Formation
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. Considère published the basic criterion for necking in 1885. 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.
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 Considère 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.
Read more about this topic: Necking (engineering)
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