Lüders bands are a type of plastic bands, slip band or stretcher-strain mark which are formed due to localized bands of

plastic deformation In engineering, deformation (the change in size or shape of an object) may be ''elastic'' or ''plastic''. If the deformation is negligible, the object is said to be ''rigid''. Main concepts Occurrence of deformation in engineering application ...

in metals experiencing tensile stresses, common to low-carbon steels and certain Al-Mg alloys. First reported by Guillaume Piobert, and later by

W. Lüders W. may refer to: * SoHo (Australian TV channel) (previously W.), an Australian pay television channel * ''W.'' (film), a 2008 American biographical drama film based on the life of George W. Bush * "W.", the fifth track from Codeine's 1992 EP ''Bar ...

, the mechanism that stimulates their appearance is known as dynamic strain aging, or the inhibition of

dislocation In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to sli ...

motion by interstitial atoms (in steels, typically

carbon Carbon () is a chemical element; it has chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—meaning that its atoms are able to form up to four covalent bonds due to its valence shell exhibiting 4 ...

and

nitrogen Nitrogen is a chemical element; it has Symbol (chemistry), symbol N and atomic number 7. Nitrogen is a Nonmetal (chemistry), nonmetal and the lightest member of pnictogen, group 15 of the periodic table, often called the Pnictogen, pnictogens. ...

), around which " atmospheres" or "zones" naturally congregate. As internal stresses tend to be highest at the shoulders of tensile test specimens, band formation is favored in those areas. However, the formation of Lüders bands depends primarily on the microscopic (i.e. average

grain A grain is a small, hard, dry fruit (caryopsis) – with or without an attached husk, hull layer – harvested for human or animal consumption. A grain crop is a grain-producing plant. The two main types of commercial grain crops are cereals and ...

size and

crystal structure In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat ...

, if applicable) and macroscopic geometries of the material. For example, a tensile-tested steel bar with a square cross-section tends to develop comparatively more bands than would a bar of identical composition having a circular cross-section. The formation of a Lüders band is preceded by a yield point and a drop in the flow stress. Then the band appears as a localized event of a single band between plastically deformed and undeformed material that moves with the constant cross head velocity. The Lüders Band usually starts at one end of the specimen and propagates toward the other end. The visible front on the material usually makes a well-defined angle typically 50–55° from the specimen axis as it moves down the sample. During the propagation of the band the nominal

stress–strain curve In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress a ...

is flat. After the band has passed through the material the deformation proceeds uniformly with positive

strain hardening Work hardening, also known as strain hardening, is the process by which a material's load-bearing capacity (strength) increases during plastic (permanent) deformation. This characteristic is what sets ductile materials apart from brittle materi ...

. Sometimes Lüders band transition into the

Portevin–Le Chatelier effect The Portevin–Le Chatelier (PLC) effect describes a serrated stress–strain curve or jerky flow, which some materials exhibit as they undergo plastic deformation, specifically inhomogeneous deformation. This effect has been long associated wi ...

while changing the temperature or

strain rate In mechanics and materials science, strain rate is the time derivative of strain of a material. Strain rate has dimension of inverse time and SI units of inverse second, s−1 (or its multiples). The strain rate at some point within the mat ...

, this implies these are related phenomena Lüders bands are known as a strain softening instability. If a sample is stretched beyond the range of the Lüder strain once, no Lüder strain occurs any more when the sample is deformed again, since the dislocations have already torn themselves away from the interstitial atoms. For this reason, deep drawing sheets are often

cold rolled In metalworking, rolling is a metal forming process in which metal stock is passed through one or more pairs of rolls to reduce the thickness, to make the thickness uniform, and/or to impart a desired mechanical property. The concept is simil ...

in advance to prevent the formation of stretcher-strain marks during the actual deep drawing process. The formation of Lüder bands can occur again with a deformation over time, since the interstitial atoms accumulate by diffusing processes called

precipitation hardening Precipitation hardening, also called age hardening or particle hardening, is a heat treatment technique used to increase the yield strength of malleable materials, including most structural alloys of aluminium, magnesium, nickel, titanium, and so ...

(or ''aging'').

See also

References

Further reading