Spherical Indentation Creep Following Ramp Loading
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Spherical Indentation Creep Following Ramp Loading Michelle L. Oyen Department of Biophysical Sciences and Medical Physics University of Minnesota Minneapolis, MN 55455
ABSTRACT: Depth-sensing indentation testing is a common way to characterize the mechanical behavior of stiff, time-independent materials but presents both experimental and analytical challenges for compliant, time-dependent materials. Many of these experimental challenges can be overcome by using a spherical indenter tip with a radius substantially larger than the indentation depth, thus restricting deformation to viscoelastic (and not plastic) modes in glassy polymers and permitting large loads and contact stiffness to be generated in compliant elastomers. Elastic-viscoelastic correspondence was used to generate spherical indenter solutions for a number of indentation testing protocols including creep following loading at a constant rate and a multiple ramp-and-hold protocol to measure creep response at several loads (and depths) within the same test. The ramp-creep solution was recast as a modification to a step-load creep solution with a finite loading rate correction factor that is a dimensionless function of the ratio of experimental ramp time to the material time constant. Creep tests were performed with different loading rates and different peak load levels on glassy and rubbery polymeric materials. Experimental data are fit to the spherical indentation solutions to obtain elastic modulus and time-constants, and good agreement is found between the results and known modulus values. Emphasis is given to the use of multiple experiments (or multiple levels within a single experiment) to test the a priori assumption of linear viscoelastic material behavior used in the modeling. INTRODUCTION: Depth-sensing indentation (DSI, “nanoindentation”) has become a common technique for measuring mechanical behavior of a large variety of materials, including polymers and biological tissues. However, standard elastic-plastic (Oliver-Pharr [1]) analysis of indentation data obtained with sharp (conical or pyramidal) indentation tips does not always result in accurate results for polymeric materials [2]. In particular, elevated estimates of the elastic modulus have been observed, due both to viscoelastic creep effects and other less-understood problems associated with the assumed contact mechanics [3]. In many cases, direct measurement of the viscoelastic behavior of a polymer or tissue is desired, as opposed to techniques that seek to eliminate viscoelastic effects and isolate the elastic modulus [4]. The current investigation was undertaken to establish simple experimental techniques for DSI analysis of polymeric and biological tissues, with an emphasis on time-dependent mechanical behavior. Elastic-viscoelastic correspondence analysis [5,6] was used to examine creep responses under spherical indentation conditions. The applicability of assumptions of linear viscoelasticity and creep functional form (made a priori in an elastic-viscoelastic corresponden
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