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  • 1.
    Alfredsson, Svante
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Högberg, J. Li
    Högskolan i Skövde, Institutionen för kommunikation och information.
    Energy release rate and mode-mixity of adhesive joint specimens2007Ingår i: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 144, nr 4, s. 267-283Artikel i tidskrift (Refereegranskat)
    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.

  • 2.
    Alfredsson, Svante
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Högberg, Jia Li
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    A closed-form solution to statically indeterminate adhesive joint problems — exemplified on ELS-specimens2008Ingår i: International Journal of Adhesion and Adhesives, ISSN 0143-7496, E-ISSN 1879-0127, Vol. 28, nr 7, s. 350-361Artikel i tidskrift (Refereegranskat)
    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.

  • 3.
    Högberg, J. Li
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Mixed mode cohesive law2006Ingår i: International Journal of Fracture, ISSN 0376-9429, E-ISSN 1573-2673, Vol. 141, nr 3-4, s. 549-559Artikel i tidskrift (Refereegranskat)
    Abstract [en]

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

  • 4.
    Högberg, J. Li
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Mixed mode testing of adhesive layer: Polymer Composite Materials for Wind Power Turbines2006Ingår i: Proceedings of the 27th Risø International Symposium on Materials Science: Polymer Composite Materials for Wind Power Turbines / [ed] H. Lilholt, B. Madsen, T. L. Andersen, L. P. Mikkelsen, A. Thygesen, Roskilde: Risø National Laboratory , 2006, s. 183-190Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    For a flexible linear adhesive, the mode mixety 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 singe-layer adhesive joints show that the mode mixety depends on the exteranl loads, the properties of the adherends and often on the flexibility of the adhesive layer. This implies some fundemantal problems that has to be adressed before an experimental method can be established. Requirements for the design of a specimen configuration for a mixed mode testing of adhesive layers are given. A new specimen configuration is proposed and some preliminary experimental results are given.

  • 5.
    Högberg, J. Li
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Salomonsson, Kent
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Simulation of an adhesive layer using a novel mixed mode cohesive law2006Ingår i: CDCM 2006 - Conference on Damage in Composite Materials 2006 18th-19th of September 2006 in Stuttgart, Germany: Online-Proceedings, 2006Konferensbidrag (Refereegranskat)
    Abstract [en]

    The purpose of this work is to develop a flexible cohesive law to simulate the constitutive behaviour of an adhesive layer under mixed mode loading. A mixed mode cohesive law that captures the linear elastic and softening behaviour before fracture is presented. This simple model uses a coupled formulation to describe the mixed mode cohesive behaviour. It also allows for different fracture parameters, such as fracture energy, strength and critical separation in different mode mixities. Thus, the fracture process in mode I (peel), in mode II (shear) or in mixed mode (a combination of peel and shear) can be modelled without the usual constraint of a common fracture energy in peel and shear. Examples are given of FE-implementation of the normalised cohesive law, namely for the Unsymmetric Double Cantilever Beam (UDCB) specimen and the Mixed-mode double Cantilever Beam (MCB) specimen. Both specimens are adhesively bonded and loaded in mixed-mode.

  • 6.
    Högberg, J. Li
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Specimen proposals for mixed mode testing of adhesive layer2006Ingår i: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 73, nr 16, s. 2541-2556Artikel i tidskrift (Refereegranskat)
    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.

  • 7.
    Högberg, J. Li
    et al.
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Sørensen, B. F.
    Tech Univ Denmark, Mat Res Dept, Riso Natl Lab, DK-4000 Roskilde, Denmark.
    Stigh, Ulf
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Constitutive behaviour of mixed mode loaded adhesive layer2007Ingår i: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 44, nr 25-26, s. 8335-8354Artikel i tidskrift (Refereegranskat)
    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.

  • 8.
    Högberg, Jia Li
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Mixed mode loaded adhesive layers: from measurement of material data to analysis of structural behaviour2007Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    In manufacturing of multi-material products, a joining method that is able to cost-effectively assemble components made of dissimilar and similar material, with irregular geometries, is optimal. As an alternative, adhesive bonding is in-creasingly adapted by the industry, which is also used in manufacturing of multi-phase materials. In practice, adhesives are constrained to thin layers. An adhesive as a constrained layer behaves differently compared to the adhesive as a bulk material. In general, adhesive layers are loaded in peel (mode I), or in shear (mode II or III), or in a combination of peel and shear (mixed mode). This thesis deals with mixed mode loaded adhesive layers, from measurement of ma-terial data to analysis of structural behaviour. For studying of structural behaviour of adhesive joints, an integrated approach is developed. Arbitrarily end-loaded single-layer adhesive joints with arbitrary ad-herends of arbitrary length are analysed with the Beam/Adhesive layer (B/A) model. Closed-form solutions are obtained for the adhesive layer as well as for the adherends. For joints with a semi-infinite symmetric geometry, i.e. relative long joints with identical adherends loaded at one end, basic loading cases are obtained. Solutions to these basic loading cases are easy to use in designing of joints with this type of geometry. For nonlinear or general adhesive layers, a mode-dependent cohesive law is de-veloped. The normalized formulation is easy to implement in numerical simula-tions, yet, it captures the characteristics of adhesive layers. For experimental studies, this cohesive law is used to obtain the constitutive behaviour of an adhe-sive layer. The results confirm the ability and suitability of this cohesive law in modelling of adhesive layers. To obtain material data of adhesive layers, experimental methods are developed based on the J-integral. Two specimens, the Mixed mode double Cantilever Beams (MCB) specimen and the Unbalanced Double Cantilever Beams (UDCB) specimen, are designed to allow adhesive layers to be loaded in mixed mode. The MCB-specimen is implemented experimentally and the constitutive behav-iour of the tested adhesive layer is obtained.

  • 9.
    Högberg, Jia Li
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Unbalanced UCB-specimen2006Ingår i: CDCM06 online proceedings, University of Stuttgart , 2006Konferensbidrag (Refereegranskat)
    Abstract [en]

    The Double Cantilever Beam (DCB) specimen is a common test geometry for testing of mode I fracture properties of adhesive joints. However, when unbalances are introduced to the adherends, the adhesive layer is loaded in a combination of peel (mode I) and shear (mode II). In this work the unbalanced DCB-specimen is studied by the use of the beam/adhesive layer (B/A) model, in which the adherends are considered as beams and the adhesive layer as a generalised spring media. The effect of the thickness of adhesive layer together with the effect of the geometrical and material unbalances is analysed. The result of the B/A model is compared to the continuum model through FE-simulations. Finally, an unsymmetric DCB-specimen is dimensioned for mixed mode testing of adhesive layer.

  • 10.
    Högberg, Li
    Högskolan i Skövde, Institutionen för teknik och samhälle.
    Mechanical Behaviour of Single-Layer Adhesive Joints: an integrated approach2004Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    Innovative products that are competitive on the market are likely to employ newtypes of materials and unusual geometries. A method that can assemble dissimilarmaterials and irregular geometries cost-effectively and at the same time offera joint that is light in weight and imperceptible, is optimal. Conventional joiningmethods, such as welding and riveting, can no longer satisfy the joining purposecompletely. Adhesive joints satisfy all mentioned requirements above and henceoffer design engineers a wider choice of materials and an increased freedom ingeometry design of the components, which most likely leads to a better design ina shorter time. The prediction of the mechanical behaviour of a joint, preferablywith simple and efficient formulas, plays an important role in the product designprocess. In this thesis, single-layer adhesive joints are analysed through the integratedapproach, i.e. an extensive stress analysis followed by a fracture analysisto determine the energy release rate and the mode-mixity due to general endloads. The purpose is to provide easy-to-use design formulas and to investigatedifferent specimen configurations for the experimental determination of the mechanicalproperties of adhesives under mixed mode loading.In the stress analysis, a systematic and easy to use closed-form solution based onthe beam/adhesive layer (B/A) model is presented to determine the stress andstrain in a linear elastic single-layer adhesive joint. In the fracture analysis, fourtypes of single-layer adhesive joints are investigated based on the closed-formsolution given in the stress analysis. The B/A model is compared to two continuummodels: one neglecting the existence of the adhesive layer (Suo and Hutchinson1990) and the other accounting the adhesive layer by the use of FEM.The results of the B/A model compares favourably to the FE-analyses. Threetypes of basic loading systems are identified for the symmetric semi-infinitejoint geometry. Two specimens for testing mode mixity are suggested. Accordingto the theoretical studies by use of the B/A model, the specimen denoted theMixed Mode B with a short crack length offers good flexibility, variety and stability.

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