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Frictional Effects on Hertzian Contact and Fracture
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).ORCID iD: 0000-0002-0596-228X
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

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.

Place, publisher, year, edition, pages
Stockholm: KTH , 2007. , ix, 16 p.
Series
Trita-HFL. Report / Royal Institute of Technology, Solid mechanics, ISSN 1654-1472 ; 0437
Keyword [en]
Contact mechanics; Elastic material; Friction; Nanoindentation; Fracture
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-4535OAI: oai:DiVA.org:kth-4535DiVA: diva2:12736
Public defence
2007-12-06, M2, M, Brinellvägen 64, 10:15
Opponent
Supervisors
Note

QC 20100729

Available from: 2007-11-14 Created: 2007-11-14 Last updated: 2013-01-14Bibliographically approved
List of papers
1. Hertz contact at finite friction and arbitrary profiles
Open this publication in new window or tab >>Hertz contact at finite friction and arbitrary profiles
2005 (English)Article in journal (Refereed) Published
Abstract [en]

Axisymmetric contact at finite Coulomb friction and arbitrary profiles is examined analytically and numerically for dissimilar linear elastic solids. Invariance and generality are aimed at and an incremental procedure is developed resulting in a reduced benchmark problem corresponding to a rigid flat 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. Save for the influence of the coefficients of friction and contraction ratio, it is shown that at partial slip the evolving relative stick-slip contour is independent of any convex and smooth contact profile at monotonic loading. For flat and conical profiles with rounded edges and apices, results are illustrated for relations between force, depth and contact contours together with surface stress distributions. The solution for dissimilar solids in a full space is transformed to a half-space problem and solved for a combination of material parameters in order to first determine interface traction distributions. Subsequently, full field values for the two solids were computed individually. In order to predict initiation of fracture and plastic flow, results are reported for the location and magnitude of maximum tensile stress and effective stress, respectively, for a range of geometrical and material parameters. In two illustrations, predicted results are compared with experimental findings related to initiation of brittle fracture and load-depth relations at nanoindentation.

Keyword
Contact mechanics, Elastic material, Fracture, Friction, Nanoindentation
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-5374 (URN)10.1016/j.jmps.2004.11.009 (DOI)000229272400009 ()2-s2.0-16344384224 (Scopus ID)
Note
QC 20100729Available from: 2006-02-14 Created: 2006-02-14 Last updated: 2010-11-17Bibliographically approved
2. Hertzian fracture at unloading
Open this publication in new window or tab >>Hertzian fracture at unloading
2006 (English)In: Journal of the mechanics and physics of solids, ISSN 0022-5096, Vol. 54, no 11, 2453-2473 p.Article in journal (Refereed) Published
Abstract [en]

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.

Keyword
Contact mechanics; Elastic material; Fracture; Friction; Unloading; Contact contour; Contact mechanics; Elastic materials; Stress fracture; Computational methods; Friction; Glass; Indentation; Interfaces (materials); Tensile stress; Fracture mechanics
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-7645 (URN)10.1016/j.jmps.2006.04.014 (DOI)000241961400009 ()2-s2.0-33749666497 (Scopus ID)
Note
QC 20100729Available from: 2007-11-14 Created: 2007-11-14 Last updated: 2010-11-17Bibliographically approved
3. Hertzian Fracture at Finite Friction: A Parametric Study
Open this publication in new window or tab >>Hertzian Fracture at Finite Friction: A Parametric Study
2008 (English)In: Wear, ISSN 0043-1648, E-ISSN 1873-2577, Vol. 265, no 5-6, 840-848 p.Article in journal (Refereed) Published
Abstract [en]

Friction has a profound influence on Hertzian fracture initiation when dissimilar materials are involved. Experimental studies show that the presence of friction results in higher fracture loads and fracture radii as compared to the frictionless case. It has also been shown recently that the experimental observations concerning Hertzian fracture initiation at unloading may be explained by the effect friction has on a surface tensile stress distribution. Presently a contact cycle between two dissimilar elastic bodies at finite Coulomb friction has been investigated numerically for a wide range of material parameters and contact geometries. Emphasis has been given to the surface tensile stress distribution which is assumed to be a governing parameter for Hertzian fracture initiation. In particular it was found that during loading the contact region divides into invariant stick and inward slip regions and the presence of outward frictional shear tractions reduces the maximum surface tensile stress and shifts it away from the contact contour as compared to the frictionless case. At unloading, the distributions of stick-slip zones were found to be severely history- and geometry-dependent and shear tractions reversed their direction over part of the contact area. Consequently, tensile stresses were found to grow at unloading. Results concerning the influence of the friction coefficient, Dundur's parameter and the specimen's Poisson's ratio on the absolute maximum surface tensile stress obtained at 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.

Keyword
Contact mechanics; Fracture; Friction; Loads (forces); Parameter estimation; Stress concentration; Contact mechanics; Hertzian fracture initiation
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-7646 (URN)10.1016/j.wear.2008.01.006 (DOI)000257452500031 ()2-s2.0-43549087612 (Scopus ID)
Note
QC 20100729. Uppdaterad från In Press till Published 20100729.Available from: 2007-11-14 Created: 2007-11-14 Last updated: 2010-07-29Bibliographically approved
4. On indentation and initiation of fracture in glass
Open this publication in new window or tab >>On indentation and initiation of fracture in glass
2008 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 45, no 10, 2993-3008 p.Article in journal (Refereed) Published
Abstract [en]

The influence of indenter elasticity on Hertzian fracture initiation at frictional dissimilar elastic contact has been examined experimentally and numerically. In flat float glass specimens initiation of cone cracks has been observed and fracture loads measured with steel and tungsten carbide indenters at monotonically increasing loading and during a load cycle. The observed effect of indenter elasticity on fracture loads was found to be qualitatively different from the one predicted by the Hertz contact theory. This discrepancy may be explained by the presence of interfacial friction. The friction coefficient between the indenters and the specimen was measured and a contact cycle at finite Coulomb friction has been analyzed numerically. The influence of the indenter elasticity and the friction coefficient on the surface maximum tensile stress has been investigated and the results concerning the influence of these parameters on the fracture loads as given based on a critical stress fracture criterion. The obtained computational results were found to be in better agreement with experimental findings as compared to the predictions based on the frictionless contact theory. A 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 a Weibull statistics was introduced. The predicted critical loads corresponding to the 50% failure probability were found to be in close agreement with experimentally observed ones.

Keyword
Contact mechanics; Elastic material; Fracture; Friction; Elasticity; Friction; Glass; Indentation; Tungsten carbide; Weibull distribution; Contact mechanics; Elastic materials; Failure probability; Fracture loads; Load cycle; Crack initiation
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-7647 (URN)10.1016/j.ijsolstr.2008.01.008 (DOI)000255323900013 ()2-s2.0-40849116138 (Scopus ID)
Note
QC 20100729. Uppdaterad från In Press till Published 20100729. Available from: 2007-11-14 Created: 2007-11-14 Last updated: 2010-07-29Bibliographically approved

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