Necking in engineering refers to a phenomenon that occurs during the deformation of materials, particularly in ductile materials like metals, under tensile stress. When a material is stretched beyond its yield strength, it begins to deform plastically. As the material is pulled, it may eventually reach a point where localized deformation occurs, leading to a reduction in cross-sectional area in a specific region. This localized thinning is known as necking.
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Necking is localization of tensile deformation into a narrowing part of a specimen. A thinner cross-section carries greater local stress at the same axial force, encouraging further thinning. Work hardening opposes this feedback by increasing the stress required for additional plastic deformation.
For a uniformly extending specimen whose plastic flow approximately conserves volume, write with logarithmic length change . Its load is , where is axial Cauchy stress tensor. ThenThe maximum-load condition is . This ideal estimate assumes uniform uniaxial deformation up to onset and neglects rate effects and damage. In tensile testing, recording both axial force and local specimen diameter distinguishes the start of localization from the later fracture; the maximum engineering stress need not be the maximum local Cauchy stress tensor.