Necking and cold-drawing a phenomenological discussion

Initially the stress rises in an approximately linear manner as the applied strain increases. 

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 . 

The specimen is of finite dimensions, so that at some stage the propagating neck occupies the whole of its length - it reaches the grips at both ends of the 

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. 

There are two ways in which a neck may be initiated. First, if the cross-section of the sample is not uniform, perhaps as a result of a flaw, the element with the smallest effective cross-section will be subjected to the highest true stress, and so will reach the yield point before any other element in the sample. Secondly, a fluctuation in material properties may cause a localized reduction of the yield stress in a given element so that this element reaches the yield point at a lower applied load. When a particular element has reached its yield point it is easier to continue deformation entirely within this element, because it has a lower flow stress stiffness than the surrounding material. Hence, further deformation of the sample is accompanied by straining in only one region and a neck is formed. 

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