Evaluation of the dynamic-mechanical properties of solids from a cooperative model for stress relaxation

Abstract

For many solid materials the stress relaxation process obeys the universal relation F = -(da/d In t)max = (0.1 -t-0.01) ((70 --0"i) , regardless of the structure of the material. Here a denotes the stress, t the time, a o the initial stress of the experiment and (7 i the internal stress. A cooperative model accounting for the similarity in relaxation behaviour between different materials was developed earlier. Since this model has a spectral character, the concepts of linear viscoelasticity are used here to evaluate the corresponding prediction of the dynamic mechanical properties, i.e. the frequency dependence of the storage E' (o)) and loss E" (o)) moduli. Useful numerical approximations of E'(~o) and E" (m) are also evaluated. It is noted that the universal relation in stress relaxation had a counterpart in the frequency dependence of E' (co). The theoretical prediction of the loss factor for high-density polyethylene is compared with experimental results. The agreement is good.

Description of the Mechanical Properties of Viscoelastic Materials Using a Modified Anelastic Element

“…the slope at the inflection point of the normalized stress relaxation curve represented as a function of In t is equal to -(0.10 k 0.01). This empirical result has been recently explained by a two-level cooperative model [45] leading to the normalized transient function of the MAE given in (21).…”

“…In this case it results w(x) = x -In [In (e) + 11 P) (45) which is represented in Fig. 4c, for different values of 8.…”

Stress Relaxation in Solids

“…In ref. [15] it is shown that agreement between the experimental values of tan6 and those calculated from the cooperative model is rather good in the case of high density polyethylene (HDPE) at room temperature.…”

“…Assuming that the concepts of linear viscoelasticity are applicable the storage and loss moduli E1(w) and E"(w), can be evaluated from and where w is the angular frequency. This evaluation can be performed numerically but useful analytical approximations of E9(w) and Elf( U) are derived in ref [15]…”