Steady-State Compliance and Normal Stress Differences

Steady-State Compliance and Normal Stress Differences 

The concept of the Graessley theory that the steady-state concentration of entanglements is diminished during flow at high shear rates implies that the steady-state compliance Ry observed in recovery after cessation of steady-state flow will be larger than J and given by the equation  

The primary normal stress coefficient at low shear rates according to equation 74 of Chapter 3 is given by i,o = 2i . At high shear rates, relations between SJ i(7) and t] y) are provided by some phenomenological theories from a qualitative molecular standpoint, it may be inferred that the decrease in with increasing y is related to the drop in rj and hence, in the framework of the entanglement model, to a decrease in the steady-state concentration of entanglements. 

Stress relaxation following sudden strain for large deformations in both shear and simple extension has been treated for the tube model by Doi and Edwards.22-74 

If the time scale is limited to the terminal zone (I tj). the time-dependent stress can be factored into a function of time and a function of strain (c/. equation 8 of 

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