Nanoindentation creep and stress relaxation tests of polycarbonate: Analysis of viscoelastic properties by different rheological models

Abstract

Feedback-controlled nanoindentation with a Berkovich diamond tip has been used to perform creep and stress relaxation tests on polycarbonate at room temperature for a wide range of loads (10 – 30000 μN) and indentation depths (30 – 3000 nm). The creep compliance J(t) and relaxation modulus G(t) have been calculated from experimental data as a function of time in the range t = 0.1 – 100 (1000) s. The data are analysed by different rheological models which are compared: (1) the Burgers model, (2) the generalised Maxwell/generalised Kelvin model, and two empirical approaches: (3) a logarithmic model, and (4) a power law model. The Burgers model gives a poor description of the material behaviour since it assumes a steady-state flow of material which is not observed in the experimental time range. The generalised models yield a set of discrete relaxation- and retardation time constants. It is shown that these time constants do not correlate with specific molecular moving processes in the polymer, but are only one of several possible parameterisations of the creep and relaxation curves. Numerical differentiation of G(t) and J(t) shows that polycarbonate has continuous relaxation- and retardation time spectra, respectively, and the dynamic viscosity η(t) of the material increases linearly with time. The behaviour of polycarbonate is best represented by the empirical power law model, which allows optimum fit of creep/relaxation curves, relaxation and retardation time spectra and time-dependent viscosity.