Wear 268 (2010) 1285–1294 Contents lists available at ScienceDirect Wear journal homepage: www.elsevier.com/locate/wear Asperity creep under constant force boundary conditions Andreas Goedecke a,b,∗ , Robert L. Jackson c , Randolf Mock b a Institute of Technical Mechanics, Johannes Kepler University, Altenbergerstrasse 69, 4040 Linz, Austria b Actuator and Drive Systems, Siemens Corporate Technology, Otto-Hahn-Ring 6, 81379 Munich, Germany c Department of Mechanical Engineering, Auburn University, Auburn, AL 36830, USA article info Article history: Received 18 July 2009 Received in revised form 24 January 2010 Accepted 27 January 2010 Available online 4 February 2010 Keywords: Asperity Creep Spherical contact Garofalo creep law abstract This work presents an analysis of the transient creep deformation of a hemisphere in contact with a rigid flat, loaded by a constant force. The analysis is based on extensive finite element simulations, using a Garofalo creep law. Motivated by the simulations, an analytical framework is derived. Starting from the trivial case of a cylinder, the analytical framework can be generalized by exchanging a few functionals; this will describe the spherical geometry under analysis. The necessary functionals are derived by using a combination of analytical and empirical models. The resulting model accurately predicts the creep evolution of arbitrary asperities for a wide parameter range, requiring only the bulk material parameters. The results are interpreted in view of transient friction effects with creep as their possible cause. © 2010 Elsevier B.V. All rights reserved. 1. Introduction The contact of an elastic-perfectly plastic hemisphere with a rigid flat has been studied intensively in recent times (see [1–7]). These models are usually studied from the perspective of the con- tact and friction between rough surfaces. Here, the hemisphere serves as a model for a contacting surface asperity or micro- junction. Especially important in this context is the derivation of universal laws for the asperity behavior, to be embedded in statis- tical (e.g. the seminal Greenwood–Williamson model [8]) or fractal or multiscale models (e.g., [9]) of surface contact. The classic Hertz [10] theory of hemisphere contact has been extended by studies of the elasto-plastic transition region [1,2,4], while recent research efforts have included a combination of normal and tangential loading [11,12], loading and unloading [3,13,14,7], adhesion [15,5], or electromagnetic effects [16], among others. The analysis of creep deformation of asperities has received increasing attention (see [6,17,18]). On the other hand, recent experimental research [19,20] has supported the early conjectures by Moore and Tabor [21], Spurr [22], Rabinowicz [23] and others that the emergence of transient friction laws are linked to asperity deformation through creep. The- ∗ Corresponding author at: Actuators and Control, Siemens Corporate Technology, 81379 Munich, Germany. Tel.: +49 1781874476; fax: +49 8963646881. E-mail addresses: Andreas.Goedecke@students.jku.at (A. Goedecke), robert.jackson@eng.auburn.edu (R.L. Jackson), Randolf.Mock@siemens.com (R. Mock). oretical analyses have supported this theory (e.g., [24,25]). Among the effects describable by this creep theory are the dwell-time dependent rise in static friction [21,22], the velocity-dependent dynamic friction [26] or friction lag and hysteresis [27]. This highlights the importance of analyzing the creep deformation of asperities. In Goedecke and Mock [18], the creep of an asperity under a constant displacement or interference boundary condition was analyzed. In the present paper, the analysis is extended to the tran- sient creep behavior of an asperity under a constant force boundary condition. The empirical laws presented in Goedecke and Mock [18] are extended to present a comprehensive one-dimensional model for this situation. This study aims both at developing a quantitative understanding of the creep deformation of an asperity and find- ing a quantitative model embeddable in a contact model for rough surfaces. 2. Modeling and simulation The geometry under analysis is a half-sphere with an unde- formed radius R in contact with a rigid flat as shown in Fig. 1a. Due to the symmetry, only a quarter sphere has to be con- sidered, using an axial symmetric element formulation. At the base of the sphere, a sliding boundary condition has been imple- mented, in line with Kucharski et al. [28] and Kogut and Etsion [1]. The commercial finite element simulation code ANSYS 11 was used to perform the simulations. A mesh of about 3300 predom- inantly rectangular elements with quadratic shape functions was 0043-1648/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2010.01.025