Polymer Melt Rheology

A Guide for Industrial Practice

F N Cogswell

• Publisher: Woodhead Publishing
• Year: 1981
• ISBN:
  9780857092984
• Topic: Ciencias físicas
• Subtopic: Mecánica de fluidos

This book explores the ways in which melt flow behaviour can be exploited by the plastics engineer and technician for increased efficiency of processing operation, control of end product properties and selection and development of polymers for specific purposes. (reissued with minor corrections 1994)

Chapter One

Fundamental Concepts

In considering the response of thermoplastics during processing we are concerned with three classes of property:

(i) deformation processes, which are necessary to form the product;

(ii) heat and heat transfer, which are necessary to achieve the plastic state;

(iii) chemical and physical change, which may be deliberately induced or adventitious.

1.1 RHEOLOGY

Rheology is the study of deformation and flow: of all the responses of materials it is the one which is most readily felt. We have all squeezed toothpaste tubes, kneaded bread dough or tried to wipe glue from our fingers. Rheology is one way of describing those sensations. For a general introduction to phenomenological rheology an hour in the kitchen is worth more than an hour’s reading, but a general textbook^1,2 can usefully be kept at hand.

The fundamentals of rheology are drawn from mechanics³ and provide the support for our study, which is mainly concerned with how materials systems differ from the ideals of classical mechanics. One approach to rheology is to broaden the field of classical mechanics by defining more generalised materials whose properties are derived logically from an equation of state. The great strength of this approach is that it offers full predictive capacity in any deformation history once the equation of state is described by a few appropriate experiments. At the other end of the spectrum lies the view that the interaction between complex materials and complex histories provides a series of unique situations which can only be studied in their own environment. An intermediate course is to analyse the response of a material system in controlled experiments which are qualitatively similar to elements of its processing history and to discover from such experiments what the properties of the material appear to be. This text takes this third approach—the quantification of the ‘feel’ of a material.

Three material states are relevant to polymer processing:

granular —the form in which materials are fed to the process

melt —the form in which they are usually shaped

solid —the form of the final product, but also one in which some shaping may take place

The great majority of this text deals with the rheology of melts, where most of the deformation occurs. However, in illustrating material property data some data on granular and solid response are included where these properties are relevant to processing.

Rheology is concerned with the relationship between stress (defined as force per unit area), strain (defined as change in dimension per unit dimension) and time.

1.1.1 The Geometry of Deformation

There are three simple deformations.

(a) In simple shear the stress is applied tangentially (Figure 1.1):

$\begin{array}{cc}\mathrm{stress}\left(\mathrm{N/}{\mathrm{m}}^2\right)\hfill & {\mathit{\sigma }}_{\mathrm{s}}=\frac{\mathit{F}}{\mathit{A}}\hfill \\ \mathrm{strain}\left(\mathrm{unity}\right)\hfill & \mathit{\gamma }=\frac{\mathit{x}}{\mathit{h}}\hfill \\ \mathrm{rate}\mathrm{of}\mathrm{strain}\left({\mathrm{s}}^{-1}\right)\hfill & \stackrel{.}{\mathit{\gamma }}=\frac{1}{\mathit{h}}\frac{\mathrm{d}\mathit{x}}{\mathrm{d}\mathit{t}}=\frac{\mathit{v}}{\mathit{h}}\hfill \end{array}$

Figure 1.1 Simple shear: area A and distance h remain constant during deformation

(b) In simple extension the stress is applied normal to the surface of the material (Figure 1.2):

$\begin{array}{cc}\mathrm{stress}\left(\mathrm{N/}{\mathrm{m}}^2\right)& {\mathit{\sigma }}_{\mathrm{E}}=\frac{\mathit{F}}{\mathit{A}}\hfill \\ \mathrm{strain}\left(\mathrm{unity}\right)\hfill & \mathit{\epsilon }={\displaystyle {\int }_{l_0}^{l_1}\frac{\mathrm{d}\mathit{l}}{\mathit{l}}}=\ln \frac{{\mathit{l}}_1}{{\mathit{l}}_0}\hfill \\ \mathrm{rate}\mathrm{of}\mathrm{strain}\left({\mathrm{s}}^{-1}\right)\hfill & \stackrel{.}{\mathit{\epsilon }}=\frac{\mathit{v}}{\mathit{l}}\hfill \end{array}$

Figure 1.2 Simple extension: cross-sectional area A and sample length l both vary during deformation

(c) In bulk deformation the stress is applied normal to all faces. The stress is the applied pressure, P, and the strain is the change in volume per unit volume, δV/V.

With Theologically complex materials, such as polymer melts, the response to a simple deformation process may be complex. Thus in a simple shearing flow there is not only a shear stress but also a ‘pull along the lines of flow’⁴ usually described as the normal stress. The practical deformations of polymer processing are themselves usually complex flows compounded of shear, extension and bulk deformations. One solution to this double complexity is to introduce the elegant simplification of tensor notation which is the starting-point of many Theological texts.⁵ For the purposes of this work it is sufficient to recognise and remember that those complexities exist: with that appreciation it is possible to seek simplifications in the practical response of real materials.

1.1.2 The Rheologicat Response of Materials

There are three types of response to an applied stress: viscous flow, elastic deformation and rupture.

In viscous flow a material continues to deform as long as the stress is applied and the energy put in to maintain the flow is dissipated as heat. Viscosity is defined as the ratio of stress to rate of strain and, in the SI system, has the unit Ns/m². The viscosities of some common materials are given in Table 1.1.

Table 1.1

Viscosities of some Common Materials

	Viscosity (Ns/m^2)	Consistency
Air	10^− 5	gaseous
Water	10^− 3	fluid
Olive oil	10^− 1	liquid
Glycerine	10^0	liquid
Golden syrup	10^2	thick liquid
Polymer melts	10^2–10^6	toffee-like
Pitch	10^9	stiff
Glas...