Rubber-like behaviour

Reactor exposure causes decrease in elongation at break and increase in the modulus of elasticity due to crosslink formation [434]. High doses are, however, required to produce appreciable change. 7-Irradiation gives decreased tensile strength and elongation at break for nylon 6 and nylon 6, 6 [433] (Fig. 47). The dynamic mechanical properties of nylon 6, 6 were studied by Sauer et al. [436] after neutron irradiation. Rubber-like behaviour was observed for temperatures above the main softening temperature. 

Equation (3.15) reminds us that rubber-like behaviour requires the thermal energy kT of rotating C—C bonds. The network chain acts as a linear spring, which is stiffer for short chains than for long chains. 

Fig. 6.2 Possible forms of the load-extension curve for a polymer (a) low extensibility followed by brittle fraction (b) localised yielding followed by fracture, (c) necking and cold drawing, (d) homogeneous deformation with indistinct yield and (e) rubber-like behaviour.

The simplest model of rubber-like behaviour is the phantom network model. The term phantom is used to emphasize that the configurations available to each strand are assumed to depend on the positions of the junctions only. Consequently, the configurations of one chain are independent of the configurations of neighbouring strands. For many purposes, the strands can be treated as Gaussian random coils. Even in this simplest case, an exact solution is not a trivial task as will be outlined in Sect. 3. 

Fig. 4. Load-extension curves for a typical polymer tested at four temperatures showing different regions of mechanical behaviour. 1. Brittle fracture. 2. Ductile failure. 3. Necking and cold drawing. 4. Rubber-like behaviour.

Glass transition temperature (Tg) The temperature where the polymer transits from a rubbery state to a glassy state. The thermal expansion coefficient in the rubbery state is two to three times greater than in the glassy state because of greater molecular (chain) mobility. Tg varies between —120 and +130°C, depending on the type of polymer. Rubbery polymers such as elastomers have —ve Tg, i.e. Tg is well below their use temperature, whereas common plastics such as polyvinyl chloride (PVC) polymers have + ve Tg, i.e. Tg is well above their use temperature. However, if used above its Tg, PVC would display the usual rubber-like behaviour. 

As already discussed (Section 6.1.1 above) molecular mass has a large effect in the glass transition range, where viscous flow transforms to a plateau range of rubber-like behaviour due to entanglements between the longer molecular chains. 

Since the sample has both viscosity and elasticity, it is said to be viscoelastic, and the phenomenon is called viscoelasticity. As the name impHes,in this region the polymer liquid exhibits flow characteristics which are reflected in the term viscosity and rubber-like behaviour reflected in elasticity . 

Figure 2.1 Load-elongation curves for a polymer at different temperatures. Curve A, brittle fracture curve B, ductile failure curve C, cold drawing curve D, rubber-like behaviour.

It will be convenient to discuss these various aspects separately as follows (1) behaviour at large strains in Chapters 3 and 4 (finite elasticity and rubber-like behaviour, respectively) (2) time-dependent behaviour in Chapters 5-7 and 10 (viscoelastic behaviour) (3) the behaviour of oriented polymers in Chapters 8 and 9 (mechanical anisotropy) (4) non-linearity in Chapter 11 (non-linear viscoelastic behaviour) (5) the non-recoverable behaviour in Chapter 12 (plasticity and yield) and (6) fracture in Chapter 13 (breaking phenomena). However, it should be recognised that we cannot hold to an exact separation and that there are many places where these aspects overlap and can be brought together by the physical mechanisms, which underlie the phenomenological description. 

Fig. 6 shows the behaviour of stress and orientation at Tg + 9 C for various strain rates. It is clearly seen that only the first part of the stress-strain curve is affected by the strain rate, but the orientation is not modified within the accuracy of our experiments. Comparison with Fig. 7 shows that at a higher temperature at Tg + 14.5 C, both the stress reflecting the rubber-like behaviour and the orientation are functions of the strain rate. 

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