Nonlinear Behavior in Uniaxial Extension

In addition to non-Newtonian shear viscosity, which has been mentioned in Sections C2 and C5. there are a wide variety of nonlinear phenomena observed in various types of deformation, especially shear and simple (uniaxial) extension for deformations with large strains and large strain rates. Some of these have been mentioned in Chapters I and 3. Nonlinear behavior in shear has been studied mostly 

The time-dependent stress observed in relaxation experiments with large uniaxial extensions is often expressed in terms of a reduced force or apparent Young s modulus, as defined in equation 10 of Chapter 6, by analogy with the statistical theory of rubberlike elasticity  

Logarithmic plot of Ea(t, X) as deHned by equation 30 against t reduced to 0°C, for a 1,2-polybutadiene at various stretch ratios X as indicated. (Noordermeer and Fcrry. ) Reproduced, by permission, from the Journal of Polymer Science. 

The course of stress relaxation in an uncross-linked polymer is illustrated in Fig. 13-19 for a 1,2-polybutadiene by plotting Ea(t, X) logarithmically against t for various X. If Ea(t) were independent of X, the curves should coincide. If the stress could be factored into a function of time and a function of strain, as in equation 8 of Chapter 6, the curves should be parallel. Such factorization has been observed over more limited time scale for stress relaxation and other time-dependent experiments, but when both plateau and terminal zones are included the curves such as in Fig. 13-19 are not parallel,as first noted by Aral and Ni-inomi.  

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