Necking, yield stresses

Figure 7.6 Idealized stress-strain curve. Material deforms elastically until yield stress, oyield or Oy is reached. Load increases until the ultimate tensile strength (UTS), which marks the onset of necking. Fracture occurs at a reduced load in the necked region. Toughness is measured by the area under the stress-strain curve.

Figure 1-2 records some typical stress-strain curves for different polymer types. Some polymers exhibit a yield maximum in the nominal stress, as shown in part (c) of this figure. At stresses lower than the yield value, the sample deforms homogeneously. It begins to neck down at the yield stress, however, as sketched in Fig. 11-20. The necked region in some polymers stabilizes at a particular reduced diameter, and deformation continues at a more or less constant nominal stress until the neck has propagated across the whole gauge length. The cross-section of the necking portion of the specimen decreases with increasing extension, so the true stress may be increasing while the total force and the nominal stress...

The tensile stress-strain response of the homopolymer, and of two rubber modified grades of polystyrene, is shown in Fig. 1. The principal mode of deformation is crazing and all three materials exhibit a craze yield stress. However, there is no evidence of localized necking in any of the three materials. The craze yield stress decreases and the elongation to fracture, and the toughness, increase significantly with increase in rubber content. 

Figure 14.5b represents the uniaxial compression test, which uses samples with cylindrical or rectangular cross section. The stress and strain are defined in an analogous way to that of the tensile test. This test overcomes the disadvantages mentioned in relation to a tensile test. The stress is compressive, and consequently there is no possibility of the brittle fracture observed in tensile deformation. Plastic yield can even be seen in thermostable materials, which, under other conditions, can be brittle. In addition, the determination of the yield stress is made under conditions of stable deformation since there is no geometrical reason for the formation of a neck such as occurs in tension. A problem that can arise in this test concerns the diameter/height ratio of the sample. If this ratio is too large friction between plates and sample will introduce a constraint, and if it is very small... 

Figure 14.6 Curve of nominal stress versus nominal strain, curve A with necking and fracture, curve B with formation and propagation of a stable neck. The broken lines represent the magnitude of the yield stress

The stress-strain curve for a material can be represented by means of the function cr, = 12 where represents the true tension stress in MPa and 8 is strain. Calculate the value of the strain at the necking point and the value of the yield stress, [Pg.642]

Figure 8.4 A tensile neck in a polyethylene Tensar soil stabilising grid. Curvature of the principal stress directions increases the average yield stress on the section AA.

It is usual to define the tensile yield stress as the engineering stress F JAq calculated from the maximum E ,ax in the force-extension curve. For metals, a yield stress can be defined as a 0.2% offset from the initial straight elastic response. However, the onset of non-linearity in polymers indicates a viscoelastic rather than a plastic response. The formation of a neck is the first sign of permanent deformation. 

In an incipient neck, the strain rate s increases. The yield stress increases with increasing strain rate (Eq. 8.17), so the second term on the right-hand side of Eq. (8.5) is a stabilising influence. The work input to the yielding process is converted to heat, which is only slowly conducted down the specimen or convected into the surrounding air. As the yield stress is a decreasing function of temperature T, the third term in Eq. (8.5) is a... 

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... 

At higher temperature the yield stress dreps and can ultemately lead to drawing witheut necking)... 

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