Hindawi Publishing Corporation ISRN Tribology Volume 2013, Article ID 871634, 13 pages http://dx.doi.org/10.5402/2013/871634 Research Article Finite-Element-Based Multiple Normal Loading-Unloading of an Elastic-Plastic Spherical Stick Contact Biplab Chatterjee and Prasanta Sahoo Department of Mechanical Engineering, Jadavpur University, Kolkata 700032, India Correspondence should be addressed to Prasanta Sahoo; psjume@gmail.com Received 30 October 2012; Accepted 19 November 2012 Academic Editors: J. Antunes and F. Findik Copyright © 2013 B. Chatterjee and P. Sahoo. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e repeated normal elastic plastic contact problem of a deformable sphere against a rigid �at under full stick contact condition is investigated with a commercial �nite element soware ANS�S. Emphasis is placed on the effect of strain hardening and hardening model with the maximum interference of load ranging from elastic to fully plastic, which has not yet been reported. Different values of tangent modulus coupled with isotropic and kinematic hardening models are considered to study their in�uence on contact parameters. Up to ten normal loading-unloading cycles are applied with a maximum interference of 200 times the interference required to initiate yielding. Results for the variation of mean contact pressure, contact load, residual interference, and contact area with the increasing number of loading unloading cycles at high hardening parameter as well as for low tangent modulus with two different hardening models are presented. Results are compared with available �nite element simulations and in situ results reported in the literature. It is found that small variation of tangent modulus results in same shakedown behavior and similar interfacial parameters in repeated loading-unloading with both the hardening rules. However at high tangent modulus, the strain hardening and hardening rules have strong in�uence on contact parameters. 1. Introduction Multiple repeated normal loading unloading is common in engineering applications. Several researchers have identi�ed the use of repeated normal loading unloading in various �elds of engineering applications such as contact resistance in MEMS micro switches [1, 2], head-disk interaction in magnetic storage systems [3], ultrasonic interfacial stiffness measurement [4], stamping mechanism, and in rolling ele- ment bearings, gears, cams, and so forth. Earlier the prob- lems of multiple loading-unloading were solved assuming a speci�c pressure distribution. e contact region related to the analysis of Kapoor et al. [5], Williams et al. [6] did not exceed greatly the elastic limit; hence they assumed Hertzian [7] contact. Merwin and Johnson [8], Kulkarni et al. [9], Bhargava et al. [10, 11] used Hertzian or modi�ed Herzian pressure distribution even for elastic plastic contacts. In most engineering applications, the contact deformation occurred in elastic plastic as well as in plastic region. e arbitrary selection of pressure distribution where the plasticity effects are dominant eventually would provide inaccurate solution. Beyond the Hertzian assumption of nonadhesive friction- less contact within elastic limit, commercial �nite element soware is best suited to calculate accurately the contact parameters like contact load, contact area, and pressure in the elastic plastic and plastic region [12]. e contact analysis of the rough surfaces involves the study of single asperity contact. Kogut and Etsion [13] �rst provided an accurate result of elastic plastic loading of a hemisphere against a rigid �at using commercial �nite element soware ANS�S. ey used �nite element analysis under frictionless condition for a wide range of material elastic properties and sphere size to present generalized empirical relations for contact area, contact load, and mean contact pressure as a function of dimensionless interference. eir investigations in elastic, elastic plastic, and plastic regions also include the effect of plastic properties of the material. Kogut and Etsion inferred that the variation of tangent modulus, plastic property of the