Stress Growth at Inception of Steady Shearing Flow

The next flow we consider is the start-up of steady shearing flow in a fluid which is initially at rest. For t 0, = 0 and for 12 0, the flow pattern vx = K0y, vy = 0, vz = 0 is maintained, where k0 is a constant for all t 0. We must then seek a solution to Eq. (5.1) with k — k0. 

The function —(tyx—TyXtS)+/(t]—t Ko from Eq.(11.8) is displayed in Fig. 7. It is seen that the shear stress exhibits the stress overshoot  

9) and (11.10) give (rxx — tyy)+ and (tyy—tzz)+ with the same sign during the stress growth process. There are no experimental data on the quantity (ryy — tzz)+ during the stress growth process. 

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Stress Growth at Inception of Steady Shearing Flow... 

Stress growth at inception of steady shearing flow... 

In stress growth at inception of steady shearing flow, the rigid dumbbells give a stress expression which is dependent on the steady-state shear rate however, elastic dumbbells do not. Also the rigid dumbbell model predicts stress overshoot, a phenomenon which the elastic dumbbell model cannot describe. 

Many of the devices mentioned in the preceding paragraph can also be used to measure stress growth following the inception of shear at a constant shear rate, as the condition of steady-state shear flow is approached. 

Figure 9.18 refers to two other standard experiments. It depicts the results of stress growth experiments, conducted again on a polyethylene melt. The figure includes both measurements probing shear and tensile properties, thus facilitating a direct comparison. Curves show the building-up of shear stress upon inception of a steady state shear flow at zero time and the development of tensile stress upon inception of a steady state extensional flow. Measurements were carried out for various values of the shear rate 7 or the Hencky rate of extension ch ... 

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