| 1. |
- Jivkov, Andrey P.
(författare)
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On crack growth in functionally graded materials
- 1999
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Stress intensity factors' behaviour is studied for long plane cracks interacting with a region of functionally graded elastic material. The region is assumed embedded into a large body treated as a homogeneous elastic continuum. The analysis is limited to small deviations of the graded region's elastic modulus from that of the surrounding body (Poisson's ratio is kept constant) and analytical solutions are sought using a perturbation technique. Emphasis is laid on the case of an infinite strip, which admits a closed form solution. A cosine change of the modulus of elasticity is treated, furnishing the solution for arbitrary variation in the form of a Fourier's expansion. Finite element analysis is subsequently performed for investigating the scope of validity of the analytical solution. The results for a set of finite changes of the elastic modulus are compared with the analytical predictions, and a remarkably wide range of validity is demonstrated. New functions, suitable for non-homogeneous material description, are introduced to approach the case of non-constant Poisson's ratio. The properties and possible applications of these functions are examined.
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| 2. |
- Jivkov, Andrey P
(författare)
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Strain-assisted corrosion cracking and growth rate inhibitors
- 2002
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- A model for evolution of cracks as a result of strain-assisted corrosion is presented. The considered cracks possess a realistic geometry, where the tip region is an integral part of the crack surface instead of being a singular point. This geometry is either implicitly defined or is a consequence of crack nucleation from surface irregularities. The evolution model poses a moving boundary value problem, where material dissolution advances the boundary exposed to the corrosive environment. A controlling mechanism for the boundary advancement is the rupture of a brittle corrosion-protective film, which is continually building-up along the corroding surface. The rate of boundary evolution is a function of the degree of the protective film damage, caused by mechanical straining. Thus, no crack growth criterion is needed for the analysis. A FEM based program with various procedures for tracking the moving boundary is used as a solution tool. A number of problems are considered – cracks with realistic geometries with tips embedded in a square-root singular stress field, and cracks nucleating from surface pits and propagating in either a homogeneous material or in a bi-material system. The presented results show the importance of the crack width, interpreted as grain boundaries inter-phase thickness, as well as the various shape parameters describing the crack tip region, for the stress corrosion crack growth rate. Further, the results clearly demonstrate that the interaction between the surface deformation and the protective film is primarily responsible for the dissolution localisation along a narrow surface region, such that a crack is formed from a pit and the crack shape is maintained during the evolution. The influence of the initial pit aspect ratio on the crack nucleation phase is investigated, as well as the competition of cracks evolving from closely situated pits. It is shown how these results could be used for estimation of the arrested cracks distribution along a corroding surface. In the cases of corrosion cracks growing across bi-material interfaces the numerical results for the crack morphology are shown to be in qualitative agreement with a real life example. In all these cases the cracks pass the interface being either accelerated or inhibited, depending on the elastic mismatch of the bi-material system. Design recommendations are proposed on the bases of the presented results. Finally, a perturbation model for a non-homogeneous material is proposed. The model is used in the analysis of an ideal crack with one tip interfering with an inclusion, introduced in a plane homogeneous elastic body, and having arbitrarily varying elastic characteristics. The solution is given in terms of an area integral and further specialised to an inclusion shaped as a layer stretching perpendicularly to the crack plane. A closed form result for this special case is derived and compared with numerical results obtained for finite variations of the elastic modulus. A wide range of validity of the perturbation solution is discovered.
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| 3. |
- Ståhle, Per, et al.
(författare)
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On dissolution driven crack growth
- 2007
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683 .- 1879-2146. ; 44:6, s. 1880-1890
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Tidskriftsartikel (refereegranskat)abstract
- The formation and growth of a crack in a body subjected to stress driven material dissolution is studied. The rate of material dissolution is proportional to strain energy and curvature of the body surface. The formation of a crack from a plane surface is preceded by an evolving surface roughness. The continued dissolution enhances roughness amplitude resulting in pit formation. As the pit grows deeper into the material, it assumes the shape of a crack. The sharpness of the crack reaches its maximum during this transition from a pit to a crack. As the crack grows, a self-similar state is gradually assumed. During this phase characteristic lengths of the crack shape scale with the crack length. In line with this the crack progressively becomes blunt. The widest part of the crack when unloaded is in the vicinity of the crack tip. A consequence of the model is that no criterion is needed for crack growth. Neither is a criterion needed for determination of the crack path. It also follows that the crack growth rate is almost independent of the remote load. Further, spontaneous crack branching is anticipated. A motivation for this is given. (c) 2006 Elsevier Ltd. All rights reserved.
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| 4. |
- Ståhle, Per, et al.
(författare)
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Selfsimilar solutions for stress driven material dissolution
- 2004
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- During corrosive dissolution of metal ions from a body surface, an oxide compound is produced. This compound forms a protective film that reduces the dissolution rate. When a fraction of a millimetre depth is dissolved the dissolution rate become insignificant. However, repeated loading will damage the film with continued dissolution as a result. In connection with this a threshold strain is assumed to exist. This paper proposes a model where electro- chemical processes and the mechanical load work together in forming a corrosion pit. The ratio between the threshold strain and the remotely applied strain is shown to control the shape of the pit. For small applied strains cracks are formed. A crack evolving from a surface irregularity is studied. The growth rate of the crack is determined by the dissolution rate at the crack tip. No crack growth criterion is needed. The growing crack is itself creating conditions for strain concentration, which leads to a high crack growth rate. The model simulates how dissolution forms a pit that grows to become a crack in a single continuous process. For small loads the crack growth rate is independent of applied load.
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