| 1. |
- Andersson, Lars-Erik, et al.
(författare)
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Existence and uniqueness of attractors in frictional systems with uncoupled tangential displacements and normal tractions
- 2014
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Ingår i: International Journal of Solids and Structures. - : Elsevier. - 0020-7683 .- 1879-2146. ; 51:21-22, s. 3710-3714
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Tidskriftsartikel (refereegranskat)abstract
- We consider the class of two or three-dimensional discrete contact problems in which a set of contact nodes can make frictional contact with a corresponding set of rigid obstacles. Such a system might result from a finite element discretization of an elastic contact problem after the application of standard static reduction operations. The Coulomb friction law requires that the tractions at any point on the contact boundary must lie within or on the surface of a friction cone, but the exact position of any stuck node (i.e., a node where the tractions are strictly within the cone) depends on the initial conditions and/or the previous history of loading. If the long-term loading is periodic in time, we anticipate that the system will eventually approach a steady periodic cycle. Here we prove that if the elastic system is uncoupled, meaning that changes in slip displacements alone have no effect on the instantaneous normal contact reactions, the time-varying terms in this steady cycle are independent of initial conditions. In particular, we establish the existence of a unique permanent stick zone T comprising the set of all nodes that do not slip after some finite number of cycles. We also prove that the tractions and slip velocities at all nodes not contained in T approach unique periodic functions of time, whereas the (time-invariant) slip displacements in T may depend on initial conditions. Typical examples of uncoupled systems include those where the contact surface is a plane of symmetry, or where the contacting bodies can be approximated locally as half spaces and Dundurs mismatch parameter beta = 0. An important consequence of these results is that systems of this kind will exhibit damping characteristics that are independent of initial conditions. Also, the energy dissipated at each slipping node in the steady state is independent of initial conditions, so wear patterns and the incidence of fretting fatigue failure should also be so independent.
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| 2. |
- Barsoum, Imad, et al.
(författare)
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Micromechanical analysis on the influence of the Lode parameter on void growth and coalescence
- 2011
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683 .- 1879-2146. ; 48:6, s. 925-938
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Tidskriftsartikel (refereegranskat)abstract
- A micromechanical model consisting of a band with a square array of equally sized cells, with a spherical void located in each cell, is developed. The band is allowed a certain inclination and the periodic arrangement of the cells allow the study of a single unit cell for which fully periodic boundary conditions are applied. The model is based on the theoretical framework of plastic localization and is in essence the micromechanical model by Barsoum and Faleskog (Barsoum, I., Faleskog, J., 2007. Rupture mechanisms in combined tension and shear-micromechanics. International Journal of Solids and Structures 44(17), 5481-5498) with the extension accounting for the band orientation. The effect of band inclination is significant on the strain to localization and cannot be disregarded. The macroscopic stress state is characterized by the stress triaxiality and the Lode parameter. The model is used to investigate the influence of the stress state on void growth and coalescence. It is found that the Lode parameter exerts a strong influence on the void shape evolution and void growth rate as well as the localized deformation behavior. At high stress triaxiality level the influence of the Lode parameter is not as marked and the overall ductility is set by the stress triaxiality. For a dominating shear stress state localization into a band cannot be regarded as a void coalescence criterion predicting material failure. A coalescence criterion operative at dominating shear stress state is needed.
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| 3. |
- Edvardsson, Sverker, et al.
(författare)
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On dissipative effects of paper web adhesion strength
- 2011
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683 .- 1879-2146. ; 48:1, s. 24-30
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Tidskriftsartikel (refereegranskat)abstract
- This work is concerned with the adhesion strength between a paper web and a metal roll surface, which is a common situation in paper machines world-wide. It is shown that the classic expression relating the work of adhesion to the peeling angle and web tension is, in general, insufficient. An improved model is suggested to take into account the energy dissipation due to elastic-plastic deformation behavior of wet paper materials. To judge the model, an industrially relevant example of wet newsprint and a mild steel surface is studied. It is found that the agreement between theory and experimental observations is excellent. A key result is that elastic-plastic material behavior must always be included for wet paper materials in peeling processes.
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| 4. |
- Faleskog, Jonas, et al.
(författare)
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Tension-torsion fracture experiments-Part I : Experiments and a procedure to evaluate the equivalent plastic strain
- 2013
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683 .- 1879-2146. ; 50:25-26, s. 4241-4257
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Tidskriftsartikel (refereegranskat)abstract
- Ductile failure experiments on a double notched tube (DNT) specimen subjected to a combination of ten-sue load and torque that was applied at a fixed ratio is presented. The experimental results extend those in Barsoum and Faleskog (2007a) down to zero stress triaxiality. A new and robust evaluation procedure for such tests is proposed, and a simple relation for the equivalent plastic strain at failure for combined normal and shear deformation, respectively, is developed. Tests were carried out on the medium strength medium hardening steel Weldox 420, and the high strength low hardening steel Weldox 960. The experimental results unanimously show that ductile failure not only depends on stress triaxiality, but is also strongly affected by the type of deviatoric stress state that prevails, which can be quantified by a stress invariant that discriminates between axisymmetric stressing and shear dominated stressing, e.g., the Lode parameter. Additional experiments on round notch bar (RNB) specimens are recapitulated in order to give a comprehensive account on how ductile failure depends on stress triaxiality, ranging from zero to more than 1.6, and the type of stress state for the two materials tested. This provides an extensive experimental data base that will be used to explore an extension of the Gurson model that incorporates damage development in shear presented in Xue et al.
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| 5. |
- Hallbäck, Nils, et al.
(författare)
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Development of a distributed dislocation dipole technique for the analysis of multiple straight, kinked and branched cracks in an elastic half-plane
- 2014
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Ingår i: International Journal of Solids and Structures. - : Elsevier. - 0020-7683 .- 1879-2146. ; 51, s. 2878-2892
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Tidskriftsartikel (refereegranskat)abstract
- A distributed dislocation dipole technique for the analysis of multiple straight, kinked and branched cracks in an elastic half plane has been developed. The dipole density distribution is represented with a weighted Jacobi polynomial expansion where the weight function captures the asymptotic behaviour at each end of the crack. To allow for opening and sliding at crack kinking and branching the dipole density representation contains conditional extra terms which fulfil the asymptotic behaviour at each endpoint. Several test cases involving straight, kinked and branched cracks have been analysed, and the results suggest that the accuracy of the method is within 1% provided that Jacobi polynomial expansions up to at least the sixth order are used. Adopting even higher order Jacobi polynomials yields improved accuracy. The method is compared to a simplified procedure suggested in the literature where stress singularities associated with corners at kinking or branching are neglected in the representation for the dipole density distribution. The comparison suggests that both procedures work, but that the current procedure is superior, in as much as the same accuracy is reached using substantially lower order polynomial expansions.
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| 6. |
- Hejman, Ulf, et al.
(författare)
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Environmentally assisted initiation and growth of multiple surface cracks
- 2010
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Ingår i: International Journal of Solids and Structures. - : Elsevier. - 0020-7683 .- 1879-2146. ; 47:14-15, s. 1838-1846
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Tidskriftsartikel (refereegranskat)abstract
- The initial stages of stress corrosion on an amorphous polymer is investigated. This is done by exposing stressed specimens of polycarbonate to an acetone and water solution. The surface develops two distinct features of degradation that appear on different length scales when subjected to tensile stress. Small pits form on the surface and make it rough. These pits are in the order of micrometers, and are found to be randomly distributed. They occur even without load and seem to slightly increase in number with increasing stress. In the millimeter domain, visible to the bare eye, surface cracks are formed transverse to the direction of loading. The occurrence of cracks is seen to have a positive stress threshold value, exceeding which, a linear increase of number of cracks with stress is found. The manners in which the cracks grow and coalesce on the surface are examined. It is seen that they do not meet crack tip to crack tip. Instead, they avoid each other initially and coalesce crack tip to crack side. The results are discussed in the light of mechanical considerations. A stress analysis for a few configurations of meeting cracks supports the experimental observations. With assumptions of stress corrosion crack growth and coalescence, a simulation of cracks growing from randomly distributed initiation sites is performed. Similar crack patterns as obtained in the experiments are found.
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| 7. |
- Isaksson, Per, et al.
(författare)
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Crack growth in planar elastic fiber materials
- 2012
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683 .- 1879-2146. ; 49:13, s. 1900-1907
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Tidskriftsartikel (refereegranskat)abstract
- Particularly attention is here given to crack growth in opening mode in fiber networks. Low- and high-density cellulose fiber materials are used in synchrotron X-ray microtomography tensile experiments to illustrate phenomena arising during crack growth. To capture the observed fundamental mechanisms, significantly different from classical continua, a mechanical model based on a strong nonlocal theory is applied in which an intrinsic length reflects a characteristic length of the microstructure. Nonlocal stress and strain tensor fields are estimated by analytical solutions on closed form to a modified inhomogeneous Helmholtz equation using LEFM crack-tip fields as source terms. Justified by experimental observations, physical requirements of finite stresses and strains at infinity and at the tip are applied to remove singularities. The near-tip nonlocal hoop stress field is used to estimate crack growth directions and sizes of fracture process zones. Experimental observations are shown to be qualitatively well in accordance with numerical predictions, which justifies the adopted approach.
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| 8. |
- Josefsson, Gabriella, et al.
(författare)
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Stiffness contribution of cellulose nanofibrils to composite materials
- 2014
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683 .- 1879-2146. ; 51:5, s. 945-953
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Tidskriftsartikel (refereegranskat)abstract
- Nanocomposites, reinforced by different types of cellulose fibrils, have gained increased interest the last years due to the promising mechanical properties. There is a lack of knowledge about the mechanical properties of the cellulose fibrils, and their contribution to the often claimed potential of the impressive mechanical performance of the nanocomposites. This paper investigates the contribution from different types of cellulose nanofibril to the overall elastic properties of composites. A multiscale model is proposed, that allows back-calculation of the elastic properties of the fibril from the macroscopic elastic properties of the composites. The different types of fibrils used were nanofibrillated cellulose from wood, bacterial cellulose nano-whiskers and microcrystalline cellulose. Based on the overall properties of the composite with an unaged polylactide matrix, the effective longitudinal Young's modulus of the fibrils was estimated to 65 GPa for the nanofibrillated cellulose, 61 GPa for the nano whiskers and only 38 GPa for the microcrystalline cellulose. The ranking and absolute values are in accordance with other studies on nanoscale morphology and stiffness estimates. Electron microscopy revealed that in the melt-processed cellulose nanofibril reinforced thermoplastics, the fibrils tended to agglomerate and form micrometer scale platelets, effectively forming a microcomposite and not a nanocomposite. This dispersion effect has to be addressed when developing models describing the structure-property relations for cellulose nanofibril composites.
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| 9. |
- Kroon, Martin
(författare)
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Asymptotic mechanical fields at the tip of a mode I crack in rubber-like solids
- 2014
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683 .- 1879-2146. ; 51:10, s. 1923-1930
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Tidskriftsartikel (refereegranskat)abstract
- Asymptotic analyses of the mechanical fields in front of stationary and propagating cracks facilitate the understanding of the mechanical and physical state in front of crack tips, and they enable prediction of crack growth and failure. Furthermore, efficient modelling of arbitrary crack growth by use of XFEM (extended finite element method) requires accurate knowledge of the asymptotic crack tip fields. In the present work, we perform an asymptotic analysis of the mechanical fields in the vicinity of a propagating mode I crack in rubber. Plane deformation is assumed, and the material model is based on the Langevin function, which accounts for the finite extensibility of polymer chains. The Langevin function is approximated by a polynomial, and only the term of the highest order contributes to the asymptotic solution. The crack is predicted to adopt a wedge-like shape, i.e. the crack faces will be straight lines. The angle of the wedge and the order of the stress singularity depend on the hardening of the strain energy function. The present analysis shows that in materials with a significant hardening, the inertia term in the equations of motion becomes negligible in the asymptotic analysis. Hence, there is no upper theoretical limit to the crack speed.
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| 10. |
- Kroon, Martin
(författare)
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Energy release rates in rubber during dynamic crack propagation
- 2014
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Ingår i: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683 .- 1879-2146. ; 51:25-26, s. 4419-4426
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Tidskriftsartikel (refereegranskat)abstract
- The theoretical understanding of the fracture mechanics of rubber is not as well developed as for other engineering materials, such as metals. The present study is intended to further the understanding of the dissipative processes that take place in rubber in the vicinity of a propagating crack tip. This dissipation contributes significantly to the total fracture toughness of the rubber and is therefore of great interest from a fracture mechanics point of view. To study this, a computational framework for analysing high-speed crack growth in a biaxially stretched rubber under plane stress is therefore formulated. The main purpose is to investigate the energy release rates required for crack propagation under different modes of biaxial stretching. The results show, that inertia comes into play when the crack speed exceeds about 50 m/s. The total work of fracture by far exceeds the surface energy consumed at the very crack tip, and the difference must be attributed to dissipative damage processes in the vicinity of the crack tip. The size of this damage/dissipation zone is expected to be a few millimetres.
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