Response of frictional receding contact problems to cyclic loading

Dundurs [Properties of elastic bodies in contact. In: de Pater AD, Kalker JJ, editors. The mechanics of the contact between deformable bodies. Delft: Delft University Press; 1975. p. 54–66] has shown that if the contact area in a frictionless elastic system under load is equal to or smaller than that before loading (i.e. the contact is receding), the extent of the contact area is load-independent and the stress field varies linearly with load. Similar results apply to problems with Coulomb friction as long as the loading is monotonic, but otherwise non-linearities and variation in the contact area occur. In this paper, we examine this effect for the simple case of an elastic block pressed against a frictional rigid plane. During unloading there is continuous variation of both contact and slip/stick boundaries. For the important case where the loading contains a mean and a periodic component, the system approaches a steady periodic state relatively slowly and in this final state there is continuous variation of the contact area, with the minimum (i.e. the maximum amount of separation) occurring at the minimum applied load. & 2008 Elsevier Ltd. All rights reserved.

[1]  Anton Dammes de Pater,et al.  The Mechanics of the contact between deformable bodies : proceedings of the symposium of the International Union of Theoretical and Applied Mechanics (IUTAM), Enschede, Netherlands, 20-23 August 1974 , 1975 .

[2]  J. Dundurs.  Properties of elastic bodies in contact , 1975 .

[3]  J. Dundurs,et al.  Role of Elastic Constants in Certain Contact Problems , 1970 .

[4]  L. K. G. Filon.  On an approximate solution for the bending of a beam of rectangular cross-section under any system of load.—additional note , 1904, Proceedings of the Royal Society of London.

[5]  Michele Ciavarella,et al.  Reduced dependence on loading parameters in almost conforming contacts , 2006 .

[6]  Louis Napoleon George Filon,et al.  On an Approximate Solution for the Bending of a Beam of Rectangular Cross-Section under any System of Load, with Special Reference to Points of Concentrated or Discontinuous Loading , 1903 .

[7]  D. A. Hills,et al.  Analysis of a Rocking and Walking Punch—Part I: Initial Transient and Steady State , 2004 .

[8]  D. A. Spence,et al.  An eigenvalue problem for elastic contact with finite friction , 1973, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  Michele Ciavarella,et al.  Shakedown in elastic contact problems with Coulomb friction , 2007 .

[10]  Saravanan Karuppanan,et al.  Frictional complete contacts between elastically similar bodies subject to normal and shear load , 2008 .

[11]  J. R. Turner.  The Frictional Unloading Problem on a Linear Elastic Half-Space , 1979 .

[12]  J J Kauzlarich,et al.  Contact between a centrally loaded plate and a rigid or elastic base, with application to pivoted pad bearings , 2001 .

[13]  H. T. Jessop,et al.  A Treatise on Photoelasticity , 1958 .

[14]  D. A. Hills,et al.  Recent developments in the understanding of fretting fatigue , 2013 .

[15]  D A Hills,et al.  Unsymmetrical shear loading and its influence on the frictional shakedown of incomplete contacts , 2004 .

[16]  Leon M Keer,et al.  Problems involving a receding contact between a layer and a half space , 1972 .