 41, no 16-17, p. 4787-1807Article in journal (Refereed)
    Abstract [en]

    The energy release rate of the ENF adhesive joint specimen is derived. The resulting formula accounts for the presence of an adhesive layer with a possibly non-linear constitutive relation. The actual form of the constitutive relation need not to be known a priori. It is shown that measurements of both the applied load and the adhesive deformation at the crack tip are needed to determine the instantaneous value of the energy release rate. Experimental results show that the influence of the deformation of the adhesive layer can be substantial. The stability of the ENF-specimen is studied and a method to estimate the critical value of the crack length, accounting for the flexibility of the adhesive layer, is presented. In the analysis, the adherends are modelled as elastically deforming Euler–Bernoulli beams and the intermediate adhesive layer is modelled as a material surface transmitting shear stress between the adherends.

  • 3.
    Alfredsson, K. Svante
    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.
    Salimi, Saeed
    University of Skövde.
    Shear testing of thick adhesive layers using the ENF-specimen2015In: International Journal of Adhesion and Adhesives, ISSN 0143-7496, E-ISSN 1879-0127, Vol. 62, p. 130-138Article in journal (Refereed)
  • 4.
    Alfredsson, K. Svante
    et al.
    University of Skövde, School of Technology and Society.
    Gawandi, A. A.
    Univ Delaware, Ctr Composite Mat, Newark, DE 19716 USA.
    Gillespie, J. W., Jr.
    Univ Delaware, Ctr Composite Mat, Newark, DE 19716 USA.
    Carlsson, L. A.
    Florida Atlantic Univ, Dept Mech Engn, Boca Raton, FL 33431 USA.
    Bogetti, T. A.
    USA, Res Lab, Aberdeen Proving Ground, MD 21005 USA.
    Stress analysis of axially and thermally loaded discontinuous tile core sandwich with and without adhesive filled core gaps2011In: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 93, no 7, p. 1621-1630Article in journal (Refereed)
    Abstract [en]

    An analytical study is performed to investigate the stress states in an axially and thermally loaded sandwich structure with a discontinuous ceramic tile core. General and simplified models are developed to determine stresses in the constituents of the sandwich structure with and without adhesive in the gaps between adjacent tiles. A general model that allows local bending of the face sheet and a simplified model which assumes uniform through-thickness stress distribution in the face sheets are developed. It is shown that the normal stress in the face sheet decreases when the gap is filled by adhesive, although the tile stress increases. The analytical model shows that normal and shear stresses at the face/core interface can be reduced by filling the gaps between tiles. Filled gaps also elevate the axial stiffness of the structure. Model results are verified by comparison to a previously developed analytical model and finite element analysis. (C) 2011 Elsevier Ltd. All rights reserved.

  • 5.
    Alfredsson, K. Svante
    et al.
    University of Skövde, School of Technology and Society. University of Skövde, The Virtual Systems Research Centre.
    Gawandi, A. A.
    University of Delaware.
    Gillespie Jr., J. W.
    University of Delaware.
    Carlsson, L. A.
    Florida Atlantic University.
    Bogetti, T. A.
    Army Research Laboratory, Aberdeen Proving Ground.
    Flexural analysis of discontinuous tile core sandwich structure2012In: Composite structures, ISSN 0263-8223, E-ISSN 1879-1085, Vol. 94, no 5, p. 1524-1532Article in journal (Refereed)
    Abstract [en]

    Three-point flexure loading of sandwich beams with a core consisting of discrete ceramic tiles (DTSS) is considered. The tile gaps may be bonded or unbonded (open gaps). The analysis utilizes a layer-wise beam theory approach. The general formulation for the displacements and stresses in the face sheets, face/core adhesive layer, and core is derived. Solutions for stresses and displacements of the beam constituents are obtained from finite element formulation based on analytical solution of the face sheet/tile unit cell. The approach is verified by comparison to stress results obtained from ordinary finite element analysis where each layer is modeled discretely. Effects of load introduction and support conditions on the effective flexural stiffness are examined. It is demonstrated that the face sheets experience substantial stress concentrations at the tile joint locations, especially if the gaps are unfilled. Analysis of beam compliance reveals sensitivity to details of load introduction and support conditions, especially when the span length becomes comparable to the tile length.

  • 6.
    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.

  • 7.
    Alfredsson, Svante
    University of Skövde, School of Technology and Society.
    Constitutive Behaviour and Fracture of Adhesive Layers: Inverse Methods and Energetic Balance2004Doctoral thesis, monograph (Other scientific)
    Abstract [en]

    In the automobile industry, current demands on reduced emissions with maintained or even increased crash worthiness, forces the industry to seek weight-reducing designs. The possibility to use lightweight materials is obviously attractive. At joints, these lightweight materials have to be connected to high-strength or low-cost materials. In this context adhesive joining can provide a flexible solution. The method adds little weight to the structure, it allows for material combinations that are not possible to weld, and it provides increased stiffness to the structure as compared to the conventional spot-welding procedure. Moreover, electrolytic isolation of the multi-material joints is achieved.

    In this thesis, experimental methods are developed to determine the complete stress-deformation relation for an adhesive layer loaded in shear. Generally, the stress distribution is non-uniform in the test geometries used. Evaluation of experiments is performed using an inverse method. The idea is to measure the energy release rate as a function of the crack tip deformation. The stress-deformation relation is obtained by a subsequent differentiation. The method is shown to be capable of capturing the complete stress-deformation relation under stable loading conditions.

    A method to accurately determine the energy release rate is needed for the inverse method to be successful. A closed form expression for the energy release rate of the end-notch flexure adhesive joint specimen (ENF) is derived in this thesis. An approximate formula containing measurable quantities is also given. It is shown that both the applied load and the crack tip deformation are needed to determine the instantaneous value of the energy release rate of the ENF-specimen. Experimental results show that the influence of the crack tip deformation can be substantial. An alternative specimen is also analysed theoretically.

    An initial theoretical study on mixed mode fracture of adhesive layers is also given in this thesis. A detailed comparison is made of the mode-mixity obtained using two different, frequently used mechanical models; the beam/adhesive layer model, and the continuum model, i.e. a model neglecting the presence of the adhesive layer. It is tempting to assume that the two methods would produce similar results for the case of a thin adhesive layer. However, this is only the case for geometries which are materially and geometrically symmetric with respect to the adhesive layer. For asymmetric joints, on the other hand, the two models are found to predict fundamentally different values of the mode-mixity. Moreover, the mode-mixity of the beam/adhesive layer model is found to depend highly on the relative stiffness of the adherends and the adhesive layer. This dependency is found to be quantified through two parameters.

  • 8.
    Alfredsson, Svante
    et al.
    University of Skövde, School of Technology and Society.
    Biel, Anders
    University of Skövde, School of Technology and Society.
    Leffler, K.
    An experimental method to determine the complete stress-deformation relatioin for a structural adhesive layer loaded in shear2003In: The 9th International Conference on The Mechanical Behaviour of Materials, 2003Conference paper (Other academic)
  • 9.
    Alfredsson, Svante
    et al.
    University of Skövde, School of Technology and Society.
    Bogetti, T. A.
    Army Res Lab, Aberdeen Proving Ground, MD 21005 USA.
    Carlsson, L. A.
    Florida Atlantic Univ, Dept Mech Engn, Boca Raton, FL 33431 USA.
    Gillespie, J. W. Jr
    Univ Delaware, Ctr Composite Mat, Newark, DE 19716 USA.
    Yiournas, A.
    Dynam Sci Inc, DTSD, Aberdeen Proving Ground, MD 21001 USA.
    Flexure of beams with an interlayer: symmetric beams with orthotropic adherends2008In: Journal of Mechanics of Materials and Structures, ISSN 1559-3959, E-ISSN 2157-5428, Vol. 3, no 1, p. 45-62Article in journal (Refereed)
    Abstract [en]

    Analysis of the three-point flexure loading of a symmetric beam configurationconsisting of two identical adherends joined by a flexible layer is presented. Aclosed-form solution is presented in the form of a layer-wise approach, andshows excellent agreement with finite element results. Particular emphasis isgiven to the global beam compliance. The results show that a thin, sheardeformable layer may effectively decouple the responses of the two beams.Furthermore, in contrast to ordinary beams, the presence of an overhangreduces the beam compliance. These effects are quantified and discussed.Experiments on aluminum adherends joined by a rubber layer were conductedover a range of overhang lengths in a three-point flexure fixture, and verygood agreement between measured and predicted beam compliance was noted.

  • 10.
    Alfredsson, Svante
    et al.
    University of Skövde, School of Technology and Society.
    Gillespie, J. W.
    University of Delaware, USA.
    Carlsson, L. A.
    Florida Atlantic University, USA.
    Bogetti, T. A.
    Army Research Laboratory, Aberdeen Proving Ground, USA.
    Yiournas, A.
    Dynamic Science Inc. DTSD, Aberdeen, USA.
    Flexure analysis of unsymmetric orthotropic beams with an interlayer2009In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 46, no 10, p. 2093-2110Article in journal (Refereed)
    Abstract [en]

    This paper presents a layer-wise stress and deformation analysis of a three-layer beam configuration consisting of two dissimilar orthotropic adherends of different thicknesses that are joined together by a deformable interlayer of finite thickness. Analytical solutions for the case of three-point flexure loading are presented for both compressible and incompressible interlayers. Parametric analysis reveals the influences of asymmetry of moduli and adherend thicknesses, interlayer thickness, and overhang of the beams on the beam compliance. Analytical predictions of beam compliance show very good agreement with finite element results. Experimental measurements of compliance of various unsymmetric beams consisting of aluminum adherends separated by a rubber interlayer were performed in order to validate the analysis. Excellent agreement between measured and predicted compliance values was observed.

  • 11.
    Alfredsson, Svante
    et al.
    University of Skövde, School of Technology and Society.
    Högberg, J. Li
    University of Skövde, School of Humanities and Informatics.
    Energy release rate and mode-mixity of adhesive joint specimens2007In: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 144, no 4, p. 267-283Article in journal (Refereed)
    Abstract [en]

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

  • 12.
    Alfredsson, Svante
    et al.
    University of Skövde, School of Technology and Society.
    Högberg, Jia Li
    University of Skövde, School of Technology and Society.
    A closed-form solution to statically indeterminate adhesive joint problems — exemplified on ELS-specimens2008In: International Journal of Adhesion and Adhesives, ISSN 0143-7496, E-ISSN 1879-0127, Vol. 28, no 7, p. 350-361Article in journal (Refereed)
    Abstract [en]

    A beam/adhesive-layer model is developed. For this model a closed-form solution method applicable to arbitrary boundary conditions is presented. This enables the solution of a large number of practical problems which may be statically indeterminate. The stress state in the adhesive layer and the adherends of the beam/adhesive-layer model is also scrutinized. The method is exemplified in an analysis of the end-loaded split (ELS) specimen, commonly used to determine fracture energies of adhesive layers. The effect of the flexibility of the adhesive layer on the energy release rate and the critical crack length for stable crack growth is examined. Both symmetric and unsymmetric ELS-specimens are studied.

  • 13.
    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

  • 14.
    Biel, Anders
    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.
    Carlberger, Thomas
    University of Skövde, School of Engineering Science. University of Skövde, The Virtual Systems Research Centre.
    Adhesive Tapes; Cohesive Laws for a Soft Layer2014In: Procedia Materials Science, ISSN 2211-8128, Vol. 3, p. 1389-1393Article in journal (Refereed)
    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.

  • 15.
    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.

  • 16.
    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.

  • 17.
    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.

  • 18.
    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.

  • 19.
    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)
  • 20.
    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.

  • 21.
    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.

  • 22.
    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.

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