| 1. |
- Alfredsson, K. Svante
(författare)
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On the determination of constitutive properties of adhesive layers loaded in shear - an inverse solution
- 2003
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Ingår i: International Journal of Fracture. - : Springer. - 0376-9429 .- 1573-2673. ; 123:1-2, s. 49-62
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Tidskriftsartikel (refereegranskat)abstract
- 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
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| 2. |
- Alfredsson, Svante, et al.
(författare)
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Energy release rate and mode-mixity of adhesive joint specimens
- 2007
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Ingår i: International Journal of Fracture. - : Springer. - 0376-9429 .- 1573-2673. ; 144:4, s. 267-283
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Tidskriftsartikel (refereegranskat)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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| 3. |
- Andersson, P., et al.
(författare)
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Shielding effects and residual stresses at cleavage due to pre-existing dislocations
- 1997
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Ingår i: International Journal of Fracture. - 0376-9429 .- 1573-2673. ; 85:4, s. 365-380
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Tidskriftsartikel (refereegranskat)abstract
- The motion of pre-existing edge dislocations in an infinite linear elastic body is studied at initiation of crack growth and at quasi-static steady-state crack growth. Dislocation nucleation is assumed not to occur. Thus, the study concerns only dislocations that are present in the virgin material. A dislocation is assumed to glide if its driving force exceeds a critical value. Changes in dislocation density, crack tip shielding and residual stresses are obtained. The shielding of a stationary crack tip is found to be small compared with the shielding of a growing crack tip. At steady-state the residual stresses far behind the crack tip are tensile near the crack, decreasing to zero at a certain distance from the crack plane. It is shown that the shielding due to pre-existing dislocations, e.g., for cleavage in α-iron crystals may be considerable.
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| 4. |
- Andersson, Tobias, et al.
(författare)
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On the effective constitutive properties of a thin adhesive layer loaded in peel
- 2006
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Ingår i: International Journal of Fracture. - : Springer Netherlands. - 0376-9429 .- 1573-2673. ; 141:1-2, s. 227-246
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Tidskriftsartikel (refereegranskat)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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| 5. |
- Banks-Sills, Leslie, et al.
(författare)
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Interface fracture toughness of a multi-directional woven composite
- 2013
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Ingår i: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 182:2, s. 187-207
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this investigation is to measure the interface fracture toughness of a woven composite. For this purpose, double cantilever beam (DCB) specimens are tested to measure the load as the delamination grows. The specimen is composed of 15 layers of a carbon-epoxy, balanced weave with alternate layers containing fibers in the directions and the directions. A thin piece of Teflon is placed between two layers of differing directions. The specimens are analyzed by means of the finite element method and an interaction energy or -integral to determine the stress intensity factors, interface energy release rate and phase angles. The first term of the asymptotic solution for the stress and displacement fields obtained by means of the Stroh and Lekhnitskii formalisms is used to define auxiliary solutions for the -integral. The critical interface energy release rate is found and exhibits a slowly increasing resistance curve. Comparisons are made to a simple expression from the literature.
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| 6. |
- Bartel, T., et al.
(författare)
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Modelling and simulation of cyclic thermomechanical behaviour of NiTi wires using a weak discontinuity approach
- 2016
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Ingår i: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 202:2, s. 281-293
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Tidskriftsartikel (refereegranskat)abstract
- In this contribution, a thermodynamically consistent and mathematically canonical modelling framework for the investigation of the cyclic thermomechanical behaviour of Nickel-Titanium shape memory alloy wires is developed. Particular focus is placed on the self-heating of the material subjected to multiple load cycles. The relatively high load rates necessitates the consideration of inertia terms, the applied load amplitudes of six percent strain motivates the use of a non-linear, Hencky-type strain measure. Comparisons of the results with experimental data on the one hand reveal reasonable results and on the other hand underline the necessity of further model enhancements.
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| 7. |
- Biel, Anders, et al.
(författare)
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Cohesive zone modelling of nucleation, growth and coalesce of cavities
- 2017
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Ingår i: International Journal of Fracture. - : Springer. - 0376-9429 .- 1573-2673. ; 204:2, s. 159-174
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 8. |
- Biel, Anders, et al.
(författare)
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Damage and plasticity in adhesive layer : an experimental study
- 2010
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Ingår i: International Journal of Fracture. - : Springer Science+Business Media B.V.. - 0376-9429 .- 1573-2673. ; 165:1, s. 93-103
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 9. |
- Bjerkén, Christina, et al.
(författare)
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Evolution of anodic stress corrosion cracking in a coated material
- 2010
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Ingår i: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 165:2, s. 211-221
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Konferensbidrag (refereegranskat)abstract
- In the present paper, we investigate the influence of corrosion driving forces and interfacial toughness for a coated material subjected to mechanical loading. If the protective coating is cracked, the substrate material may become exposed to a corrosive media. For a stress corrosion sensitive substrate material, this may lead to detrimental crack growth. A crack is assumed to grow by anodic dissolution, inherently leading to a blunt crack tip. The evolution of the crack surface is modelled as a moving boundary problem using an adaptive finite element method. The rate of dissolution along the crack surface in the substrate is assumed to be proportional to the chemical potential, which is function of the local surface energy density and elastic strain energy density. The surface energy tends to flatten the surface, whereas the strain energy due to stress concentration promotes material dissolution. The influence of the interface energy density parameter for the solid-fluid combination, interface corrosion resistance and stiffness ratios between coating and substrate is investigated. Three characteristic crack shapes are obtained; deepening and narrowing single cracks, branched cracks and sharp interface cracks. The crack shapes obtained by our simulations are similar to real sub-coating cracks reported in the literature.
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| 10. |
- Bremberg, Daniel, et al.
(författare)
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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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Ingår i: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 157:1-2, s. 109-118
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Tidskriftsartikel (refereegranskat)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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| 11. |
- Carlberger, Thomas, et al.
(författare)
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Influence of temperature and strain rate on cohesive properties of a structural epoxy adhesive
- 2009
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Ingår i: International Journal of Fracture. - : Springer. - 0376-9429 .- 1573-2673. ; 155:2, s. 155-166
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Tidskriftsartikel (refereegranskat)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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| 12. |
- Eklind, Alexander, et al.
(författare)
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High cycle fatigue crack growth in Mode I of adhesive layers : modelling, simulation and experiments
- 2014
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Ingår i: International Journal of Fracture. - : Springer Netherlands. - 0376-9429 .- 1573-2673. ; 190:1-2, s. 125-146
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Tidskriftsartikel (refereegranskat)abstract
- The capability to predict high cycle fatigue properties of adhesive joints is important for cost-efficient and rapid product development in the modern automotive industry. Here, the adaptability of adhesives facilitates green technology through the widening of options of choosing and joining optimal materials. In the present paper a continuum damage mechanics model is developed based on the adhesive layer theory. In this theory, through-thickness averaged variables for the adhesive layer are used to characterise the deformation, damage and local loading on the adhesive layer. In FE-simulations, cohesive elements can thereby be used to model the adhesive layer. This simplifies simulations of large scale complex built-up structures. The model is adapted to experimental results for two very different adhesive systems; one relatively stiff rubber based adhesive and one soft polyurethane based adhesive. The model is able to reproduce the experimental results with good accuracy except for the early stage of crack propagation when the loads are relatively large. The model also predicts a threshold value for fatigue crack growth below which no crack growth occurs. The properties of the model are also compared with the properties of Paris’ law. The relations between the parameters of the continuum damage mechanics law and the parameters of Paris’ law are used to adapt the new law. It also shows that the properties of a joined structure influence the Paris’ law properties of the adhesive layer. Thus, the Paris’ law properties of an adhesive layer are not expected to be transferable to joints with adherends having different mechanical properties.
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| 13. |
- Elmukashfi, Elsiddig, et al.
(författare)
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Numerical analysis of dynamic crack propagation in rubber
- 2012
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Ingår i: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 177:2, s. 163-178
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Tidskriftsartikel (refereegranskat)abstract
- In the present paper, dynamic crack propagation in rubber is analyzed numerically using the finite element method. The problem of a suddenly initiated crack at the center of stretched sheet is studied under plane stress conditions. A nonlinear finite element analysis using implicit time integration scheme is used. The bulk material behavior is described by finite-viscoelasticity theory and the fracture separation process is characterized using a cohesive zone model with a bilinear traction-separation law. Hence, the numerical model is able to model and predict the different contributions to the fracture toughness, i.e. the surface energy, viscoelastic dissipation, and inertia effects. The separation work per unit area and the strength of the cohesive zone have been parameterized, and their influence on the separation process has been investigated. A steadily propagating crack is obtained and the corresponding crack tip position and velocity history as well as the steady crack propagation velocity are evaluated and compared with experimental data. A minimum threshold stretch of 3.0 is required for crack propagation. The numerical model is able to predict the dynamic crack growth. It appears that the strength and the surface energy vary with the crack speed. Finally, the maximum principal stretch and stress distribution around steadily propagation crack tip suggest that crystallization and cavity formation may take place.
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| 14. |
- Eriksson, Kjell
(författare)
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A general expression for an area integral of a point-wise J for a curved crack front
- 2000
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Ingår i: International Journal of Fracture. - 0376-9429 .- 1573-2673. ; 106:1, s. 65-80
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Tidskriftsartikel (refereegranskat)abstract
- The expression for the J-integral at a point on a three-dimensional crack front, obtained from a surface independent integral, is in general a sum of a contour integral and an area integral. In this work a general expression of an area integral for a crack with a curved front is derived in curvilinear coordinates. In certain situations the area integral vanishes and previously known cases are a straight crack front in plane stress or plane strain. The general conditions for a vanishing area integral are studied. It is shown that the area integral is non-zero for cracks with a curved front in the direction of crack extension. Some examples of curved cracks are given, for which the area integral vanishes and that are of interest in practice.
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| 15. |
- Eriksson, Kjell
(författare)
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A note on the derivation of the J-integral from potential energy
- 2004
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Ingår i: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 130:4, s. L201-L203
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- In a recent work Z.-H. Jin and C. T. Sun (2004) presented a derivation of the J-integral from the potential energy of a system, which is thought to circumvent previous cumbersome or flawed derivations. Two items in this work call for discussion; one is related to the effect of a singularity upon different types of contour integrals and the other to the strain energy difference term.
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| 16. |
- Eriksson, Kjell
(författare)
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Crack extension force of a curved crack derived from the principle of virtual work
- 2000
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Ingår i: International Journal of Fracture. - 0376-9429 .- 1573-2673. ; 102:1, s. 15-20
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Tidskriftsartikel (refereegranskat)abstract
- A general method to determine the crack extension force F related to a finite segment of a curved crack is presented. A path independent integral expression that holds in curvilinear coordinates is derived from the principle of virtual work. An appropriate virtual displacement field allows variation of the position of a crack tip. F is related to the path independent integral expression through variation of a total energy expression. To illustrate the applicability of the method F is derived for the conical crack in axisymmetric loading. For a plane crack with a straight front F is identical to the J-integral, Rice (1968).
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| 17. |
- Eriksson, Kjell
(författare)
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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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Ingår i: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 144:1-2, s. 215-225
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Tidskriftsartikel (refereegranskat)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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| 18. |
- Eriksson, Kjell
(författare)
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Energy release rates for the penny-shaped crack in a linear piezoelectric solid
- 2002
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Ingår i: International Journal of Fracture. - 0376-9429 .- 1573-2673. ; 116:2, s. L23-L28
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- A domain independent integral expression that is derived from the principle of virtual work and holds in curvilinear coordinates is used to derive the energy release rate for a penny-shaped crack in a linear piezoelectric solid. The virtual mechanical and electric displacement fields are chosen to allow variation of the crack tip position. Results for the energy release rate for a finite crack segment and point-wise show the effect of crack front curvature in a piezoelectric material.
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| 19. |
- Eriksson, Kjell
(författare)
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On the point-wise J-value of axisymmetric plane cracks
- 1998
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Ingår i: International Journal of Fracture. - 0376-9429 .- 1573-2673. ; 91:3, s. L31-L36
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- A point-wise value of the J-integral for a radially expanding plane axisymmetric crack, which is path independent an yields the energy release rate, has been derived from Eshelby's energy momentum tensor taken in cylindrical coordinates. In particular the area integral in the expression for J by Carpenter et al. has not been found to be zero, as recently advanced by Jonsson and Nilsson, but in agreement with results of others, e.g. Bergkvist and Lan Huong
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| 20. |
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| 21. |
- Hallström, Stefan, 1968-, et al.
(författare)
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Mixed mode fracture of cracks and wedge shaped notches in expanded PVC foam
- 1998
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Ingår i: International Journal of Fracture. - 0376-9429 .- 1573-2673. ; 88:4, s. 343-358
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Tidskriftsartikel (refereegranskat)abstract
- Fracture initiated from a sharp crack or wedge shaped notch in a homogeneous material, subjected to different loading is considered. Singularities in the stress fields at edges and vertices are discussed. A point-stress criterion is used to predict fracture for sharp cracks as well as 90° wedge notches in expanded PVC foam. The point-stress criterion is formulated in a manner allowing failure predictions in general 3D stress situations. The influence of non-singular T-stress at cracks is discussed and substantiated by experimental results.
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| 22. |
- Hansson, Per, et al.
(författare)
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Grain boundary influence on short fatigue crack growth rate
- 2010
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Ingår i: International Journal of Fracture. - : Springer Science and Business Media LLC. - 0376-9429 .- 1573-2673. ; 165:2, s. 199-210
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Tidskriftsartikel (refereegranskat)abstract
- The influence from different grain boundary configurations on the crack growth rate of a microstructurally short edge crack, located within one grain and subjected to remote fatigue loading, is studied. The study is performed using a dislocation formulation, were the geometry is described by dislocation dipole elements in a boundary element approach and the plasticity by discrete dislocations, located along specific slip planes in the material. Plane strain and quasi-static conditions are assumed. The crack is assumed to grow in a single shear mechanism due to nucleation, glide and annihilation of discrete dislocations. Different grain boundary configurations in front of the growing crack are considered, including both high angle and low angle grain boundaries. It is shown that both grain boundary configuration and distance between the crack and a grain boundary has a pronounced influence on the crack growth rate.
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| 23. |
- Högberg, J. Li
(författare)
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Mixed mode cohesive law
- 2006
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Ingår i: International Journal of Fracture. - : Springer Netherlands. - 0376-9429 .- 1573-2673. ; 141:3-4, s. 549-559
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Tidskriftsartikel (refereegranskat)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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| 24. |
- Isaksson, Per, et al.
(författare)
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Crack kinking under high pressure in an elastic-plastic material
- 2001
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Ingår i: International Journal of Fracture. - 0376-9429 .- 1573-2673. ; 108:4, s. 351-366
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Tidskriftsartikel (refereegranskat)abstract
- Directional crack growth criteria in compressed elastic–plastic materials are considered. The conditions at the crack tip are evaluated for a straight stationary crack. Remote load is a combined hydrostatic stress and pure shear, applied via a boundary layer assuming small scale yielding. Strains and deformations are assumed to be small. Different candidates for crack path criteria are examined. Maximum non-negative hoop stress to judge the risk of mode I and maximum shear stress for mode II extension of the crack are examined in some detail. Crack surfaces in contact are assumed to develop Coulumb friction from the very beginning. Hence, a condition of slip occurs throughout the crack faces. The plane in which the crack extends is calculated using a finite element method. Slip-line solutions are derived for comparison with the numerically computed asymptotic field. An excellent agreement between numerical and analytical solutions is found. The agreement is good in the region from the crack tip to around halfway to the elastic–plastic boundary. The relation between friction stress and yield stress is varied. The crack is found to extend in a direction straight ahead in shear mode for sufficiently high compressive pressure. At a limit pressure a kink is formed at a finite angle to the crack plane. For lower pressures the crack extends via a kink forming an angle to the parent crack plane that increases with decreasing pressure.
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| 25. |
- Isaksson, Per, et al.
(författare)
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Prediction of shear crack growth direction under compressive loading
- 2002
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Ingår i: International Journal of Fracture. - 0376-9429 .- 1573-2673. ; 113:2, s. 175-194
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Tidskriftsartikel (refereegranskat)abstract
- A directional crack growth prediction in a compressed homogenous elastic isotropic material under plane strain conditions is considered. The conditions at the parent crack tip are evaluated for a straight stationary crack. Remote load is a combined biaxial compressive normal stress and pure shear. Crack surfaces are assumed to be frictionless and to remain closed during the kink formation wherefore the mode I stress intensity factor KI is vanishing. Hence the mode II stress intensity factor KII remains as the single stress intensity variable for the kinked crack. An expression for the local mode II stress intensity factor k2 at the tip of a straight kink has been calculated numerically with an integral equation using the solution scheme proposed by Lo (1978) and refined by He and Hutchinson (1989). The confidence of the solution is strengthened by verifications with a boundary element method and by particular analytical solutions. The expression has been found as a function of the mode II stress intensity factor KII of the parent crack, the direction and length of the kink, and the difference between the remote compressive normal stresses perpendicular to, and parallel with, the plane of the parent crack. Based on the expression, initial crack growth directions have been suggested. At a sufficiently high non-isotropic compressive normal stress, so that the crack remains closed, the crack is predicted to extend along a curved path that maximizes the mode II stress intensity factor k2. Only at an isotropic remote compressive normal stress the crack will continue straight ahead without change of the direction. Further, an analysis of the shape of the crack path has revealed that the propagation path is, according the model, required to be described by a function y = cxγ , where the exponent γ is equal to 3/2. In that case, when γ = 3/2, predicts the analytical model a propagation path that is selfsimilar (i.e. the curvature c is independent of any length of a crack extension), and which can be described by a function of only the mode II stress intensity factor KII at the parent crack tip and the difference between the remote compressive normal stress perpendicular to, and parallel with, the parent crack plane. Comparisons with curved shear cracks in brittle materials reported in literature provide limited support for the model discussed.
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