Page 59 - Plastics Engineering

42 Mechanical Behaviour of Plastics
the modulus may be regarded as a constant. In contrast, thermoplastics at room
temperature behave in a similar fashion to metals at high temperatures so that
design procedures for relatively ordinary load-bearing applications must always
take into account the viscoelastic behaviour of plastics.
For most traditional materials, the objective of the design method is to deter-
mine stress values which will not cause fracture. However, for plastics it is more
likely that excessive deformation will be the limiting factor in the selection of
working stresses. Therefore this chapter looks specifically at the deformation
behaviour of plastics and fracture will be treated separately in the next chapter.

2.2 Viscoelastic Behaviour of Plastics
For a component subjected to a uniaxial force, the engineering stress, (T, in the
material is the applied force (tensile or compressive) divided by the original
cross-sectional area. The engineering strain, E, in the material is the extension
(or reduction in length) divided by the original length. In a perfectly elastic
(Hookean) material the stress, (T, is directly proportional to be strain, E, and
the relationship may be written, for uniaxial stress and strain, as

(T = constant x E (2.1)
where the constant is referred to as the modulus of the material.
In a perfectly viscous (Newtonian) fluid the shear stress, t is directly propor-
tional to the rate of strain (dy/dt or p) and the relationship may be written as
t = constant x i. (2.2)

where the constant in this case is referred to as the viscosity of the fluid.
Polymeric materials exhibit mechanical properties which come somewhere
between these two ideal cases and hence they are termed viscoelastic. In a
viscoelastic material the stress is a function of strain and time and so may be
described by an equation of the form

(J = f(E, t) (2.3)
This type of response is referred to as non-linear viscoelastic but as it is not
amenable to simple analysis it is often reduced to the form

0 = E. f(t) (2.4)
This equation is the basis of linear viscoelasticity and simply indicates that,
in a tensile test for example, for a fixed value of elapsed time, the stress will
be directly proportional to the strain. The different types of response described
are shown schematically in Fig. 2.1.
The most characteristic features of viscoelastic materials are that they exhibit
a time dependent strain response to a constant stress (creep) and a time depen-
dent stress response to a constant strain (relaxation). In addition when the