Evaluation of different methods of relaxation modulus extraction for linear viscoelastic materials from ramp-constant strain experiments

Abstract

Experimental determination of relaxation modulus of linear viscoelastic materials, in principle, requires the application of an ideal step strain to the specimen. This could not be achieved in practice, however, and is replaced by a ramp-constant strain history. The material response to the ramp-constant strain deviates from its ideal step response and should be corrected. Different correction methods have been proposed for the full-range modulus extraction from ramp-constant strain experiments, and among them the three methods of Zapas–Phillips, Lee–Knauss, and Sorvari–Malinen are distinguishable. Few comparative studies have been performed on these methods, all of which have been based on the simulated response of a hypothetic material rather than on the real experimental data. Furthermore, the simulations have been performed assuming specific material models not essentially appropriate for the material parameter extraction purposes, leading to undesirable errors in the simulation results. In this paper, the above-mentioned methods are compared based on both simulation and experimental approaches. The simulation results show that all methods effectively improve the range of modulus extraction compared to the well-known “ten-times rule”, and the Lee–Knauss method provides the best predictions, in contrast to some of the previously published results. Considering the experimental results, however, it is observed that all the modulus extraction methods lose their performance if a sufficiently small sampling rate is not provided by the experimental data acquisition system. It has been discussed that the conclusion of some authors regarding the invalidity of ten-times-rule stems from a misinterpretation of their simulation results and is faultful.