Indentation Creep and Relaxation Measurements of Polymers
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Indentation Creep and Relaxation Measurements of Polymers Mark R. VanLandingham1, Peter L. Drzal2, and Christopher C. White2 1 U. S. Army Research Laboratory, Weapons & Materials Research Directorate, Aberdeen Proving Ground, MD 21005-5069 2 National Institute of Standards and Technology, Building and Fire Research Laboratory, Gaithersburg, MD 20899-8615 ABSTRACT Instrumented indentation was used to characterize the mechanical response of polymeric materials. A model based on contact between a rigid probe and a linear viscoelastic material was used to calculate values for creep compliance and stress relaxation modulus for epoxy, poly(methyl methacrylate) (PMMA), and two poly(dimethyl siloxane) (PDMS) elastomers. Results from bulk rheometry studies were used for comparison to the indentation creep and stress relaxation results. For the two glassy polymers, the use of sharp pyramidal tips produced responses that were considerably more compliant (less stiff) than rheometry values. Additional study of the deformation remaining in epoxy after creep testing revealed that a large portion of the creep displacement measured was due to post-yield flow. Indentation creep measurements of the epoxy using a rounded conical tip also produced nonlinear responses, but the creep compliance values appeared to approach linear viscoelastic values with decreasing creep force. Responses measured for the PDMS were mainly linear elastic, but the filled PDMS exhibited some time-dependence and nonlinearity in both rheometry and indentation measurements. INTRODUCTION Instrumented indentation is increasingly being used to probe the mechanical response of polymeric and biological materials. These types of materials behave in a viscoelastic fashion, i.e., their mechanical behavior is a function of the test conditions, including the amount of strain, the strain rate, and the temperature. Often in instrumented indentation, however, properties are measured using loading histories and analysis developed for elastic and elasto-plastic materials, where time dependent behavior is normally neglected. Additionally, linear viscoelastic behavior is normally observed only at small strain levels [1] such that the intense strains local to the indenter tip could cause nonlinear behavior. Thus, appropriately accounting for the viscoelastic behavior is important for analyzing indentation data for these types of materials. To better assess the indentation response of viscoelastic materials, analyses of quasi-static contact between a rigid indenter and a linear viscoelastic solid [2, 3] can be used. For the simple loading cases of indentation creep, in which a constant force P0 is applied at t = 0 and held, and relaxation under conditions in which a constant penetration depth h0 is applied at t = 0 and held, solutions by Lee and Radok [2] and Ting [3] appear to be applicable. For the case of indentation creep, these models can be used to relate creep compliance, J(t), to P0, contact area, A(t) = πr2(t), and penetration depth, h(t), for a paraboloidal indent
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