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2020 | OriginalPaper | Buchkapitel

1. Fundamentals of Elastic Contacts

verfasst von : David Hills, Hendrik Andresen

Erschienen in: Modeling and Simulation of Tribological Problems in Technology

Verlag: Springer International Publishing

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Abstract

Contacts are classified into the fundamental types and their characteristics briefly explored. The formulation of incomplete contacts using a half-plane formulation is then developed, and used to obtain the plane solution for a Hertzian contact, while providing the framework for many other geometries. Williams’ solution for a sharp infinite elastic wedge is described in detail, and it is shown how this may be applied to advantage in understanding complete contacts and especially their near-edge properties. We then go back to look at incomplete contacts and analyse how they respond when there is interfacial friction present and they remain stationary, but a partial slip state evolves. The chapter concludes by reviewing the other possible types of contact.

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Nächstes Kapitel Contact Problems Involving Friction

Dundurs (1969) showed that plane elastic problems composed of two bodies depend not on the obvious three dimensionless properties \(\nu _{1},\nu _{2}, E_{1}/E_{2}\) but, in fact, on only two quantities (\(\alpha ,\beta \)). Half-plane problems have a further reduced dependence on only the solitary quantity \(\beta .\)

Note that, in defining crack tip stress intensity factors, for historical reasons the stress intensity factors have an extra factor of \(\sqrt{2\pi }\) included in both Eq. (1.51) in the denominator, and in the right hand side of the definitions of stress intensity factor, Eqs. (1.52) and (1.53).

Andresen, H. N., Hills, D. A., Barber, J. R., & Vázquez, J. (2019) Frictional half-plane contact problems subject to alternating normal and shear loads and tension. International Journal of Solids and Structures, 168, 166–171.

Barber, J. R. (2001). Intermediate mechanics of materials. McGraw-Hill.

Barber, J. R. (2010). Elasticity (3rd ed.). Springer.

Barber, J. R., Davies, M., & Hills, D. A. (2011). Frictional elastic contact with periodic loading. International Journal of Solids and Structures, 48, 2041–2047.CrossRef

Cattaneo, C. (1938). Sul contato di due corpo elastici. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei, 27, 342–348, 434–436, 474–478.

Chaise, T., Paynter, R. J. H., & Hills, D. A. (2014). Contact analysis of a semi-infinite strip pressed onto a half plane by a line force. International Journal of Mechanical Sciences, 81, 60–64.CrossRef

Churchman, C. M., & Hills, D. A. (2006a). General results for complete contacts subject to oscillatory shear. Journal of the Mechanics and Physics of Solids, 54, 1186–1205.CrossRef

Churchman, C. M., & Hills, D. A. (2006b). Slip zone length at the edge of a complete contact. International Journal of Solids and Structures, 43, 2037–2049.CrossRef

Ciavarella, M. (1998). The generalised cattaneo partial slip plane contact problem, part i theory, part ii examples. International Journal of Solids and Structures, 35, 2349–2378.MathSciNetCrossRef

Ciavarella, M., Baldini, A., Barber, J. R., & Strozzi, A. (2006). Reduced dependence on loading parameters in almost conforming contacts. International Journal of Mechanical Sciences, 48, 917–925.CrossRef

Comninou, M. (1976). Stress singularity at a sharp edge in contact problems with friction. Journal of Applied Mathematics and Physics, 27, 493–499.

Dini, D., & Hills, D. A. (2009). Frictional energy dissipation in a rough hertzian contact. ASME Journal of Tribology, 131, 021401–1–8.

Dundurs, J. (1969). Discussion of edge-bonded dissimilar orthogonal wedges under normal and shear loading (by D. Bogey). Journal of Applied Mechanics, 36, 342–348, 650–652.CrossRef

Erdogan, F., Gupta, G. D., & Cook, T. S. (1973). Numerical solution of singular integral equations. In G.C. Sih (Ed.), Methods of analysis and solutions of crack problems. Noordhoff.

Hertz, H. (1881). über die berührung fester elastischer körper. Journal für die reine und angewandte Mathematik, 92, 156–171.MATH

Hills, D. A., Nowell, D., & Sackfield, A. (1993). Mechanics of elastic contacts. Butterworth-Heinemann.

Jäger, J. (1998). A new principle in contact mechanics. Journal of Tribology, 120, 677–684.CrossRef

Kartal, M. E., Hills, D. A., Barber, J. R., & Nowell, D. (2010). Torsional contact between elastically similar flat-ended cylinders. International Journal of Solids and Structures, 47(10), 1375–1380.CrossRef

Karuppanan, S., & Hills, D. A. (2008). Frictional complete contacts between elastically similar bodies subject to normal and shear load. International Journal of Solids and Structures, 17, 4662–4675.CrossRef

Mindlin, R. D. (1949). Compliance of elastic bodies in contact. Journal of Applied Mechanics, Transactions ASME, 16, 259–268.MathSciNetMATH

Moore, M. R., & Hills, D. A. (2018). Solution of half-plane contact problems by distributing climb dislocations. International Journal of Solids and Structures, 147, 61–66.CrossRef

Moore, M. R., Ramesh, R., Hills, D. A., & Barber, J. R. (2018). Half-plane partial slip contact problems with a constant normal load subject to a shear force and a differential bulk tension. Journal of the Mechanics and Physics of Solids, 118, 245–253.MathSciNetCrossRef

Munisamy, R. L., Hills, D. A., & Nowell, D. (1994). Static axi-symmetric hertzian contacts subject to sharing forces. ASME Journal of Applied Mechanics, 61(2), 278–283.CrossRef

Persson, A. (1964). On the stress distribution of cylindrical bodies in contact. Doktosavhandlingar vid Chalmers Tekniska Hogskola.

Truman, C. E., Sackfield, A., & Hills, D. A. (1995). Contact mechanics of wedge and cone indenters. International Journal of Mechanical Sciences, 37, 261–275.CrossRef

Titel: Fundamentals of Elastic Contacts
verfasst von: David Hills
Hendrik Andresen
Verlag: Springer International Publishing
Buch: Modeling and Simulation of Tribological Problems in Technology
Print ISBN: 978-3-030-20376-4

Electronic ISBN: 978-3-030-20377-1

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-20377-1_1

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