Necking phenomenon, polymer

In most polymers, a marked necking phenomenon occurs very early after the yield point. This is the reason why it is not possible, in the range of large deformations, to determine strains in a large representative volume element (RVE). Consequently none of the dilatometers utilized to date can be used, except in a very restricted strain range. The latter statement concerns dual clip gage extensometers (axial + transversal) and also hquid displacement dilatometers (23). Once plastic instability has... 

The necking phenomenon observed upon stretching a polymer film at a constant temperature is a well-known consequence of a negative feedback loop driven by the interplay between the increase in temperature associated with the sample deformation and its glassification caused by the heat exchange with the environment (55). Oscillatory behavior and period-doubling in the stress resulting from a constant strain rate have been experimentally observed. 

Thermoplastic polymers subjected to a continuous stress above the yield point experience the phenomenon of cold-drawing. At the yield point, the polymer forms a neck at a particular zone of the specimen. As the polymer is elongated further, so this neck region grows, as illustrated in Figure 7.7. 

There is, however, a limit to the amount of stretch that can be given to a polymer because the phenomenon of necking can intervene and cause rupture of the fiber. In other words, in a polymeric fiber there is a limit to the modulus enhancement that can be obtained by subjecting it to an ever higher draw ratio. As we shall see in Chapter 4, this led to other means of obtaining high stiffness polymeric fibers such as aramid and polyethylene. 

The phenomenon of strain hardening in polymers is a consequence of orientation of molecular chains in the stretch direction. If the necked material is a semicrystalline polymer, like polyethylene or a crystallizable polyester or nylon, the crystallite structure will change during yielding. Initial spherulitic or row nucleated structures will be disrupted by sliding of crystallites and lamellae, to yield morphologies like that shown in Fig. 11-7. 

Stretched films in order to reduce brittleness. Also blister packs from crystalline polymers are often made from biaxially oriented film to obtain good mechanical and optical properties and in addition to avoid variations in wall thickness. An unoriented film may show the necking-in phenomenon in highly strained regions, resulting in an article with thick unoriented and thin highly oriented parts. A biaxially oriented film does not show this necking and a more even wall thickness is obtained. 

In practice then, the point at which a polymer will form a neck is given by drawing a tangent to the true stress-strain curve from the point e = -1, as illustrated in Figure 2. [We note here that in this condition, yielding is a localization phenomenon. It is also possible that yielding can be a material property unrelated to localization and this is touched upon in a subsequent section.]... 

As we have seen above in Section 12.1, sometimes the tensile stretching of a polymer results in strain localisation. So far it has been assumed that the localisation takes the form of a neck, but an alternative geometric form is possible - the shear band. In uniaxial straining, localisation of strain occurs in a narrow band at an oblique angle to the straining direction, as illustrated in Figure 12.38. Shear bands have been observed in many ductile materials. Nadai [2], for instance, gives an account of their occurrence in mild steel. Bowden [110] has described the phenomenon for polymers. 

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