Uniaxial Extension at Constant Strain Rate

The time dependence of stress under conditions of constant strain rate has been discussed for the case of linear viscoelasticity in Section FI of Chapter 3. For uniaxial extension at constant strain rate ei = (l/ ) d /dt), the time-dependent tensile stress ffriO is often expressed in terms of a time-dependent viscosity = An example of the stress growth in such elongational flow from 

It is evident that the steady-state elongational viscosity, unlike the shear viscosity, increases with strain rate, at least at first. From other experiments by Laun and Munstedt in which the steady state was reached, a comparison of and 11(7) can be made, as in Fig. 13-22. With increasing strain rate, rj ris by nearly an order of magnitude and subsequently falls, while i decreases monotonically with in- 

Logarithmic plots of elongational growth viscosity against time for a polyethylene at I S0°C at various rates of elongation as indicated. The shaded area is where is obtained from shear flow experiments. (Bird, after Meissner. ) Reproduced, by permission, from Meissner, Rheol. Acta, 10,230 (1971). Steinkopff Verlag, Darmstadt. 

Comparison of shear viscosity and elongational viscosity plotted logarithmically 

Tensile creep and creep recovery of polyisobutylene of high molecular weight, under large tensile stress X = 1 + 

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FIG. 19-1. Stress-strain hysteresis loop for uniaxial extension at constant strain rate R with reversal of direction at upper right, for cross-linked natural rubber at two temperatures as shown or/X is the engineering stress. After Harwood and Schallamach. Reproduced, by permission, from the Journal of Applied Polymer Science. 

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