| 1. |
- Alfredsson, Svante, et al.
(author)
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Energy release rate and mode-mixity of adhesive joint specimens
- 2007
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In: International Journal of Fracture. - : Springer. - 0376-9429 .- 1573-2673. ; 144:4, s. 267-283
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Journal article (peer-reviewed)abstract
- 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.
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| 2. |
- Andersson, Tobias, et al.
(author)
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On the effective constitutive properties of a thin adhesive layer loaded in peel
- 2006
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In: International Journal of Fracture. - : Springer Netherlands. - 0376-9429 .- 1573-2673. ; 141:1-2, s. 227-246
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Journal article (peer-reviewed)abstract
- 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.
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| 3. |
- Bremberg, Daniel, et al.
(author)
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Automatic 3-D crack propagation calculations : a pure hexahedral element approach versus a combined element approach
- 2009
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In: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 157:1-2, s. 109-118
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Journal article (peer-reviewed)abstract
- This article presents an evaluation of two different crack prediction approaches based on a comparison of the stress intensity factor distribution for three example problems. A single edge notch specimen and a quarter circular corner crack specimen subjected to shear displacements and a three point bend specimen with a crack inclined to the mid-plane are examined. The stress intensity factors are determined from the singular stress field close to the crack front. Two different fracture criteria are adopted for the calculation of an equivalent stress intensity factor and crack deflection angle. The stress intensity factor distributions for both numerical methods agree well to available reference solutions. Deviations are recorded at crack front locations near the free surface probably due to global contraction effects and the twisting behaviour of the crack front. Crack propagation calculations for the three point bending specimen give results that satisfy intuitive expectations. The outcome of the study encourages further pursuit of a crack propagation tool based on a combination of elements.
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| 4. |
- Carlberger, Thomas, et al.
(author)
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Influence of temperature and strain rate on cohesive properties of a structural epoxy adhesive
- 2009
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In: International Journal of Fracture. - : Springer. - 0376-9429 .- 1573-2673. ; 155:2, s. 155-166
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Journal article (peer-reviewed)abstract
- 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.
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| 5. |
- Eriksson, Kjell
(author)
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Decomposition of Eshelby's energy momentum tensor and application to path and domain independent integrals for the crack extension force of a plane circular crack in Mode III loadiing
- 2007
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In: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 144:1-2, s. 215-225
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Journal article (peer-reviewed)abstract
- Vanishing divergence of Eshelby's energy momentum tensor allows formulation of path or domain independent integral expresssions of the crack extension force. In this work, a decomposition scheme of this tensor is presented, which results in zero divergence decomposed parts that allow formulation of expressions yielding the Mode I, II and III crack tip parameters J and K, with particular emphasis on Mode III, at present. By using the Mode III decomposed part of Eshelby's tensor and the virtual crack extension method, a path and a domain independent integral, both new, for the crack extension force of a plane cirular crack in axi-symmetric Mode III loading, are derived as examples of applicatioin.
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| 6. |
- Högberg, J. Li
(author)
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Mixed mode cohesive law
- 2006
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In: International Journal of Fracture. - : Springer Netherlands. - 0376-9429 .- 1573-2673. ; 141:3-4, s. 549-559
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Journal article (peer-reviewed)abstract
- 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
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| 7. |
- Isaksson, Per, et al.
(author)
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Strain energy distribution in a crack-tip region in random fiber networks
- 2009
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In: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 156:1, s. 1-9
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Journal article (peer-reviewed)abstract
- A closed form relation for the strain energy density in the vicinity of a macroscopic mode I crack in a random fiber network is derived using an implicit gradient nonlocal continuum field theory. An expression for the characteristic length, used in the nonlocal formulations, in terms of microstructural properties is derived and it is found that the characteristic length is proportional to the average fiber segment length to the power of two. It is illustrated that the crack-tip singularity vanishes for a characteristic length greater than zero. An open fiber structure exhibits a distributed strain energy field in the crack tip vicinity. As the network becomes relatively denser, the characteristic length decreases and the networks mechanical behavior approaches the behavior of a classic elastic continuum. Only for an infinitely dense network is the r −1-singularity in strain energy field achieved. The theory explains why open network structures have difficulties in localizing failure to macroscopic cracks. It is found that there is a one-to-one relation between characteristic length and size of the smallest crack that can initiate macroscopic failure.
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| 8. |
- Nilsson, Fred L.
(author)
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A tentative method for determination of cohesive zone properties in soft materials
- 2005
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In: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 136:04-jan, s. 133-142
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Journal article (peer-reviewed)abstract
- A method is outlined for the determination of cohesive zone properties in soft materials. The goal of the study was to extend earlier work assuming linear kinematics and linear elasticity to include non-linear kinematics and finite elasticity Explicit results for cohesive traction determination are given and discussed. A comparison is made between expressing the cohesive law in a Lagrangian or an Eulerian description, respectively Some implications of either choice are discussed. Two suitable geometries for experimental use are analysed as examples of the method.
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| 9. |
- Nilsson, Fred L.
(author)
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Large displacement aspects on fracture testing with double cantilever beam specimens
- 2006
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In: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 139:2, s. 305-311
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Journal article (peer-reviewed)abstract
- The double cantilever beam specimen for fracture testing was investigated for large displacement conditions. J-expressions were derived for arbitrary loading of the beam-ends. As special cases two different loadings, transverse force and bending moment were studied. Explicit relations for use in experimental situations were derived.
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| 10. |
- Stec, Mateusz, et al.
(author)
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Influence of grain size on arrest of a dynamically propagating cleavage crack in ferritic steels-micromechanics
- 2009
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In: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 158:1, s. 51-71
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Journal article (peer-reviewed)abstract
- Cleavage fracture in ferritic steels is controlled by several critical steps. First a microcrack must nucleate, grow and overcome barriers, such as grain boundaries. The latter is examined here by use of a periodic, axisymmetric model representing two grains. A microcrack nucleated at the center in one grain is driven by a constant remotely applied stress towards the second grain. The cleavage planes of the grain in which the microcrack is nucleated coincide with the principal loading direction. In the adjacent grain, due to misalignment in possible cleavage planes, the propagation direction changes and separation occurs in mixed mode, involving both normal and shear separations. The temperature dependence of the mechanical properties of the material is accounted for by use of a temperature dependent elasto viscoplastic material model. The largest grain size that can arrest a rapidly propagating microcrack is defined as the critical grain size. The effects of stress state and temperature on the critical grain size are examined. The influence of mismatch in lattice orientation between two adjacent grains in terms of a tilt angle is both qualitatively and quantitatively described. It is shown that the critical grain size is influenced by plastic geometry change and prestraining, which depend on the applied stress state. The results also show that a microcrack can be arrested in an adjacent grain under specific conditions.
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