A comprehensive study of simulated cyclic indentation response of linear viscoelastic materials

This paper presents and analyzes the cyclic indentation response of a linear viscoelastic material over the entire time range of the relaxation processes using conical or spherical indenters. Finite Element simulations of cyclic indentation on two Generalized Maxwell materials with different relaxation spectra were performed. A variety of cyclic responses to indentation were generated and analyzed using an analytical method based on elastic contact. It is shown that the elastic contact depth and contact stiffness from the loading curves should be used to identify the relaxation modulus corresponding to the time of loading. The stabilization of the loop has also been studied through the energy ratio, a parameter that describes the evolution of the dissipated energy with cycles. A simple time shift between cyclic creep and monotonous indentation creep of a linear viscoelastic material is demonstrated. The simulated indentation curves and the parameters derived from them were found to be qualitatively similar to the experimental cyclic indentation data on HDPE polymer at different loading rates. Assuming that the first loading is affected by plasticity due to the use of a sharp indenter, a correction was suggested to obtain the elastic relaxation modulus from the experiments. The values of the modulus identified in this way for HDPE compared well with the relaxation modulus identified for this material from previous cyclic tensile experiments. The small discrepancy was attributed to the non-linear viscoelasticity or the viscoplasticity of the polymer.