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- Elaguine, Denis, et al.
(författare)
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Hertzian fracture at unloading
- 2006
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Ingår i: Journal of the mechanics and physics of solids. - : Elsevier BV. - 0022-5096 .- 1873-4782. ; 54:11, s. 2453-2473
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Tidskriftsartikel (refereegranskat)abstract
- Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally. Initiation of cone cracks has been observed and failure loads together with contact and fracture radii determined at monotonically increasing load but also during unloading phases. Contact of dissimilar elastic solids under decreasing load may cause crack inception triggered by finite interface friction and accordingly the coefficient of friction was determined by two different methods. In order to make relevant predictions of experimental findings, a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. It was found that at continued loading it is possible to specify in advance how the contact domain divides into invariant regions of stick and slip. The maximum tensile stress was found to occur at the free surface just outside the contact contour, the relative distance depending on the different elastic compliance properties and the coefficient of friction. In contrast, at unloading invariance properties are lost and stick/slip regions proved to be severely history dependant and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. Predictions of loads to cause crack initiation during full cycles were made based on a critical stress fracture criterion and proved to be favourable as compared to the experimental results.
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| 2. |
- Jelagin, Denis, 1979-
(författare)
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Frictional Effects on Hertzian Contact and Fracture
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis addresses normal axisymmetric contact of dissimilar elastic solids at finite interfacial friction. It is shown that in the case of smooth and convex but otherwise arbitrary contact profiles and monotonically increasing loading a single stick-slip contour evolves being independent of loading and profile geometry. This allows developing an incremental procedure based on a reduced problem corresponding to frictional rigid flat punch indentation of an elastic half-space. The reduced problem, being independent of loading and contact region, was solved by a finite element method based on a stationary contact contour and characterized by high accuracy. Subsequently, a tailored cumulative superposition procedure was developed to resolve the original problem to determine global and local field values for two practically important geometries: flat and conical profiles with rounded edges and apices. Results are given for relations between force, depth and contact contours together with surface stress distributions and maximum von Mises effective stress, in particular to predict initiation of fracture and plastic flow. It is also observed that the presence of friction radically reduces the magnitude of the maximum surface tensile stress, thus retarding brittle fracture initiation.Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally for a full load cycle. It has been observed that if the specimen survived during loading to a maximum level it frequently failed at decreasing load. It has been proposed by Johnson et al. (1973) that the underlying physical cause of Hertzian fracture initiation during load removal is that at unloading frictional tractions reverse their sign over part of the contact region. Guided by these considerations a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. In contrast to the situation at monotonically increasing loading, at unloading invariance properties are lost and stick-slip regions proved to be severely history dependent and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. It is shown that the experimental observations concerning Hertzian fracture initiation at unloading are at least in qualitative correlation with the effect friction has on the maximum surface tensile stress.A contact cycle between two dissimilar elastic bodies at finite Coulomb friction has been further investigated analytically and numerically for a wider range of material parameters and contact geometries. With the issue of Hertzian fracture initiation in mind, results concerning the influence of the friction coefficient and compliance parameters on the absolute maximum surface tensile stress during a frictional contact cycle are reported along with the magnitudes of the relative increase of maximum tensile stresses at unloading. Based on a critical stress fracture criterion it is discussed how the predicted increases will influence the critical loads required for crack initiation.Fracture loads are measured with steel and tungsten carbide spherical indenters in contact with float glass specimens at monotonically increasing loading and during a load cycle. Computational predictions concerning the fracture loads are given based on Hertz and frictional contact theories combined with a critical stress fracture criterion. The computational results obtained for frictional contact are shown to be in better agreement with experimental findings as compared to the predictions based on the Hertz theory. The remaining quantitative discrepancy was attributed to the well-known fact that a Hertzian macro-crack initiates from pre-existing defects on the specimen’s surface. In order to account for the influence of the random distribution of these defects on the fracture loads at monotonic loading, Weibull statistics was introduced. The predicted critical loads corresponding to 50% failure probability were found to be in close agreement with experimentally observed ones.
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| 3. |
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| 4. |
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| 5. |
- Skrinjar, Olle, et al.
(författare)
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Local contact compliance relations at compaction of composite powders
- 2007
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Ingår i: Journal of applied mechanics. - : ASME International. - 0021-8936 .- 1528-9036. ; 74:1, s. 164-168
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Tidskriftsartikel (refereegranskat)abstract
- Local contact behavior of composite powders has been investigated by using the finite element method. In previous analyses of such problems it has in general been assumed that one of the powder materials is rigid while the other deforms at loading as in such a case self-similarity prevails. This is a very good approximation for ceramic/metallic composites but may not be so when the composite consists of two materials of roughly equal hardness. An approximate compliance formula for describing this feature is proposed showing good agreement with corresponding finite element results for representative cases.
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| 6. |
- Storåkers, Bertil, et al.
(författare)
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On Brinell and Boussinesq indentation of creeping solids
- 1994
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Ingår i: Journal of the mechanics and physics of solids. - : Elsevier BV. - 0022-5096 .- 1873-4782. ; 42:2, s. 307-332
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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.
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| 7. |
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| 8. |
- Storåkers, Bertil, et al.
(författare)
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On delamination growth in shallow shells
- 2004
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Ingår i: Journal of applied mechanics. - : ASME International. - 0021-8936 .- 1528-9036. ; 71:2, s. 247-254
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Tidskriftsartikel (refereegranskat)abstract
- A theoretical and computational study has been carried out for compressive loading of a thin circular embedded delamination located below a cylindrical surface. The delaminated member is subjected to nominally uniaxial and balanced biaxial loading with the main objective to analyze its influence on surface curvature especially as regards imminent crack growth. The analysis is based on nonlinear shell theory combined with linear fracture mechanics. A finite element program earlier developed for delaminated plates has been generalized to apply also for shells and used to determine energy release rates and mode intensities along the delaminated front. A parameter study, is made of the influence of curvature of the delaminated shell in particular as regards initiation and stability of crack growth.
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| 9. |
- Storåkers, Bertil, et al.
(författare)
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Similarity analysis of inelastic contact
- 1997
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Ingår i: International Journal of Solids and Structures. - 0020-7683 .- 1879-2146. ; 34:24, s. 3061-3083
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Tidskriftsartikel (refereegranskat)abstract
- Analysis of mechanical contact of solids is of interest not only regarding a variety of mechanical assemblies but also on a smatter scale such as roughness properties of surfaces and compaction of powder particles. indentation testing is another prominent problem in the context. To analyse the phenomena involved is inherently difficult at application essentially due to the presence of large strains, nonlinear material behaviour, time dependence and moving contact boundaries. Recently, progress has been made, however, to explicitly solve basic boundary value problems especially due to advances in computational techniques. A substantial ingredient which facilitates solution procedures is self-similarity and it is the present purpose to explore in detail the advantages in a general setting when this feature prevails. A viscoplastic framework is laid down for a wide class of constitutive properties where strain-hardening plasticity, creep and also nonlinear elasticity arise as special cases. It is then shown that when surface shapes and material properties are modelled by homogeneous functions, associated boundary value problems posed may be reduced to stationary ones. As a consequence, within Hertzian kinematics, relations between contact impression and regions become independent of loading and time and the connection to loading characteristics does not usually require a full solution of the problem. In particular it is shown that for general head-shapes it proves efficient to use an approach where an intermediate Aat die solution serves as a basic tool also for hereditary materials. An invariant computational procedure based on the intermediate problem is arrived at and decisive results shown to be found by simple cumulative superposition. Illustrations are given analytically for ellipsoidal contact of Newtonian fluids and by detailed computations for spherical indentation of viscoplastic solids for which also universal hardness formulae an proposed. For several bodies in contact it is shown how general results may be extracted from fundamental solutions for a half-space.
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