| 1. |
- Bjerkén, Christina, PhD, 1962-, et al.
(författare)
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A numerical method for calculating stress intensity factors for interface cracks in bimaterials
- 2001
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Ingår i: Engineering Fracture Mechanics. - : Elsevier. - 0013-7944 .- 1873-7315. ; 68:2, s. 235-246
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a method For obtaining the complex stress intensity factor (or alternatively the corresponding energy release rate and mode mixity) for an interface crack in a bimaterial using a minimum number of computations. A crack closure integral method for homogeneous materials developed by Rybicki and Kanninen has been modified to include mismatch in material properties. This was achieved directly from the nodal forces at the crack tip and the displacements near the tip as obtained from a finite element analysis using only four-node constant strain elements. Numerical calculations for tensile and mixed mode loading showed good agreement with results from corresponding analytical solutions. The main advantages of this method are that it is straightforward and easy to use and that the number of calculations needed to obtain the stress intensity Factors can be held to a minimum. (C) 2000 Elsevier Science Ltd. All rights reserved.
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| 2. |
- Bjerkén, Christina, et al.
(författare)
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A study of the influence of grain boundaries on short crack growth during varying load using a dislocation technique
- 2004
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Ingår i: Engineering Fracture Mechanics. - : Elsevier BV. - 1873-7315 .- 0013-7944. ; 71:15, s. 2215-2227
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Tidskriftsartikel (refereegranskat)abstract
- The propagation of short cracks in the neighbourhood of grain boundaries have been investigated using a technique were the crack is modelled by distributed dislocation dipoles and the plastic deformation is represented by discrete dislocations. Discrete dislocations are emitted from the crack tip as the crack grows. Dislocations can also nucleate at the grain boundaries. The influence on crack growth characteristics of the distance between the initial crack tip and the grain boundary has been studied. It was found that crack growth rate is strongly correlated to the dislocation pile-ups at the grain boundaries. (C) 2004 Elsevier Ltd. All rights reserved.
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| 3. |
- Bjerkén, Christina, et al.
(författare)
-
A tool to model short crack fatigue growth using a discrete dislocation formulation
- 2003
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Ingår i: International Journal of Fatigue. - : Elsevier. - 1879-3452 .- 0142-1123. ; 25:6, s. 559-566
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Tidskriftsartikel (refereegranskat)abstract
- A method is presented that combines the modelling of cracks by distributed dislocation dipoles with developing plasticity represented by discrete dislocations moving along slip bands. Crack growth is due to the emission of dislocations from the crack tip along preferred slip planes. Eventual annihilation of dislocations occurs by reunion with the corresponding displacement steps of the crack surface. Crack surface overlap is not allowed. The equilibrium state for each load increment is solved iteratively, allowing various crack geometries. The method is applied to the problem of a short edge crack growing in mode I due to fatigue loading. It is shown that the development of a local plastic zone and the propagation of the crack can be monitored in detail.
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| 4. |
- Bjerkén, Christina
(författare)
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Branching of a dissolution driven stress corrosion crack
- 2009
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Ingår i: Proceedings of the International Conference on Crack Paths 2009. - : European Structural Integrity Society.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Stress corrosion cracking occurs due to the synergistic interaction between mechanical load and corrosion reactions. Some types of stress corrosion crack branch heavily. Here, branching during dissolution driven crack growth is studied using an adaptive FE method. A strain-assisted evolution law is used for the inherently blunted crack. No criterion for crack growth is needed as for a sharp crack, neither for the growth direction. Several simulations are performed with different degrees of load biaxiality. It is found that large biaxiality promotes branching, but no conditions for when branching takes place is found. Instead, branching seems to occur rather randomly due to the perturbation sensitivity of a dissolution driven crack. Also crack growth rates for branched cracks are investigated, and it is found that both constant growth rates can be reached, as well as decreasing rates and eventual arrest. The cracks follow a mode I crack path, however local changes may occur due to the perturbation sensitivity.
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| 5. |
- Bjerkén, Christina, et al.
(författare)
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Branching of growing corrosion fatigue cracks
- 2005
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Strain-driven corrosion of branching cracks, initiated from a virtually plane surface, has been studied using a moving boundary technique. The material is assumed linear elastic and is subjected to fatigue loading under plain strain conditions. The surface of the material is covered by a protective film. During loading this film can be damaged if it is strained above a threshold value, thus revealing an unprotected surface. Corrosion advances by material dissolution, eventually evolving into cracks. The rate of surface evolution is a function of the degree of protective film damage. During unloading the protective film is assumed to develop and heal the surface. A low frequency cyclic loading is applied to ensure that total healing is assumed. The moving boundary technique, simulating corrosion, results in arc-shaped crack tips, rather than singular crack tip points, thus no crack growth criterion is needed in the analysis. For each load step, the strain distribution is found using the finite element method, followed by required the movement the boundary and then remeshing. The crack growth has been investigated for at least 2000 cycles. A more or less pronounced branching of the cracks is found to develop. The crack branches can be classified in three groups; main cracks that grows with maximum rate and branches further, branch cracks that initially retards and then find a steady state growth rate that is a fraction of maximum speed, and finally, arresting cracks that after a period of retardation stop growing. The crack patterns are realistic, showing a sort of self-similarity with tree-like structure, cf. the picture below that shows a typical finite element result. The width of a crack branch together with the shielding from the applied stresses, caused by the other branches and main cracks, seem to govern the evolution of the crack branch. A steady-state growth rate is achieved during parts of the evolution as the crack width and the strain field surrounding the crack tip is in balance, i.e. the crack widens while the crack grows longer. As the bluntness of the tip reaches an upper limit, branching results.
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| 6. |
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| 7. |
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| 8. |
- Bjerkén, Christina
(författare)
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Dissolution Driven Fracture - Simulation of Crack Growth
- 2006
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Ingår i: Proceedings of 19th Nordic Seminar on Computational Mechanics. - : Structural Mechanics, LTH, Sweden.. ; , s. 130-134
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Konferensbidrag (refereegranskat)abstract
- The growth of a crack subjected to corrosion fatigue is studied using adaptive finite elements. The crack growth is the result of a repeated cycle of dissolution of the material, formation of a protective oxide film and break-down of the oxide film due to straining at the surface. The dissolution rate is assumed to be proportional to this stretching. The growth of a semi-infinite crack lying in an infinite strip subjected to different degrees of mixed-mode loading is studied.
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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. |
- Bjerkén, Christina, et al.
(författare)
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Fracture Mechanisms of a Thin Elastic Plastic Laminate
- 2006
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Konferensbidrag (refereegranskat)abstract
- The fracture toughness of a polymer-metal laminate composite is obtained by mechanical testing of a specimen containing a pre-crack. The laminate is a material used for packaging. It consists of a thin aluminium foil and a polymer coating. A centre cracked panel test geometry is used. Each of the layers forming the laminate is also tested separately. The result is compared with the measured fracture strength of the individual layers. It is observed that the load carrying capacity increases dramatically for the laminate. At the strain when peak load is reached for the laminate only aluminium is expected to carry any substantial load because of the low stiffness of the LDPE. However, the strength of the laminate is almost twice the strength of the aluminium foil. The reason seems to be that the aluminium forces the polymer to absorb large quantities of energy at small nominal strain. The toughness compares well with the accumulated toughness of all involved layers. Possible fracture of the interface between the layers is discussed.
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