Stable necking

Fig. 11.9. Polythene forms o stable neck when it is drown out drown polythene is very strong.

Finally, mild steel can sometimes show an instability like that of polythene. If the steel is annealed, the stress/strain curve looks like that in Fig. 11.10. A stable neck, called a Luders Band, forms and propagates (as it did in polythene) without causing fracture because the strong work-hardening of the later part of the stress/strain curve prevents this. Luders Bands are a problem when sheet steel is pressed because they give lower precision and disfigure the pressing. 

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

For curve A it is possible to draw only one tangent from e = — 1. This implies that once the neck has started in the sample it will continue becoming thinner and thinner until fracture is reached. In the case of curves B and B2 there is the possibility of drawing two tangents that fit Eq. (14.7). The second tangent in each case corresponds to the appearance of a minimum in the curve of nominal stress versus nominal strain, which is necessary for the neck to be stable. Therefore it can be stated that the formation of a stable neck, and thus the existenced of cold drawing, will take place when the condition established by Eq. (14.7) is met at two points of the curve of Of vs. E . 

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. 5.31 Sketches of two particle contact geometries for various dihedral angles (and intetfacial energy ratios). During hquid-phase sintering, the stable neck size to grain size ratio is determined by the equilibrium dihedral angle. Reproduced with permission from [74]. Copyright 2001, Springer...

Stress-strain curves for the transitional Copolymer D/PPO and incompatible PpClS/PPO blends given in Figs. 3 and 4, respectively, again indicate embrittlement at 60 to 80% PPO. Unlike unblended PPO and the high PPO content compatible blends that yield and cold draw, the high PPO content two-phase blends do not appear to initiate a stable neck region and failure occurs shortly after the yield point. 

The nominal stress reaches a minimum. The strain at this point corresponds to the natural draw ratio. In tensile stretching, the strain stays at this approximately constant level for some considerable time as the neck propagates through the specimen and the specimen continues to be elongated - a phenomenon termed stable necking . 

In some materials, notably metals, there is no minimum region 3 and the stress continues to decrease. Then, there is no stable necking and the neck continues to stretch, becoming continuously thinner until fracture. 

Unstable neck Stable neck propagation propagation... 

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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