Experimental analysis of viscoelastic behavior in nanoindentation

Conventional analysis of load displacement curves in nanoindentation experiments determine modulus by using the elastic portion of the unloading slope or power law fitting the unloading slope. For polymeric materials, however, this analysis is not adequate because they behave viscoelastically. In companion research, L. Cheng has developed analytical models for flat tip and spherical tip indentation using a three element Kelvin-Voigt model, with a spring in series with a parallel dashpot and a spring for compressible and incompressible materials. Incompressible (v = 0.5) polydimethylsiloxane coatings with thicknesses of 2 and 78 microns, a compressible (v = 0.33) bulk polystyrene (PS) and a 16 μm styrene-acrylate block copolymer coating (v = 0.33) have been used to verify the models. The polymers were indented using flat tip and spherical tip indenters with a nanoindentation apparatus in creep (constant load) and relaxation modes (constant depth). The data was fit to the analytical models using a non-linear least squares fit algorithm varying three parameters. In general the fitted elastic and shear moduli compared favorably with conventional rheological and mechanical measurements on the same bulk polymers. However, it appears that the agreement for the thin film analysis can be improved by taking the hydrostatic pressure dependence of the modulus and substrate effects into consideration.