necking

A polyethylene sample with a stable neck.

Necking, in engineering or materials science, is a mode of tensile deformation where relatively large amounts of strain localize disproportionately in a small region of the material.^[1] The resulting prominent decrease in local cross-sectional area provides the basis for the name "neck". Because the local strains in the neck are large, necking is often closely associated with yielding, a form of plastic deformation associated with ductile materials, often metals or polymers.^[2]

Formation

The criterion for neck formation was first published in 1885 by Considére.^[3] Three concepts provide the framework for understanding why necks form:

1. Before deformation, in any physical sample of material, local variations in thickness or properties always exist to some degree. (Properties such as hardness or the presence of flaws that cause local concentration of stress are particularly relevant for necking.) To cause the eventual initiation of a neck, such variations need only be infinitesimal in magnitude.
2. During deformation the material's cross-sectional area decreases (Poisson effect).
3. During deformation the material strain hardens. The amount of hardening varies with extent of deformation.

The plot of true stress vs. draw ratio below right shows the quantitative relation between hardening (depicted by the curve's slope) and decrease in cross-sectional area (assumed in this treatment to vary inversely with draw ratio.)

As the material deforms, all locations undergo approximately the same amount of strain as long as it hardens more than its cross-sectional area decreases. But if less hardening occurs, as indicated by the first tangent point in the diagram, strain begins to accumulate disproportionately at the location of highest stress or lowest hardness.

Graphical construction indicating criteria for neck formation and neck stabilization.

The greater the local strain, the greater the local decrease in cross-sectional area, which in turn causes even more localization of strain, leading to an instability that causes the formation of a neck. This instability is called "geometric" or "extrinsic" because it involves the material's macroscopic decrease in cross-sectional area.

Neck Stability

As deformation proceeds the geometric instability causes strain to continue localizing in the neck until the material either ruptures or the necked material hardens enough, as indicated by the second tangent point in the diagram, to cause other regions of the material to deform instead. The amount of strain in the stable neck is called the natural draw ratio^[4] because it is determined by the material's hardening characteristics, not the amount of drawing imposed on the material. Ductile polymers often exhibit stable necks because molecular orientation provides a mechanism for hardening that predominates at larger strains.^[5]

References