Elastic aspects of melt behaviour

11.2.5 Elastic aspects of melt behaviour

While being deformed and forced through an extru- sion die, the melt stores elastic strain energy. As extrudate emerges from the die, stresses are released, some elastic recovery takes place and the extrudate swells. Dimensionally, the degree of swell is typically expressed by the ratio of extrudate diameter to die diameter; the elastic implications of the shear process are expressed by the following modulus:

⊲ 11.3⊳ Figure 11.8 Typical curves of apparent shear viscosity

versus shear stress for five thermoplastics at atmospheric

stress at die wall, and R is the recoverable shear strain. extrusion-grade PP at 230 ° C ; C moulding-grade acrylic at

pressure. A Extrusion-grade LDPE at 170 ° C ;B

230 ° C ; D moulding-grade acetal copolymer at 200 ° C ;E

mer, molecular mass distribution and the level of shear

stress. (Unlike viscosity, dependency of elasticity upon courtesy of Plastics Division, Imperial Chemical Industries

moulding-grade nylon at 285 ° C (after Powell, 1974;

temperature, hydrostatic pressure and average molec- Plc.) .

ular mass is slight.) If the molecular mass distribution is wide, the elastic shear modulus is low and elastic recovery is appreciable but slow. For a narrow distribu-

and that PP is suited to the much faster deformation tion, with its greater similarities in molecular lengths, process of injection-moulding. In all cases, Newtonian

recovery is less but faster. With regard to stress level, flow is evident at relatively low levels of shear stress.

the modulus remains constant at low shear stresses but The following type of power law equation has been

usually increases at the high stresses used commer- found to provide a reasonable fit with practical data and

cially, giving appreciable recovery. has enabled pseudo-plastic behaviour to be quantified

The balance between elastic to viscous behaviour in a convenient form:

during deformation can be gauged by comparing the

deformation time with the relaxation time or ‘natural

from the Maxwell model of deformation. The term vis- can be derived from the line gradient of a graphical

coelasticity originated from the development of such plot of log viscosity versus log shear rate. In practice,

models (e.g. Maxwell, Voigt, standard linear solid the power law index n ranges from unity (Newtonian

(SLS)). The Maxwell model is a mechanical analogue flow) to <0.2, depending upon the polymer. This index

that provides a useful, albeit imperfect, simulation of decreases in magnitude as the shear rate increases

viscoelasticity and stress relaxation in linear polymers and the thermoplastic melt behaves in an increasingly

above T g (Figure 11.9). It is based upon conditions pseudo-plastic manner.

of constant strain. A viscously damped ‘Newtonian’ So far, attention has been concentrated on the vis-

dashpot, representing the viscous component of defor- cous aspects of melt behaviour during extrusion and

mation, and a spring, representing the elastic compo- injection-moulding, with emphasis on shear processes.

In forming operations such as blow-moulding and

0 , as follows: filament-drawing, extensional flow predominates and

0 ⊲ 11.4⊳ tensile stresses become crucial; for these conditions,

it is appropriate to define tensile viscosity, the coun- terpart of shear viscosity, as the ratio of tensile stress

is sufficient time for viscous movement of chain

360 Modern Physical Metallurgy and Materials Engineering

36 kN s m 2 and 4.6 kN m 2 , respectively, the relax- ation time is roughly 8 s. Hence sagging of the parison under its own weight will be predominantly elastic.