General Behaviour of Polymer Melts

In a fluid under stress, the ratio of the shear stress, r. to the rate of strain, y, is called the shear viscosity, rj, and is analogous to the modulus of a solid. In an ideal (Newtonian) fluid the viscosity is a material constant. However, for plastics the viscosity varies depending on the stress, strain rate, temperature etc. A typical relationship between shear stress and shear rate for a plastic is shown in Fig. 5.1. 

As a starting point it is useful to plot the relationship between shear stress and shear rate as shown in Fig. 5.1 since this is similar to the stress-strain characteristics for a solid. However, in practice it is often more convenient to rearrange the variables and plot viscosity against strain rate as shown in Fig. 5.2. Logarithmic scales are common so that several decades of stress and viscosity can be included. Fig. 5.2 also illustrates the effect of temperature on the viscosity of polymer melts. 

When a fluid is flowing along a channel which has a uniform cross-section then the fluid will be subjected to shear stresses only. To define the flow behaviour we may express the fluid viscosity, rj, as the ratio of shear stress, r. 

on the other hand, the channel section changes then tensile stresses will also be set up in the fluid and it is often necessary to determine the tensile viscosity, k, for use in flow calculations. If the tensile stress is a and the tensile strain rate is s then 

For many polymeric melts the tensile viscosity is fairly constant and at low stresses is approximately three times the shear viscosity. 

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