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Necking results from an instability during tensile deformation when a material's cross-sectional area decreases by a greater proportion than the material strain hardens

Necking results from an instability during tensile deformation when a material's cross-sectional area decreases by a greater proportion than the material strain hardens. Three concepts provide the framework for understanding neck formation.

Before deformation, all real materials have heterogenieties such as flaws or local variations in dimensions or composition that cause local fluctuations in stresses and strains. To determine the location of the incipient neck, these fluctuations need only be infinitesimal in magnitude.

During tensile deformation the material decreases in cross-sectional area. (Poisson effect)

During tensile deformation the material strain hardens. The amount of hardening varies with extent of deformation.

The latter two items determine the stability while the first item determines the neck's location.

Graphical construction for a material that deforms homogeneously at all draw ratios.

The plots at left show the quantitative relation between hardening depicted by the curve's slope and decrease in cross-sectional area assumed in the treatment to vary inversely with draw ratio for a material that forms a stable neck top and a material that deforms homogeneously at all draw ratios bottom.

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, as shown at small draw ratios in the top diagram and at all draw ratios in the bottom. But if the material begins to harden by a smaller proportion than the decrease in cross-sectional area, as indicated by the first tangent point in the top diagram, strain concentrates at the location of highest stress or lowest hardness. The greater the local strain, the greater the local decrease in cross-sectional area, which in turn causes even more concentration 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

'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. The resulting prominent decrease in local cross-sectional area provides the basis for the name "neck". Because the local strains in the neck are great, necking is often closely associated with yielding, a form of plastic deformation associated with ductile materials, often metals or polymers


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