Yield stresses activated process models

Emulsions with a high volume fraction of droplets (0 > 0.64) and foams show solidlike properties such as a yield stress and a low-frequency plateau value of G. The magnitudes of the yield stress and elastic modulus can be estimated using simple cellular foam models. These and related models show that at low shear rates where the shear stress is close to the yield value, the flow occurs by way of intermittent bubble-reorganization events. The dissipative processes that occur during foam and emulsion flows are still under active investigation. 

Phenomenologically, the rate and temperature dependence of the yield stress of semi-crystalline poljuners can be described by the Eyring activated state model, as discussed earlier, with either one (100,101) or two (46,102) activated processes. However, developing a theory for the yield of semi-crystalline polymers is clearly complicated by the presence of two distinct phases. It is imclear at present whether... 

Two principal approaches have been used to model the yield behaviour of polymers. The first approach addresses the temperature and strain-rate dependence of the yield stress in terms of the Eyring equation for thermally activated processes [39]. This approach has been applied to many amorphous and crystalline polymers (see Section 12.5.1) and links have been established with molecular relaxation processes determined by dynamic mechanical and dielectric measurements and with non-linear viscoelastic behaviour determined by creep and stress relaxation. The Eyring approach assumes that the yield process is velocity controlled, i.e. the yield process relates to existing thermally activated processes that are accelerated by the application of the yield stress to the point where the rate of plastic deformation reaches the applied macroscopic strain rate. This approach has... 

A final consideration is that the Argon theory essentially regards yield as nucleation controlled, analogous to the stress-activated movement of dislocations in a crystal produced by the applied stress, aided by thermal fluctuations. The application of the Eyring theory, on the other hand, implies that yield is not concerned with the initiation of the deformation process, but only that the application of stress changes the rate of deformation until it equals imposed rate of change of strain. The Eyring approach is consistent with view that the deformation mechanisms are essentially present at zero stress, and are identical to those observed in linear viscoelastic measurements (site model analyses in Section 7.3.1). Here, a very low stress is applied merely to enable detection of the thermally activated process, without modification of the polymer structure. 

The Bauschinger effect is the term for asymmetry in the yield response of a material between tension in compression. For isotropic polymers the effect is small (the yield stress in compression being slightly higher than that in tension) and can be seen as a consequence of the differing levels of hydrostatic pressure. It can thus be adequately modelled by the inclusion of the pressure activation volume in the Eyring process. For oriented polymer, however, the asymmetry is much greater (see the early results for oriented polypropylene of Duckett et al. [18], where a draw ratio of 5 increased the yield stress by a factor of 8). 

In a further development of the continuous chain model it has been shown that the viscoelastic and plastic behaviour, as manifested by the yielding phenomenon, creep and stress relaxation, can be satisfactorily described by the Eyring reduced time (ERT) model [10]. Creep in polymer fibres is brought about by the time-dependent shear deformation, resulting in a mutual displacement of adjacent chains [7-10]. As will be shown in Sect. 4, this process can be described by activated shear transitions with a distribution of activation energies. The ERT model will be used to derive the relationship that describes the strength of a polymer fibre as a function of the time and the temperature. 

First, the role of rubber modification in high rate impact is to suppress spallation by inducing the material to yield in the presence of dynamic tensile stresses arising from impact. Second, this yield-spall transition occurs at different strain rates for different rubber contents and may be predictable using quasistatic, low temperature tests of this type. These tests can also provide information concerning the basic nature of the yield process in these materials through the activation parameters which are obtained. Third, the Bauwens-Crowet equation seems to be a good model for the rate and temperature sensitive behavior of the American Cyanamid materials and is therefore a likely candidate for a yield criterion to use in the analytical code work on these materials which we hope to perform as a continuation of this work. 

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