A comparison of JKR-based methods to analyze quasi-static and dynamic indentation force curves

The Johnson-Kendall-Roberts (JKR) theory of elastic contact, extended to take viscoelastic effects into account, is used to evaluate work of adhesion and modulus of elastomeric films. In this paper, we present a comparison of five approaches to analyze quasi-static and dynamic JKR force curve data obtained using instrumented indentation. The load-displacement experiments were performed using a 200-microm radius borosilicate glass sphere against poly(dimethyl siloxane) (PDMS). By applying a small oscillation to the tip during indentation, dynamic stiffness vs load data were also obtained for frequencies between 25 and 160 Hz. Direct curve fitting as well as simplified 2- and 3-point analysis methods were used to compare modulus values obtained from load-displacement and stiffness-load data. Fit methods not requiring determination of the initial point of tip-sample contact ("zero" displacement) provided modulus values closest to those obtained by direct curve fitting. The dynamic stiffness-load data revealed a frequency dependent modulus; load-displacement measurements obtained simultaneously were consistent with the relaxed, or low-frequency, modulus of the PDMS sample. These experiments demonstrate that both the frequency dependent and relaxed modulus can be obtained from a single experiment.