Stable neck, true stress

To see what is going on physically, it is easier to return to our first condition. At low stress, if we make a little neck, the material in the neck will work-harden and will be able to carry the extra stress it has to stand because of its smaller area load will therefore be continuous, and the material will be stable. At high stress, the rate of workhardening is less as the true stress-true strain curve shows i.e. the slope of the o/e curve is less. Eventually, we reach a point at which, when we make a neck, the workhardening is only just enough to stand the extra stress. This is the point of necking, with... 

Figure 14.7 Considere construction for tensile strain. The maximum and minimum values of a in Figure 14.6 are given by the tangents to the curve of true stress ct, from 8 = -1. Polymer A forms an unstable neck polymers Bj and B2 form stable necks.

Fig. 5.25 Schematic curves of true stress, cr against nominal strain, e for polymers showing the Considere construction, (a) Unstable neck, (b) stable neck.

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