Uncertainty in Characterizations of Isotropic Linear Viscoelastic Shear and Bulk Moduli from 1 - D Tensile Experiments

Abstract

Previous experiments at constant strain rates, while valuable in their own right, indicated that relaxation experiments at nominally constant strains are more conducive to obtaining data over numerous time decades in order to establish proper moduli/compliances, which cover the entire time range from instantaneous to fully relaxed moduli. The purpose of this paper, then, is to report on a series of relaxation experiments in order to produce high fidelity characterization of the statistical properties of viscoelastic materials, such as relaxation moduli, creep compliances, times to achieve constant strains, etc. Photometric, load cell, extensometers and accelerometer equipment was employed for data harvesting. Beta probability density functions with time dependent parameters were used to best describe the statistics as they answer the need to represent the data in a finite interval. A new analytical protocol for material determination, called the direct numerical calculation of viscoelastic moduli (DVM), has been developed and tested. Various protocols to determine the actual time to complete experimental loading phases are formulated as well as simple dynamic experiments for evaluating instantaneous moduli. Parallel to the above development the instantaneous modulus is determined from separate dynamic experiments and its statistical results are combined with 1 Copyright© the quasi-static experimental statistical data, thus providing time dependent probability density functions covering the entire positive time domain t ≥ 0. The time when the loading cycle ends is calculated from extensometers and its non-trivial influence on the characterization process is evaluated.It is shown that a stochastic elastic/viscoelastic correspondence principle can only be formulated based on integral transforms, since the constitutive relations are no longer of the convolution type. However, its utility for purposes of analysis of stress and strains is severely limited compared deterministic EVCPs because of the complicated non-convolution type constitutive relations.