| 1. |
- Eriksson, Kjell
(författare)
-
A domain independent integral expression for the crack extension force of a curved crack in three dimensions
- 2002
-
Ingår i: Journal of the mechanics and physics of solids. - 0022-5096 .- 1873-4782. ; 50:2, s. 381-403
-
Tidskriftsartikel (refereegranskat)abstract
- An integral expression that is domain independent in curvilinear coordinates and compatible with zero divergence of Eshelby's (Phil. Trans. Roy. Soc. (London) 244 (1951) 87.) energy momentum tensor was obtained from the principle of virtual work. By applying Eshelby's definition of the force on a material defect a general expression of the crack extension force for a curved crack in three dimensions, here called the F-integral, was derived from the domain independent integral expression. The F-integral is given explicitly for a number of curved cracks and found to be in agreement with previously known solutions, when available. The influence of crack surface and crack front curvature upon the various forms of the F-integral is discussed. The F-integral presented in this work is a generalisation of the J-integral (Rice, J. Appl. Mech. 35 (1968) 379.) to curved cracks in orthogonal curvilinear coordinates.
|
|
| 2. |
- Gudmundson, Peter
(författare)
-
Acoustic emission and dynamic energy release rate for steady growth of a tunneling crack in a plate in tension
- 1999
-
Ingår i: Journal of the mechanics and physics of solids. - 0022-5096 .- 1873-4782. ; 47:10, s. 2057-2074
-
Tidskriftsartikel (refereegranskat)abstract
- The dynamic steady state growth of tunneling cracks in membrane loaded isotropic Kirchhoff plates is considered. Explicit solutions for the asymptotic displacement and velocity fields are presented. It is shown that the asymptotic fields are inversely proportional to the square root of distance from the crack tip, and that a wake may or may not develop behind the crack tip depending on the static membrane state. If the crack tip velocity is smaller than a certain critical velocity, the asymptotic solution will completely vanish. An explicit solution for the dynamic energy release rate is also presented. Due to elastic waves radiated from the crack tip, the dynamic energy release rate will generally be smaller than the corresponding static energy release rate.
|
|
| 3. |
- Gudmundson, Peter
(författare)
-
Anisotropic microcrack nucleation in brittle materials
- 1990
-
Ingår i: Journal of the mechanics and physics of solids. - 0022-5096 .- 1873-4782. ; 38:4, s. 531-551
-
Tidskriftsartikel (refereegranskat)abstract
- A constitutive model for anisotropic microcracking in brittle materials is developed. The model is based on a stress controlled microcrack nucleation criterion, which can vary in a random way between different microcracks. The effects of microcrack closure and a random distribution of residual stresses are included in the analysis. The resultant inelastic strains are determined using a standard homogenization technique Numerical results are presented for three simple loading cases : pure tension, biaxial tension and triaxial tension. Crack tip shielding resulting from microcrack nucleation is also analysed, and numerical results of are presented for two different microcrack nucleation criteria.
|
|
| 4. |
- Gudmundson, Peter
(författare)
-
Eigenfrequency changes of structures due to cracks, notches or other geometrical changes
- 1982
-
Ingår i: Journal of the mechanics and physics of solids. - : Elsevier BV. - 0022-5096 .- 1873-4782. ; 30:5, s. 339-353
-
Tidskriftsartikel (refereegranskat)abstract
- A first order perturbation method is presented which predicts the changes in resonance frequencies of a structure resulting from cracks, notches or other geometrical changes. The eigenfrequency changes due to a crack are shown to be dependent on the strain energy of a static solution which is easily obtainable for small cracks and other small cut-outs. The method has been tested for three different cases, and the predicted results correlate very closely to experimental and numerical results.
|
|
| 5. |
- Gudmundson, Peter
(författare)
-
The dynamic behaviour of slender structures with cross-sectional cracks
- 1983
-
Ingår i: Journal of the mechanics and physics of solids. - : Elsevier BV. - 0022-5096 .- 1873-4782. ; 31:4, s. 329-345
-
Tidskriftsartikel (refereegranskat)abstract
- A dynamic model for beams with cross-sectional cracks is discussed. It is shown that a crack can be represented by a consistent, static flexibility matrix. Two different methods for the determination of the flexibility matrix are discussed. If the static stress intensity factors are known, the flexibility matrix can be determined from an integration of these stress intensity factors. Alternatively, static finite element calculations can be used for the determination of the flexibility matrix. Both methods are demonstrated in the present paper. The mathematical model was applied to an edge-cracked cantilevered beam and the eigenfrequencies were determined for different crack lengths and crack positions. These results were compared to experimentally obtained eigenfrequencies. In the experiments, the cracks were modelled by sawing cuts. The theoretical results were, for all crack lengths, in excellent agreement with the experimental data. The dynamic stress intensity factor for a longitudinally vibrating, centrally cracked bar was determined as well. The results compared very well with dynamic finite element calculations. The crack closure effect was experimentally investigated for an edge-cracked beam with a fatigue crack. It was found that the eigenfrequencies decreased, as functions of crack length, at a much slower rate than in the case of an open crack.
|
|
| 6. |
- Storåkers, Bertil, et al.
(författare)
-
On Brinell and Boussinesq indentation of creeping solids
- 1994
-
Ingår i: Journal of the mechanics and physics of solids. - : Elsevier BV. - 0022-5096 .- 1873-4782. ; 42:2, s. 307-332
-
Tidskriftsartikel (refereegranskat)abstract
- As an alternative to traditional tensile testing of materials subjected to creep, indentation testing is examined. Axisymmetric punches of shapes defined by smooth homogeneous functions are analysed in general at power law behaviour both from a theoretical and a computational point of view. It is first shown that by correspondence to nonlinear elasticity and self-similarity the problem to determine time-dependent properties admits reduction to a stationary one. Specifically it is proved that the creep rate problem posed depends only on the resulting contact area but not on specific punch profiles. As a consequence the relation between indentation depth and contact area is history independent. So interpreted, the solution for a flat circular cylinder (Boussinesq) is not only of intrinsic interest but serves as a reference solution to generate results for various punch profiles. This is conveniently carried out by cumulative superposition and in particular ball indentation (Brinell) is analysed in depth. A carefully designed finite element procedure based on a mixed variational principle is used to provide a variety of explicit results of high accuracy pertaining to stress and deformation fields. Universal relations for hardness at creep are proposed for Boussinesq and Brinell indentation in analogy with the celebrated formula by Tabor for indentation of strain-hardening plastic materials. Quantitative comparison is made with a diversity of experimental data attained by earlier writers and the relative merits of indentation strategies are discussed.
|
|
| 7. |
- Varias, A G, et al.
(författare)
-
Hydride-induced embrittlement and fracture in metals - effects of stress and temperature distribution
- 2002
-
Ingår i: Journal of the mechanics and physics of solids. - : Elsevier Science Ltd.. - 0022-5096 .- 1873-4782. ; 50:7, s. 1469-1510
-
Tidskriftsartikel (refereegranskat)abstract
- A mathematical model for the hydrogen embrittlement of hydride forming metals has been developed. The model takes into account the coupling of the operating physical processes, namely: (i) hydrogen diffusion, (ii) hydride precipitation, (iii) non-mechanical energy flow and (iv) hydride/solid-solution deformation. Material damage and crack growth are also simulated by using de-cohesion model, which takes into account the time variation of energy of de-cohesion, due to the time-dependent process of hydride precipitation. The bulk of the material, outside the de-cohesion layer, is assumed to behave elastically. The hydrogen embrittlement model has been implemented numerically into a finite element framework and tested successfully against experimental data and analytical solutions on hydrogen thermal transport (in: Wunderlich, W. (Ed.), Proceedings of the European Conference on Computational Mechanics, Munich, Germany, 1999, J. Nucl. Mater. (2000a) 279 (2–3) 273). The model has been used for the simulation of Zircaloy-2 hydrogen embrittlement and delayed hydride cracking initiation in (i) a boundary layer problem of a semi-infinite crack, under mode I loading and constant temperature, and (ii) a cracked plate, under tensile stress and temperature gradient. The initial and boundary conditions in case (ii) are those encountered in the fuel cladding of light water reactors, during operation. The effects of near-tip stress intensification as well as of temperature gradient on hydride precipitation and material damage have been studied. The numerical simulation predicts hydride precipitation at a small distance from the crack-tip. When the remote loading is sufficient, the near-tip hydrides fracture. Thus a microcrack is generated, which is separated from the main crack by a ductile ligament, in agreement with experimental observations
|
|
| 8. |
- Wikström, Adam, et al.
(författare)
-
Thermoelastic analysis of periodic thin lines deposited on a substrate
- 1999
-
Ingår i: Journal of the mechanics and physics of solids. - 0022-5096 .- 1873-4782. ; 47:5, s. 1113-1130
-
Tidskriftsartikel (refereegranskat)abstract
- Thermoelastic stresses and curvatures arising from patterned thin lines on initially flat isotropic substrates are analyzed. A connection is made between substrates with patterned lines and laminated anisotropic composites containing transverse matrix cracks. Using this analogy along with anisotropic plate theories, approximate analytical expressions are derived for volume-averaged stresses as well as curvatures along and normal to the lines, for any thickness, width and spacing of the lines. The predictions of the analysis are shown to compare favorably with finite element simulations of stresses and curvatures for Si substrates with Al, Cu or SiO2 lines. The predictions also match prior experimental measurements of curvatures along and normal to patterned SiO2 lines on Si wafers, and further capture the general experimental trends reported previously for curvature evolutions in Si wafers with Al lines. The model presented here thus provides a very convenient and simple analytical tool for extracting stresses in thin lines on substrates from a knowledge of experimentally determined film stress, thereby circumventing the need for detailed computations for a wide range of unpassivated line geo metries of interest in microelectronic applications.
|
|
| 9. |
- Alastrue, V, et al.
(författare)
-
Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling
- 2009
-
Ingår i: Journal of the Mechanics and Physics of Solids. - : Elsevier BV. - 1873-4782 .- 0022-5096. ; 57:1, s. 178-203
-
Tidskriftsartikel (refereegranskat)abstract
- A fully three-dimensional anisotropic elastic model for vascular tissue modelling is here presented. The underlying strain energy density function is assumed to additively decouple into volumetric and deviatoric contributions. A straightforward isotropic neo-Hooke-type law is used to model the deviatoric response of the ground substance, whereas a micro-structurally or rather micro-sphere-based approach will be employed to model the contribution and distribution of fibres within the biological tissue of interest. Anisotropy was introduced by means of the use of von Mises orientation distribution functions. Two different micro-mechanical approaches -- a, say phenomenological, exponential ansatz and a worm-like-chain-based formulation -- are applied to the micro-fibres and illustratively compared. The passage from micro-structural contributions to the macroscopic response is obtained by a computational homogenisation scheme, namely numerical integration over the surface of the individual micro-spheres. The algorithmic treatment of this integration is discussed in detail for the anisotropic problem at hand, so that several cubatures of the micro-sphere are tested in order to optimise the accuracy at reasonable computational cost. Moreover, the introduced material parameters are identified from simple tension tests on human coronary arterial tissue for the two micro-mechanical models investigated. Both approaches are able to recapture the experimental data. Based on the identified sets of parameters, we first discuss a homogeneous deformation in simple shear to evaluate the models' response at the micro-structural level. Later on, an artery-like two-layered tube subjected to internal pressure is simulated by making use of a non-linear finite element setting. This enables to obtain the micro- and macroscopic responses in an inhomogeneous deformation problem, namely a blood-vessel-representative boundary value problem. The effect of residual stresses is additionally included in the model by means of a multiplicative decomposition of the deformation gradient tensor which turns out to crucially affect the simulation results.
|
|
| 10. |
- Almqvist, Andreas, et al.
(författare)
-
Interfacial separation between elastic solids with randomly rough surfaces : Comparison between theory and numerical techniques
- 2011
-
Ingår i: Journal of the mechanics and physics of solids. - : Elsevier BV. - 0022-5096 .- 1873-4782. ; 59:11, s. 2355-2369
-
Tidskriftsartikel (refereegranskat)abstract
- We study the distribution of interfacial separations at the contact region between two elastic solids with randomly rough surfaces. An analytical expression is derived for the distribution of interfacial separations using Persson's theory of contact mechanics, and is compared to numerical solutions obtained using (a) a half-space method based on the Boussinesq equation, (b) a Green's function molecular dynamics technique and (c) smart-block classical molecular dynamics. Overall, we find good agreement between all the different approaches.
|
|
