Wear 274–275 (2012) 238–247 Contents lists available at SciVerse ScienceDirect Wear j o ur nal ho me p age: www.elsevier.com/locate/wear Scratching polycarbonate: A quantitative model L.C.A. van Breemen a,b,∗ , L.E. Govaert a,b , H.E.H. Meijer a,b a Polymer Technology, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands b Dutch Polymer Institute (DPI), P.O. Box 902, NL-5600 AX, Eindhoven, The Netherlands a r t i c l e i n f o Article history: Received 30 March 2011 Received in revised form 29 August 2011 Accepted 6 September 2011 Available online 17 September 2011 Keywords: Contact mechanics Single-asperity sliding friction Polymer glasses Intrinsic behavior Scratch testing Finite element modeling a b s t r a c t Generally it is understood that friction is additively decomposed into an adhesion- and a deformation- related component, suggesting independence. Experimentally these components cannot be separated and only by combining experiments with simulations, a decoupled analysis is possible. We apply this hybrid experimental–numerical approach in the single-asperity scratch test, simplifying the friction geometry. Simulations without adhesive interaction between tip and surface result in friction forces that are only half of the experimental ones, and are almost not influenced by the sliding velocity. In case of an additive decomposition, this would imply a large contribution of the adhesive component which, moreover, should take care of all rate dependency. This sounds unrealistic. By inclusion of constant fric- tion between tip and polymer, we find that the adhesive component strongly influences the contribution of the deformation component by the formation of a bow wave in front of the sliding tip. Experimental friction forces are quantitatively predicted, including the rate dependency. This entails that the suggested additive decomposition is not applicable and the large macroscopic deformation response proves to be the result of small changes in local processes. Using the model, for the first time, quantitative relations between the polymer’s intrinsic mechanical properties and its frictional properties are established. © 2011 Elsevier B.V. All rights reserved. 1. Introduction Polymers display a unique strength-to-weight ratio and are, therefore, applied also in structural applications. In combination with their excellent tribological properties [1] they are moreover favored above their metal counterparts in applications where fric- tion and wear are important, like e.g. in bearings and gears, and in hip-joints and artificial knees. However, tribology of polymers is still poorly understood and the relation between intrinsic poly- mer properties and frictional behavior is blurred, also because experiments usually have too many variables. Even in the case of single-asperity scratching, we find a dependence on scratch load, time, temperature, and speed, on the tip geometry [2–10], and the amount and type of fillers or additives [11–15]. The earliest model trying to predict the frictional response dates back to the pioneering work of Bowden and Tabor [16,17]. They pre- sumed that the friction force can be additively decomposed into an adhesion- and a deformation-related component. Confirmation of this hypothesis was demonstrated by experiments on rubbers using ∗ Corresponding author at: Polymer Technology, Eindhoven University of Tech- nology, P.O. Box 513, NL-5600 MB, Eindhoven, The Netherlands. Tel: +31 0 40 247 3092; fax: +31 0 40 244 7355. E-mail address: l.c.a.v.breemen@tue.nl (L.C.A. van Breemen). URL: http://www.mate.tue.nl/mate/showemp.php/4008 (L.C.A. van Breemen). rather specific boundary conditions, e.g. lubrication of the interface [18,19] or application of rolling friction [20,21]. With lubrication of the two contacting surfaces the adhesion component could be neglected and, as a result, the deformation related component was studied individually. To prevent a contribution of the lubricant in the shear layer, rolling friction was used, i.e. rolling a hard asperity over the rubber surface. Grosch [22], Ludema and Tabor [21], and Bueche and Flom [19] demonstrated by sliding at various velocities and temperatures on a given surface, that the frictional behavior of a rubber can be described by a single master curve, constructed by application of the WLF transform. Similar observations were reported by McLaren and Tabor [23] for polymers below their glass transition temperature. In the case of lubricated or rolling friction the comparison is most successful [24]. These observations indicate that capturing visco-elastic properties is of utmost importance. To study mechanical properties of coatings, of thin films and on a small scale, usually indentation tests are performed, where a single-asperity contact (a well-defined indenter) is pressed into a substrate. In particular for the elastic modulus, based on a fully elas- tic response, quantitative analytical methods are available [25,26], and with the aid of the elastic-visco-elastic correspondence prin- ciple these methods can be applied to visco-elastic properties [27–31]. These approaches, in some sense, all assume an elas- tic response upon unloading, which is impossible to realize in a visco-elastic medium. Hence all attempts to improve on these methods will prove to be uphill battles. Less straightforward is the 0043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2011.09.002