Abstract
All problems of non-linear creep are very difficult. We have developed an approximate approach to solve the contact problems of power-law creep in the case, when one of bodies in contact is a rigid punch with corners and the other one - thin deformable layer or half-space. The main merit of this approach consists in the simpliciy of calculations and in the clearity of assumptions. First of all the local problem of contact between a rigid corner and creeping half-space is investigated. It is similar to the old one of Cherepanov - Rice - Hutchinson for a crack. Hence we have the stress-strain state near the punch corner in function of one free parameter. Internal solution for a thin layer has been found by asymptotic analysis, for a half-space - by Arutyunyan’s technics, both also as functions of another free parameter. The size of boundary layer may be regarded as a third free parameter. The integral equilibrum condition and the claim of continuity of main contact problem characteristics give a non-linear algebraic equation to determine free constants by calculations. Its solution may be given by explicit formulae in particular cases. Besides mentioned problems, a periodical problem, modeling the forming by poinsoning of a plate with ribes, has been solved. Moreover, we have completely studied as a separed situation the local solution near a creeping edge tip (arbitrary angle, various boundary conditions), and we have found the internal asymptotics for a thin layer of Nadai or of Imbert materials.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aleksandrov, V.M., and Brudnij, S.R., 1986, On the method of generalized superposition in contact problem of anti-plane shear, Mech.of Solids U.S.S.R. 21: No 4.
Aleksandrov, V.M., and Grishin, S.A., 1987, State of stress and strain of a small neighbourhood of the apex of a wedge for a physical non-linearity and different boundary conditions, PMM U.S.S.R. 51: No 4.
Aleksandrov, V.M., and Sumbatyan, M.A., 1983, On some solution of contact problem of non-linear steady creep for a half-plane, Mech.of Solids U.S.S.R. 18: No 1.
Amazigo, J.C., 1974, Fully plastic crack in an infinite body under anti-plane shear, Int.J.Solids Structures 10:1003.
Arutyunyan, N.Kh., 1959, Plane contact problem of creep theory, PMM U.S.S.R. 23: No 5.
Bell, J.F., 1984, “Experimental Fundations of Mechanics of Solids, ”Nauka, Moscow. (Russian translation from: Enciclopedia of Phisics, vol.VIa/1, Mechanics of Solids I, Springer-Verlag, Berlin-Heidelberg-New York (1973))
Cherepanov, G.P., 1967, On crack propagation in a continuous medium, PMM U.S.S.R. 31: No 3.
Galanov, B.A., 1984, Numerical solution to the problem about concentrated force acting onto the boundary of the half-space of power-law hardening material, in:”Strength of Materials and Building Theory, issue 44, Budivelnik, Kiev.
Grishin, S.A., 1988, Periodical contact problem of non-linear steady creep for a thin layer, Mech.of Solids U.S.S.R. 23: No 2.
Grishin, S.A., and Manzhirov, A.V., 1986, Contact problems for a thin layer under conditions of non-linear creep, Mech.of Solids U.S.S.R. 21: No 6.
Hutchinson, J.W., 1968, Singular behaviour at the end of a tensile crack in a hardening material, J.Mech.Phys.Solids 16:13.
Hutchinson, J.W., 1968, Plastic stress and strain fields at a crack tip, J.Mech.Phys.Solids 16:337.
Iljushin, A.A., 1948, “Plasticity” Gostekhizdat, Moscow-Leningrad.
Johnson, K.L., 1985, “Contact Mechanics, ”Cambrige University Press, Cambrige.
Kachanov, L.M., 1960, “Creep Theory, ”Fizmatgiz, Moscow.
Kuznetsov, A.I., 1962, Pressing of rigid punches into half-space under conditions of power-law hardening and non-linear creep of material, PMM U.S.S.R. 26: No 3.
Manzhirov, A.V., 1983, Plane and axisymmetric problems about load acting onto thin viscoelastic layer, Journ.Appl.Mech.and Tech.Phys. U.S.S.R. No 5.
Martynenko, M.D., and Svirskij, E.A., 1984, Axisymmetric stress-strain fields in the problem about concentrated force acting onto non-linear half-space, Differential Equations U.S.S.R. 20:2007.
Rabotnov, Yu.N., 1966, “Creep of Structure Elements, ”Nauka, Moscow.
Rice, J.R., and Rosengren, G.F., 1968, Plane strain deformation near a crack tip in a power-law hardening material, J.Mech.Phys.Solids 16:1.
Sneddon, J.N., and Berry, D.S., 1961, “The Classical Theory of Elasticity, ” Fizmatgiz, Moscow. (Russian translation of Handbuch der Physic, band VI, Springer-Verlag, Berlin-GottingenHeidelberg (1958))
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Grishin, S.A. (1995). Contact Problems for Power-Law Creeping Solids. In: Raous, M., Jean, M., Moreau, J.J. (eds) Contact Mechanics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1983-6_43
Download citation
DOI: https://doi.org/10.1007/978-1-4615-1983-6_43
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5817-6
Online ISBN: 978-1-4615-1983-6
eBook Packages: Springer Book Archive