Hard protective overlayers on viscoelastic-plastic substrates
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Hard protective overlayers on viscoelastic-plastic substrates W. W. Gerberich, A. Strojny, K. Yoder, and L-S. Cheng Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 (Received 2 October 1998; accepted 17 March 1999)
A simple superposition solution for a point-loaded elastic plate on a soft substrate is proposed. The solution considers a “drumhead” being elastically bent into a compliant substrate that is viscoelastic-plastic. With simplifying assumptions it is found that the drumhead and substrate support loads proportional to d 1/2 and d 3/2 , respectively, where d is the vertical point displacement. At fixed displacement, relaxation proceeds at high loads, but if sufficiently unloaded, recovery or increased load results with time. Qualitative verification of the time-dependent drumhead solution is shown by relaxation and recovery data on polycarbonate covered by polysiloxane, composite or diamondlike carbon (DLC) coatings, and films.
I. INTRODUCTION
There are four basic problems associated with the determination of properties and their application to modeling protective overlayers on viscoelasticplastic substrates: (i) How to best characterize elastic moduli in both the overlayer and the substrate, the latter if viscoelastic-plastic is yet to be properly modeled; (ii) A yield stress for the viscoelastic-plastic substrate as well as the overlayer if appropriate; (iii) The modeling of a bilayer system wherein the overlayer is acting as a stretched elastic membrane under bending and the substrate is elastic-plastic (or viscoelastic-plastic). This has been defined as the platebending effect by Page et al.1–3 which we will dub the “drumhead” effect; (Drumhead credit goes to D. F. Bahr, Washington State University.) (iv) Experimental and theoretical approaches to the interpretation of sphericaltip indentation into viscoelastic-plastic media via creep and relaxation analysis; (v) Modeling and measurement of the combined relaxation or recovery of partially unloaded indentations into such a bilayer system. We will refer to these four basic problems and their Ù combination (the fifth) as E p , sys , D, E p std, and D p p where E , E std, and sys are the time independent or Ù dependent reduced moduli and yield strength and D, D refer to the time independent loading and subsequent relaxation or recovery. Addressing all of these problems with rigor is beyond the scope of this paper. We further reduce the complexity by making a few simplifying assumptions: (i) Sufficiently short loading and unloading times are considered so as to allow moduli to be analyzed; (ii) Similarly, short-time loading sequences considered for constitutive behavior of the viscoelasticplastic substrate allow yield strength determinations; (iii) The membrane or hard overlayer is assumed to be elastic with no cracking, crushing, or permanent indenter 2210
http://journals.cambridge.org
J. Mater. Res., Vol. 14, No. 6, Jun 1999
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