Relating viscoelastic nanoindentation creep and load relaxation experiments

Nanoindentation characterization of polycarbonate is considered for load-controlled creep testing and displacement-controlled load-relaxation testing using a pyramidal Berkovich tip. An elastic - viscoelastic correspondence approach is used to obtain closed-form analytical solutions for fitting experimental data to deconvolute spring coefficients and viscosity values independently from creep and from relaxation tests. The a priori assumption of linear viscoelasticity is tested by varying the peak load and displacement levels by a factor of twenty. Results demonstrate surprisingly good ageement between parameters computed from relaxation and creep tests and little variation with load or depth. This result supports a linearly viscoelastic analysis under the conditions utilized in the current experiment, namely a Berkovich indenter tip and a glassy polymer. Plastic deformation is not explicitly considered in the current analysis, as all time-independent elastic and plastic deformation was lumped into a single effective deformation resistance term with a quadratic dependence of load on displacement. As such, obtained numerical values of the shear modulus are not representative of the material's elastic modulus. However, the technique demonstrates predictive capability across the interface between load-control and displacement-control, motivating further research on displacement-controlled nanoindentation relaxation for polymeric and biological material characterization.