Thermo-mechanical contact between a rigid sphere and an elastic–plastic sphere Wenping Song a , Longqiu Li a,n , Andrey Ovcharenko b , Frank E. Talke c a Harbin Institute of Technology, Harbin, China b Western Digital Corporation, San Jose, USA c University of California, San Diego, USA article info Article history: Received 30 May 2015 Received in revised form 15 October 2015 Accepted 10 November 2015 Available online 1 December 2015 Keywords: Thermo-mechanical contact Spherical contact Plowing Flattening abstract The mechanical and thermal response of a rigid sphere sliding over an elastic–plastic sphere with radius larger than that of the rigid sphere, namely, plowing contact model, are investigated using a finite ele- ment method. Dimensionless solutions for the maximum values of contact force, friction force, contact area, residual interference, and interfacial temperature rise are obtained as a function of dimensionless contact time. A detailed comparison is performed with the results between the plowing contact model and the flattening contact model in which an elastic–plastic sphere flattened by a rigid sphere with radius larger than that of the elastic–plastic sphere. & 2015 Elsevier Ltd. All rights reserved. 1. Introduction Contact mechanics is important for design of mechanical and electromechanical components, such as gears [1], hard disk drives [2] and micro-switches [3]. In many studies involving spherical contacts, two different models of spherical contact have been used. One is the flattening model, where a rigid sphere is sliding over an elastic–plastic sphere with a radius smaller than that of the rigid sphere. The other one is the so-called plowing model, where a rigid sphere is sliding over an elastic–plastic sphere with a radius larger than that of the rigid sphere. These two models look similar at first glance. However, the contact characteristics of both models are quite different, especially in the elastic–plastic and the fully plastic deformation regimes. In many publications, a hard indenter plowing into a soft flat has been used to study frictional behavior of the plowing process [4–9]. During plowing, sliding motion of the indenter is resisted by both adhesive friction and plowing friction, imposed by the elastic– plastic deformation of the soft flat [4]. Liu et al. [5] analyzed a diamond conical indenter sliding on the surface of a deformable metal, assuming that the deformation was perfectly plastic. On the other hand, elastic recovery was observed experimentally at the rear edge of an indenter during scratching tests by Bucaille et al. [6]. Considering the elastic recovery, Lafaye et al. [7,8] provided a solution for plowing friction of a conical tip. The authors found that a tip with a large radius of curvature leads to a small plowing component of friction. Kamminga and Janssen [9] studied a dia- mond spherical indenter plowing into a CrN coated steel to inves- tigate the effect of substrate and contact condition on adhesive and plowing components of friction. It was observed that the adhesive component of friction is determined by the surface condition. Taking into account the combined effect of thermo-mechanical stress, Ye and Komvopoulos [10] studied the mechanical and thermal response of an elastic sphere sliding over an elastic– plastic layered flat under normal and tangential loading. The stress and strain fields were investigated, as well as the interfacial temperature rise. Thermo-mechanical contact of an elastic–plastic sphere sliding on an elastic–plastic layered flat was studied by Gong and Komvopoulos [11]. The effect of friction coefficient, sphere radius and repetitive sliding on stress and temperature distributions was studied. Song et al. [12] developed a thermo- elastic–plastic transient contact model to study the contact between slider and disk asperity in hard disk drives. They found that both plastic deformation and high interfacial temperature induced by slider/asperity contacts can cause head degradation. Universal solutions for transient contacts between a rigid sphere and a moving flat were provided by Ovcharenko et al. [13]. Plowing was observed during transient impact which led to large contact force and high interfacial temperature. In the above literature review, no investigation was found dealing with the thermo-mechanical transient response between Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/triboint Tribology International http://dx.doi.org/10.1016/j.triboint.2015.11.019 0301-679X/& 2015 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail address: longqiuli@hit.edu.cn (L. Li). Tribology International 95 (2016) 132–138