The repeated normal elastic plastic contact problem of a deformable sphere against a rigid flat under full stick contact condition is investigated with a commercial finite element software ANSYS. 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 influence 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 finite 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 influence on contact parameters. 1. Introduction Multiple repeated normal loading unloading is common in engineering applications. Several researchers have identified the use of repeated normal loading unloading in various fields 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 element bearings, gears, cams, and so forth. Earlier the problems of multiple loading-unloading were solved assuming a specific pressure distribution. The 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 modified 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. The arbitrary selection of pressure distribution where the plasticity effects are dominant eventually would provide inaccurate solution. Beyond the Hertzian assumption of nonadhesive frictionless contact within
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