Numerical analysis of the creep of the contact and recovery of the imprint on amorphous polymer surfaces
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Numerical analysis of the creep of the contact and recovery of the imprint on amorphous polymer surfaces T. Chatel · V. Le Houérou · H. Pelletier · C. Gauthier
Received: 29 March 2012 / Accepted: 20 December 2012 © Springer Science+Business Media Dordrecht 2012
Abstract This article attempts to analyze the viscoelastic behavior of an amorphous polymer during a microindentation test. The viscoelastic behavior of an amorphous polymer (poly(methyl methacrylate), PMMA) is derived from different relaxation tests performed under different applied true strains. A generalized Maxwell model is then used to identify the mechanical parameters of the viscoelastic behavior. The numerical results display good correlation with experiments during the creep phase. The uniaxial relaxation test used to identify the viscoelastic behavior is chosen in relation to the experimental conditions of indentation. The results obtained for the recovery phase allow a first analysis of the strain and von Mises equivalent stress fields during indentation test. The recovery of the imprint left on the surface seems to depend on the location of the strain maxima. If a strain level of 10 % or more reaches the surface of the deformed volume, a permanent imprint is obtained. Otherwise the residual imprint may be considered to be completely healed even if the subsurface has partially yielded during the loading phase or creep time. Keywords Indentation · Numerical analysis · Viscoelasticity · Polymer · Creep · Recovery · Spherical tip
1 Introduction Previous experimental data (Chatel et al. 2011) are compared to the results obtained by numerical analysis. The analysis of the creep during the contact between a sphere and a surface started with the analytical description of Lee and Radok (1960), where the creep of a sphere/plane contact was modeled with a linear viscoelastic behavior. Different studies (Cheng et al. 2005; Lu et al. 2003; Galli and Oyen 2009; Pelletier et al. 2008) permitted identification of the mechanical properties of a viscoelastic material. If assimilation with the bulk mechanical properties of the material is almost satisfactory during the loading phase, T. Chatel · V. Le Houérou · H. Pelletier · C. Gauthier () CNRS Institut Charles Sadron, UPR22, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France e-mail: [email protected]
Mech Time-Depend Mater
our understanding of the phenomena appearing during the creep phase needs to be improved with the help of an analysis of the discharge phase and recovery. The experimental results for a creep test under microindentation have revealed the difficulty of analyzing the phenomena observed (Chatel et al. 2011). The study of residual imprints as a function of recovery time has improved our understanding of the creep phase, but the global prediction of the viscoelastic behavior of PMMA during a microindentation test remains incomplete. A numerical analysis is commonly employed to obtain more information on the evolution of the strain and stress fields (Dooling et al
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