Prediction of Creep Behavior from Stress Relaxation Data for Nonlinearly Viscoelastic Materials

Abstract

Abstract The stress relaxation behavior of many polymeric materials can be expressed in a very simple fashion, because the logarithm of nominal stress fi(t) (based upon the undeformed cross-sectional area of the sample) plotted against the logarithm of time, t, is a straight line. Furthermore, these lines are often parallel, and with linearly viscoelastic materials, one obtains a straight line for the stress-relaxation modulus E(t)=fi(t)/εi, independent of the strain level. Thus, the linear stress-relaxation modulus can be expressed as: Ei(t)=Ei0·t−m, with Ei0 the modulus at t=1 s and m the slope of the straight line in the double logarithmic plot. Most polymers are, of course, nonlinearly viscoelastic (except for infinitesimal deformations); that is, the stress-relaxation modulus is a function of both time and strain. These time and strain effects can be factored out, if the log fi(t) versus log t curves are parallel: Ei(t,εi)=Ei0·t−mϕ(ε), where ϕ(ε), the strain function, is a measure of the nonlinearity of the viscoelastic response. It has been shown elsewhere that Ei0/ϕ(ε) is approximately identical to the modulus observed in the stress-strain measurement. With many polymers, creep experiments also yield approximately straight lines of slope n, when the logarithm of strain εi(t) is plotted against the logarithm of time. With nonlinearly viscoelastic materials, one generally does not obtain a set of parallel lines, when the stress fi, is changed. Therefore, it is not possible to separate the influence of time and stress on the creep compliance Di(t)=εi(t)/fi, as was the case for stress relaxation. It has been shown previously that the creep behavior can be predicted from stress-relaxation data with the help of the convolution integral. The numerical method involved is very laborious, however. It has been shown that the rate of creep may be predicted from the slope of stress-relaxation curves and the shape of the stress-strain curve. The purpose of this paper is to present a method by which the creep behavior of nonlinearly viscoelastic materials can be predicted in a simple fashion from stress-relaxation data. The theoretical predictions have been tested with the stress-relaxation and creep data of a block copolymer.