| 1. |
|
|
| 2. |
|
|
| 3. |
|
|
| 4. |
- Jivkov, Andrey, et al.
(författare)
-
A model for graded materials with application to cracks
- 2003
-
Ingår i: International Journal of Fracture. - 0376-9429 .- 1573-2673. ; 124:1-2, s. 93-105
-
Tidskriftsartikel (refereegranskat)abstract
- Stress intensity factors are calculated for long plane cracks with one tip interacting with a region of graded material characteristics. The material outside the region is considered to be homogeneous. The analysis is based on assumed small differences in stiffness in the entire body. The linear extent of the body is assumed to be large compared with that of the graded region. The crack tip, including the graded region, is assumed embedded in a square-root singular stress field. The stress intensity factor is given by a singular integral. Solutions are presented for rectangular regions with elastic gradient parallel to the crack plane. The limiting case of infinite strip is solved analytically, leading to a very simple expression. Further, a fundamental case is considered, allowing the solution for arbitrary variation of the material properties to be represented by Fourier's series expansion. The solution is compared with numerical results for finite changes of modulus of elasticity and is shown to have a surprisingly large range of validity. If an error of 5% is tolerated, modulus of elasticity may drop by around 40% or increase with around 60%.
|
|
| 5. |
- Jivkov, Andrey
(författare)
-
A moving boundary model for fatigue corrosion cracking
- 2003
-
Ingår i: Moving Boundaries VII. - : WIT Press. - 9781853129872 ; , s. 55-64
-
Konferensbidrag (refereegranskat)abstract
- Fatigue corrosion crack initiation and propagation is modelled as a moving boundary value problem. The model is based on three physical processesoperating at the solid-environment interface ñ material dissolution, passive filmformation and surface straining. The dissolution triggers boundary advancement.The rate of boundary advancement depends on the passive film damage causedby the surface straining. Plane edge cracks, nucleating from surfaceirregularities, are considered. The cracks obtain realistic geometrical shapeswhere the near-tip region is an integral part of the crack surface. Elastic-perfectlyplastic materials are considered and a low-cycle fatigue load is assumed. Theproblem is solved using a FEM based program and procedures for movingboundary tracking and interior re-meshing. A crucial ingredient of the boundarytracking is the evolved surface re-meshing, where a scheme based on length andcurvature constraints is utilised. The work studies how the choice of theseconstraints influences the results for crack surface evolution. It is shown thatcharacteristic length parameters in crack nucleation and short crack growthdepend on the choice of the constraints. It is concluded that an additionalphysical process operating at the surface has to be accounted for in order todescribe the length scales observed in reality.
|
|
| 6. |
|
|
| 7. |
|
|
| 8. |
|
|
| 9. |
- Jivkov, Andrey, et al.
(författare)
-
Corrosion crack growth in a bi-material system
- 2003
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Bi-materials composed of thin layers ideally bonded to large substrates are considered. Cracks emerging from an almost flat surface and propagating through the bi-materials are studied. The cracks acquire realistic geometrical shapes, where the tips are integral parts of the crack surfaces. Crack propagation is related to surface evolution resulting from material loss due to corrosion. Controlling mechanism for the evolution is the rupture of a brittle passive film, which is frequently building-up along the surface. The evolution rate is a function of the degree of film damage caused by the surface straining. The model leads to a moving boundary formulation, for which a numerical solution is used. The mismatch of the material plastic properties is being varied in the study. The results show how cracks pass the interface. The growth rate variation close to the interface is studied. Typical surface evolution for a crack passing through a soft-hard material interface is presented. The resulting crack morphology of the model resembles what has been observed in reality. It is shown how the results can be used in designing bi-material systems to inhibit corrosion crack growth.
|
|
| 10. |
|
|
| 11. |
|
|
| 12. |
- Jivkov, Andrey
(författare)
-
Evolution of fatigue crack corrosion from surface irregularities
- 2003
-
Ingår i: Theoretical and applied fracture mechanics (Print). - 0167-8442 .- 1872-7638. ; 40:1, s. 45-54
-
Tidskriftsartikel (refereegranskat)abstract
- A moving boundary model is presented for crack nucleation and growth from surface flaws. It concerns with chemical attack that results in material dissolution. A controlling mechanism for evolution is the rupture of a brittle corrosion-protective film that is built up along the corroding surface. The evolution rate is a function of the degree of protective film damage caused by the surface straining. The problem is formulated for an elastic body containing a single and double pits. Low-frequency cyclic loading is considered. Numerical solution is proposed. The behaviours of a growing crack and of two competing cracks are described. Stages of incubation, blunting and steady-state growth characterise a single crack evolution. The steady-state growth rate is found independent of the initial geometry. Stages of independent growth, interactive growth and arrest of one crack characterise the evolution of two competing cracks. The lengths of the arrested cracks are presented as functions of the ratio between the pit depth for a series of different distances between the pits. It is emphasized that the solutions correspond to a homogeneous material. Further work is required to account for the material microstructure.
|
|
| 13. |
- Jivkov, Andrey
(författare)
-
Fatigue corrosion crack extension across the interface of an elastic bi-materia
- 2004
-
Ingår i: Engineering Fracture Mechanics. - 0013-7944 .- 1873-7315. ; 71:7, s. 1139-1153
-
Tidskriftsartikel (refereegranskat)abstract
- In this work crack propagation in a bi-material composed of a thin elastic layer ideally bonded to a large elastic substrate is studied. A flaw is assumed existing on the surface of the layer. Cracks nucleate from the flaw and propagate through the bi-material. The cracks have realistic geometrical shapes, where the crack tip is an integral part of the crack surface. Thus the crack propagation is associated with a crack surface evolution. Material loss due to corrosion of the crack surface is the physical ground for the evolution. A controlling mechanism for the surface advancement is the rupture of a brittle corrosion-protective film, which is continually building-up along the corroding surface. The rate of surface evolution is a function of the degree of protective film damage, caused by the surface straining. This leads to a moving boundary formulation, for which a numerical solution is proposed. Fatigue loading is considered as a suitable way to maintain crack evolution at a constant peak load level. Under the assumed model, the cracks always pass the interface. The elastic mismatch is shown to influence the growth rate variation around the interface. Crack extensions are presented as functions of the elastic mismatch and as functions of the initial flaw size. It is shown how the results can be used in designing bi-material systems. A typical morphology evolution of a crack passing through an interface with a weak-stiff transition is presented. An example of fatigue corrosion fracture is offered, which shows that the crack morphology of the model resembles the one observed in reality. It is concluded that the realistic crack geometry is an effective concept and the moving boundary formulation could be a very successful tool for simulating realistic crack propagation.
|
|
| 14. |
|
|
| 15. |
|
|
| 16. |
|
|
| 17. |
|
|
| 18. |
|
|
| 19. |
|
|
| 20. |
|
|
| 21. |
|
|
| 22. |
- Jivkov, Andrey P.
(författare)
-
On crack growth in functionally graded materials
- 1999
-
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.
|
|
| 23. |
- Jivkov, Andrey P
(författare)
-
Strain-assisted corrosion cracking and growth rate inhibitors
- 2002
-
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.
|
|
| 24. |
|
|
| 25. |
- Jivkov, Andrey, et al.
(författare)
-
Strain-driven corrosion crack growth : A pilot study of intergranular stress corrosion cracking
- 2002
-
Ingår i: Engineering Fracture Mechanics. - 0013-7944 .- 1873-7315. ; 69:18, s. 2095-2111
-
Tidskriftsartikel (refereegranskat)abstract
- This work proposes a model for corrosion driven crack growth. The model poses a moving boundary problem, where a chemical attack removes material from the body. The rate of the chemical attack is a function of the strain along the body surface. No crack growth criterion is needed for the analysis. A finite strain formulation is used and the material model is assumed hyperelastic. The problem is stated for a large body, containing a large crack. A low frequency cyclic loading is considered. Thus, corrosion is assumed to dissolve material with a rate approximately proportional to the strain rate. The problem is solved using finite element method based program, enhanced with a procedure handling the moving boundary. Parametric studies are performed for a series of different initial shapes of the near-tip region. Presented results show that the crack growth rate is largely dependent on the initial crack geometry. For a set of initial shapes and load levels steady-state conditions of growth are achieved, while for the others the cracks show tendency to branch.
|
|
| 26. |
- Jivkov, Andrey
(författare)
-
Surface irregularities as sources for corrosion fatigue
- 2003
-
Ingår i: Mesomechanics of computation and design of use-specific materials: simulation and fabrication of advanced materials with mesoscopic structures. ; , s. 184-191
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Corrosion fatigue crack nucleation from surface irregularity is modelled as a moving boundary value problem. The model is based on material dissolution proportional to the surface stretch. Dissolution and repassivation processes are forming the geometry of the crack tip, thus creating conditions for strain concentration. No crack growth criterion is used. The interaction between the electrochemical processes and the deformation of the crack tip region is incorporated in continuum mechanical theory. Elastic-perfectly plastic materials under low frequency cyclic load are considered. The model simulates how cracks form and grow in a single continuous process. The resulting natural variation of lengths of the formed cracks makes them grow with different rates. One crack after another falls into a wake behind a larger crack and the crack tip load of the smaller decreases leading to its arrest.
|
|
| 27. |
|
|
| 28. |
- Ståhle, Per, et al.
(författare)
-
A model for calculation of stress corrosion crack growth
- 2004
-
Ingår i: Configurational mechanics.
-
Konferensbidrag (refereegranskat)abstract
- As much as 25% of all accidents in process industry reported to the Swedish Plant Inspectorate are caused by stress corrosion crack growth. The situation is believed to be similar in the all industrialised countries. It contributes to the severity of the accidents that they often occurs unexpectedly and at loads that may be far below what normally causes crack growth Experts in the fields of metallurgy, corrosion have treated stress corrosion using mechanical models based on elastic or elastic plastic stress fields where the crack tip is treated as a point. In view of the near tip load distribution this leads to paradoxic results. In the present model corrosion is forming the geometry of the crack tip and is thus itself creating the conditions for strain concentration. We incorporate an interaction between electro-chemical processes and the deformation of the crack tip region in a fracture mechanical theory. The model is based on material dissolution simply being proportional to the surface stretch. No crack growth criteria is used. Computation of the mechanical state is based on a finite element formulation for large strains. The formation of a crack from a surface depression via a pit is studied. Low frequency cyclic load is considered. At the end of a load cycle a metal oxide compound is growing on the crack surface. We assume that there is sufficient time for the chemical process to form a protective film that fully covers the crack surface. This temporarily interrupts the corrosion process. During the application of next load cycle the stretch of the surface breaks the protective film. This creates gaps in the film, which allow dissolution of the underlaying metal. The chemical environment of the crack tip is assumed to be constant and unaffected by the changing geometry as the crack is developing. We assume that there is a linear relationship between strain and corrosion rate, in the sense of removed material per unit of area during each load cycle. The model simulates how dissolution lead to surface roughness, how pits form and grow to become cracks in one continuous process. The resulting natural variation of lengths of the formed cracks causes the cracks to grow with different speeds. During continuation one crack after the other falls into a wake behind a larger crack. Thus, crack tip load of the smaller decreases and finally causes crack arrest: At the end of the simulation only one growing crack remains. The results are compared with experimental observations.
|
|
| 29. |
|
|
| 30. |
- Ståhle, Per, et al.
(författare)
-
On dissolution driven crack growth
- 2007
-
Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683 .- 1879-2146. ; 44:6, s. 1880-1890
-
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.
|
|
| 31. |
- Ståhle, Per, et al.
(författare)
-
Selfsimilar solutions for stress driven material dissolution
- 2004
-
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.
|
|
