Strain rubber-like state

Finite strain elasticity the behaviour of polymers in the rubber-like state... 

Confirmation of this idea comes from the observation that the natural draw ratio observed for melt-spun fibres is sensitive to the degree of molecular orientation introduced during the spinning process. It appears that the molecular network is formed as the polymer freezes from the melt, is subsequently stretched in the rubber-like state before the polymer cools below Tg and is eventually collected as a frozen stretched rubber. The amount of stretching in the threadline can be measured by shrinking these spun fibres back to a state of zero strain, i.e. isotropy. These results then can be combined with measurements of the natural draw ratio to give the limiting extensibility of the network [33]. 

The Behaviour in the Rubber-Like State Finite Strain Elasticity... 

Here we describe the strain history with the Finger strain tensor C 1(t t ) as proposed by Lodge [55] in his rubber-like liquid theory. This equation was found to describe the stress in deforming polymer melts as long as the strains are small (second strain invariant below about 3 [56] ). The permanent contribution GcC 1 (r t0) has to be added for a linear viscoelastic solid only. C 1(t t0) is the strain between the stress free state t0 and the instantaneous state t. Other strain measures or a combination of strain tensors, as discussed in detail by Larson [57], might also be appropriate and will be considered in future studies. A combination of Finger C 1(t t ) and Cauchy C(t /. ) strain tensors is known to express the finite second normal stress difference in shear, for instance. 

Region C is only observed above Jg and is attributed to the irreversible flow of polymer chains and perhaps some rubber-like extension of chains that are not highly oriented. The temperature dependence of the stress-strain curves measured in water and silicone oil are compared in Figure 12.44 and Figure 12.45, respectively. The measurements in silicone oil are assumed to be characteristic of the dry fiber, since the oil does not plasticize the fiber. The disappearance of the yield point indicates that a transition from the glassy to the rubbery state has occurred near 115 and 70°C in the dry and wet measurements, respectively this corroborates the strong plasticization effect of water that was discussed in Section 12.4. 

The phenomenological approach to rubber-like elasticity is based on continuum mechanics and symmetry arguments rather than on molecular concepts [2, 17, 26, 27]. It attempts to fit stress-strain data with a minimum number of parameters, which are then used to predict other mechanical properties of the same material. Its best-known result is the Mooney-Rivlin equation, which states that the modulus of an elastomer should vary linearly with reciprocal elongation [2],... 

As we can see, both are independent of the strain rate 7. Hence, as a first conclusion. Lodge s equation of state cannot describe the shear thinning phenomenon. Equation (7.147) is in fact identical with Eq. (5.107) derived in the framework of linear response theory. The new result contributed by Lodge s formula is the expression Eq. (7.148) for the primary normal stress difference. It is interesting to note that the right-hand side of this equation has already appeared in Eq. (5.108) of the linear theory, formulating the relationship between G t) and the recoverable shear compliance. If we take the latter equation, we realize that the three basic parameters of the Lodge s rubber-like liquid, rjo, and 1,0 are indeed related, by... 

In uniaxial extension, for example, the cross-sectional area of the body becomes thiner and thiner with increasing creep strain and then the body is broken like the break down of a thread. This class is also a kind of the combined type of. the first and the second factors. Another class of creep failure, which will be considered in this article is that in which the creep strain is not so large and the stress state is kept nearly constant and failure occurs suddenly at some time. The creep process of vulcanized rubbers is one of the processes closest to this second class. That is, both the strain rate and the creep strain are not so high in this creep process except at the moment just after... 

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