Rubbery stress

A rubber-like solid is unique in that its physical properties resemble those of solids, liquids, and gases in various respects. It is solidlike in that it maintains dimensional stability, and its elastic response at small strains (<5%) is essentially Hookean. It behaves like a liquid because its coefficient of thermal expansion and isothermal compressibility are of the same order of magnitude as those of liquids. The implication of this is that the intermolecular forces in an elastomer are similar to those in liquids. It resembles gases in the sense that the stress in a deformed elastomer increases with increasing temperature, much as the pressure in a compressed gas increases with increasing temperature. This gas-like behavior was, in fact, what first provided the hint that rubbery stresses are entropic in origin. 

Whether or not a polymer is rubbery or glass-like depends on the relative values of t and v. If t is much less than v, the orientation time, then in the time available little deformation occurs and the rubber behaves like a solid. This is the case in tests normally carried out with a material such as polystyrene at room temperature where the orientation time has a large value, much greater than the usual time scale of an experiment. On the other hand if t is much greater than there will be time for deformation and the material will be rubbery, as is normally the case with tests carried out on natural rubber at room temperature. It is, however, vital to note the dependence on the time scale of the experiment. Thus a material which shows rubbery behaviour in normal tensile tests could appear to be quite stiff if it were subjected to very high frequency vibrational stresses. 

In the lightly cross-linked polymers (e.g. the vulcanised rubbers) the main purpose of cross-linking is to prevent the material deforming indefinitely under load. The chains can no longer slide past each other, and flow, in the usual sense of the word, is not possible without rupture of covalent bonds. Between the crosslinks, however, the molecular segments remain flexible. Thus under appropriate conditions of temperature the polymer mass may be rubbery or it may be rigid. It may also be capable of ciystallisation in both the unstressed and the stressed state. 

Figure 9.3. Stress-strain curves for (a) rigid amorphous plastics material showing brittle fracture and (b) rubbery polymer. The area under the curve gives a measure of the energy required to break the...

Traditional rubbers are shaped in a manner akin to that of common thermoplastics. Subsequent to the shaping operations chemical reactions are brought about that lead to the formation of a polymeric network structure. Whilst the polymer molecular segments between the network junction points are mobile and can thus deform considerably, on application of a stress irreversible flow is prevented by the network structure and on release of the stress the molecules return to a random coiled configuration with no net change in the mean position of the Junction points. The polymer is thus rubbery. With all the major rubbers the... 

It is somewhat difficult conceptually to explain the recoverable high elasticity of these materials in terms of flexible polymer chains cross-linked into an open network structure as commonly envisaged for conventionally vulcanised rubbers. It is probably better to consider the deformation behaviour on a macro, rather than molecular, scale. One such model would envisage a three-dimensional mesh of polypropylene with elastomeric domains embedded within. On application of a stress both the open network of the hard phase and the elastomeric domains will be capable of deformation. On release of the stress, the cross-linked rubbery domains will try to recover their original shape and hence result in recovery from deformation of the blended object. 

Typically, a semicrystalline polymer has an amorphous component which is in the elastomeric (rubbery) temperature range - see Section 8.5.1 - and thus behaves elastically, and a crystalline component which deforms plastically when stressed. Typically, again, the crystalline component strain-hardens intensely this is how some polymer fibres (Section 8.4.5) acquire their extreme strength on drawing. 

The problem of concentration dependence of yield stress will be discussed in detail below. Here we only note that (as is shown in Figs 9 and 10) yield stress may change by a few decimal orders while elastic modulus changes only by several in the field of rubbery plateau and, moreover, mainly in the range of high concentrations of a filler. 

A representative measure of rubbery elasticity of a material may be two quantities dimensionless ratio (ct/t) and characteristic relaxation time 9 = ct/2ty. According to the data of works [37, 38] when fibers are introduced into a melt, ct/t increases (i.e. normal stresses grow faster than stresses) and 0 also increases on a large scale, by 102-103 times. However, discussing in this relation the papers published earlier, we noted in the paper cited that the data were published according to which if fibers were used as a filler (as in work [37]), 9 indeed increased [39], but if a filler represented disperse particles of the type Ti02 or CaC03, the value of 0 decreased [40],... 

In reality the ideal elastic rubber does not exist. Real rubbery materials do have a small element of viscosity about their mechanical behaviour, even though their behaviour is dominated by the elastic element. Even so, real rubbers only demonstrate essentially elastic behaviour, i.e. instantaneous strain proportional to the applied stress, at small strains. 

We conclude that high internal stresses are generated by simple shear of a long incompressible rectangular rubber block, if the end surfaces are stress-free. These internal stresses are due to restraints at the bonded plates. One consequence is that a high hydrostatic tension may be set up in the interior of the sheared block. For example, at an imposed shear strain of 3, the negative pressure in the interior is predicted to be about three times the shear modulus p. This is sufficiently high to cause internal fracture in a soft rubbery solid [5]. 

Rubbery materials beyond the gel point have been studied extensively. A long time ago, Thirion and Chasset [9] recognized that the relaxation pattern of a stress r under static conditions can be approximated by the superposition of a power law region and a constant limiting stress rq at infinite time ... 

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