Flattening of a deformable sphere by a rigid sphere during transient thermo-mechanical contact Wenping Song a,b,n , Andrey Ovcharenko c , Longqiu Li a , Frank E. Talke b a Harbin Institute of Technology, Harbin, China b University of California, San Diego, USA c Western Digital Corporation, San Jose, USA article info Article history: Received 9 July 2012 Received in revised form 26 November 2012 Accepted 24 January 2013 Available online 17 February 2013 Keywords: Thermo-mechanical contact Spherical contact Sliding Flattening abstract A finite element model is developed to study the transient thermo-mechanical contact between a rigid sphere and an elastic–plastic sphere. Interference and tangential displacement are applied to the rigid sphere while the elastic–plastic sphere is stationary. The radius of the rigid sphere is larger than that of the elastic–plastic sphere to model flattening. Universal solutions are obtained for the maximum contact force, the maximum contact area, the maximum residual interference, and the maximum temperature rise independent of sphere radius, material properties and loading parameters. The effects of various parameters (sphere radius, interference, coefficient of friction, sliding velocity and material properties) on the contact characteristics of the deformable sphere are discussed. & 2013 Elsevier B.V. All rights reserved. 1. Introduction Mechanical deformation and temperature rise of contacting parts during sliding play a vital role in determining failure and life of mechanical components. As an example, in hard disk drives, media defects due to the manufacturing process can cause surface degradation leading to failure of the hard disk drive [1–3]. Temperature rise in the read element due to frictional heating may also contribute to surface degradation [2–3]. A number of models have been proposed in the literature for contact of sliding surfaces [4–12]. Elastic–plastic contact has been studied in Refs. [4–7] for a deformable sphere and a rigid flat in the presence of normal and tangential forces. In the latter investigations, perfect slip (frictionless contact) or full stick was assumed. The evolution of the plastic zone, the static friction coefficient and tangential stiffness of the contact were studied. A finite element model for sliding of two elastic–plastic asperities was developed by Faulkner and Arnell [8], considering the lateral flow of displaced material. The authors found that the overall friction coefficient is lower for spherical asperities compared to cylindrical ones. Vijay- wargiya and Green [9] developed a model of sliding interaction of two elastic–plastic cylinders. They studied deformation, normal and tangential forces, stress distribution and energy loss as a function of the friction coefficient. Boucly et al. [10] analyzed the rolling and sliding contacts between two spherical asperities using the con- jugate gradient method and the discrete convolution and fast Fourier transform method. In Ref. [10], the normal and tangential forces during a transient contact were found to be asymmetric. Jackson et al. [11] provided a solution for the tangential and normal contact force for sliding contact between two elastic–plastic spheres. Mulvihill et al. [12] developed a finite element model to predict the coefficient of friction during sliding, allowing material failure within the sliding asperities. They found that the sliding friction coefficient increases with asperity interference and interface shear strength. The investigations in Refs. [4–12] have been concerned with quasi-static solutions for spherical and cylindrical sliding contacts. The analysis of transient contacts, on the other hand, is equally or even more important in mechanical component design, especially in situations related to the prediction of reliability. Toward this end, Ovcharenko et al., [13] developed a dynamic finite element model of a sphere impacting on a layered disk to predict failures in hard disk drives. The thermo-mechanical damage of the disk surface, i.e., plastic deformation and temperature rise of the disk, were deter- mined as a function of contact time. Additional models have addressed frictional heating of con- tacting bodies. Tian and Kennedy [14] developed approximate analytical solutions for the maximum and average interfacial temperature rise due to frictional heating. Bos and Moes [15] developed numerical solutions for the steady state heat partition- ing and temperature rise for an elliptical heat resource. Gao and Lee [16] developed a transient flash temperature model to analyze heat partition and investigate the effect of surface topography. Ertz and Knothe [17] compared semi-analytical and Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/wear Wear 0043-1648/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.wear.2013.01.092 n Corresponding author at: Harbin Institute of Technology, Harbin, China. Tel.: þ86 0451 86413111. E-mail address: wenping.song1985@gmail.com (W. Song). Wear 300 (2013) 29–37