Stress-strain behaviour necking

Figure 11.4 Nominal stress-strain behaviour of a necking tensile specimen...

The argument above is based on the assumption that the stress-strain curve completely defines the material behaviour. In reality, with polymers, stress depends on the strain rate and because necking is associated with a local increase in strain rate the issue is more complex. A strong dependence of stress on strain rate can inhibit necking even when the nominal stress reaches a maximum the existence of the maximum is a necessary condition for necking, but not a sufficient one. Necking in rate-dependent materials has been discussed recently by Sweeney et al. [4]. 

Ductile fracture is accompanied by large deformation. In metals, there are deformations along slip planes and in specimens under test, which are subjected to tensile load, and can be observed as necking and horizontal sections of the stress-strain curves. It is also called plastic behaviour. ... 

Tg especially wl en deformed under the influence of an overall hydrostatic compressive stress. This behaviour is illustrated in Fig. 5.37 where true stress-strain curves are given for an epoxy resin tested in uniaxial tension and compression at room temperature. The Tg of the resin is 100°C and such cross-linked polymers are found to be brittle when tested in tension at room temperature. In contrast they can show considerable ductility in compression and undergo shear yielding. Another important aspect of the deformation is that glassy polymers tend to show strain softening . The true stress drops after yield, not because of necking which cannot occur in compression, but because there is an inherent softening of the material. 

The incorporation of rubber particles into a brittle polymer has a profound effect upon the mechanical properties as shown from the stress-strain curves in Fig. 5.66. This can be seen in Fig. 5.66(a) for high-impact polystyrene (HIPS) which is a blend of polystyrene and polybutadiene. The stress-strain curve for polystyrene shows brittle behaviour, whereas the inclusion of the rubbery phase causes the material to undergo yield and the sample to deform plastically to about 40% strain before eventually fracturing. The plastic deformation is accompanied by stress-whitening whereby the necked region becomes white in appearance during deformation. As will be explained later, this is due to the formation of a large number of crazes around the rubber particles in the material. 

Thus, it seems to be of interest to examine the influence of stress-induced polymorphic changes on the microhardness. While in the case of f-PP two samples comprising the a or phase were characterized, here we wish to follow the microhardness behaviour during the a-j6 polymorphic transition caused by a mechanical field. For this purpose PBT has been selected as a suitable material because of its ability to undergo stress-induced polymorphic transition from the a (relaxed) to the P (strained) form. Bristles of commercial PBT with a diameter of about 1 mm were drawn at room temperature via neck formation (final diameter about 0.5 mm and draw ratio of 3.4) and thereafter annealed in vacuum at 200°C for 6 h with fixed ends (Fakirov etal., 1998). 

This short discussion of non-linear viscoelasticity has been included in order to show that most of the features associated with yield in constant strain-rate tests are directly related to aspects of the creep behaviour. It is not yet clear what significance, if any, can be attributed to a measurement of a yield stress from a load-maximum (especially if the latter is complicated by the occurrence of a necking instability), or to an arbitrary proof strain, although the flow stress (Tf, at which the long-term creep... 

Changes in the morphology and the degree of crystallinity have considerable effects on the mechanical properties of polymers. In particular, the deformation mode of polyethylene changes from uniform extension to necking behaviour above about 50% crystallinity, and while the yield-stresses increase with density, the strain at fracture apparently decreases. In understanding deformation mechanism, and so mechanical properties, morphological studies play a central part,... 

---