2.4 Viscoelastic Behavior
2.4.1 Linear Viscoelastic Behavior
A simple definition of linear viscoelastic behavior is that the ratio
of stress to strain is a function of time only and not a function of the
magnitudes of stress and strain [16]. In linear viscoelasticity, effects are
simply additive as in classical elasticity, the difference being that in linear
viscoelasticity it matters at which instant an effect is created [6].
Stress-strain curves for all viscoelastic solids (time dependent
materials) are linear for sufficiently small deformations and strains [17].
To ensure that the specimen cross section does not change appreciably.
Generally polymers exhibit the properties of linear viscoelastic
behavior at low stresses where strain below (0.2-0.5)% [17]. The end of
the region of linear viscoelasticity corresponds to ε = 0.005 [18], so above
this limit the material exhibits nonlinear viscoelastic behavior. Linear
constitutive model is also valid to represent viscoelastic behavior [15].
2.4.1.1 Transient Properties: Creep and Stress Relaxation
If a polymeric material is subjected to a constant stress, the strain
will not be constant but will increase slowly and continuously with time.
The effect is due to a molecular rearrangement induced by the stress .On
the release of the stress, the molecules slowly recover their former spatial
arrangement and the strain simultaneously returns to zero. This effect is
termed creep and is a manifestation of a general property of polymeric
solids known as viscoelasticity [8]. Creep is one of the simplest
experimental modalities for characterizing viscoelastic behavior [13].
For metals except that the very soft metals like lead, creep effects
are negligible at ordinary temperatures. For polymers, creep is often quite
significant at ordinary temperatures and even more noticeable at higher
temperatures [4]. All plastics creep to a certain extent. The degree of
creep depends on several factors, such as the type of plastic, temperature,
and stress level. In this work, creep behavior will be studied.
If the applied load is released before creep rupture occurs, an
immediate elastic recovery will happen, equal to the elastic deformation,
followed by a period of slow recovery as shown in Fig. (2.1), where a
constant load is applied at to and removed at t1. The material in most cases
does not recover to the original shape and a permanent deformation
remains [19]. On removing the load from a polymer, the material can
recover most, or even all, of the strain through giving it sufficient time.
This is different from metals where the strain produced by creep is not
recoverable. The time taken to recover depends on the initial strain and
the time for which the material was creeping under the load [4].
Fig. (2.1): Creep curve with recovery. Ref. [19]
The general form of stress-strain-time relationship can be thought
of a 3-D surface as in Fig. (2.2) [19]. The 3-D figure can be transformed
into three additional ways by which creep data can be presented for
polymers [4], these ways are:
1. Creep curve: strain-time curve at constant stress.
2. Isochronous curve: strain-stress curve at constant time.
3. Isometric (stress relaxation) curve: stress-time curve at constant strain.
Fig. (2.2): 3-D plot of material behavior. Ref. [38]
The counterpart of creep is stress relaxation, which is defined as a
gradual decrease in stress with time under a constant deformation or
strain as shown in Fig. (2.3). This behavior of a polymer is studied by
applying a constant deformation to the specimen and measuring the time
dependent stress required for maintaining that strain [19].
Fig. (2.3): Stress relaxation of plastics. Ref. [38]
Relaxation in polymers is of great practical significance when the
polymers are used in applications involving seals and gaskets [2]. The
stress relaxation test is more difficult to perform than a creep test and has
limited practical applications [19]. The rates of relaxation and creep
depend on the particular material [20].