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The Lankford coefficient (also called Lankford value, R-value, or plastic strain ratio) is a measure of the
plastic Plastics are a wide range of synthetic polymers, synthetic or Semisynthesis, semisynthetic materials composed primarily of Polymer, polymers. Their defining characteristic, Plasticity (physics), plasticity, allows them to be Injection moulding ...
anisotropy Anisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit ve ...
of a rolled
sheet metal Sheet metal is metal formed into thin, flat pieces, usually by an industrial process. Thicknesses can vary significantly; extremely thin sheets are considered foil (metal), foil or Metal leaf, leaf, and pieces thicker than 6 mm (0.25  ...
. This
scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers *Scalar (physics), a physical quantity that can be described by a single element of a number field such a ...
quantity is used extensively as an indicator of the
formability Formability is the ability of a given metal workpiece to undergo plastic deformation without being damaged. The plastic deformation capacity of metallic materials, however, is limited to a certain extent, at which point, the material could experien ...
of recrystallized low-carbon steel sheets.Ken-ichiro Mori, ''Simulation of Materials Processing: Theory, Methods and Applications'', (), p. 436


Definition

If x and y are the coordinate directions in the plane of rolling and z is the thickness direction, then the R-value is given by : R = \cfrac where \epsilon^p_ is the in-plane plastic strain, transverse to the loading direction, and \epsilon^p_ is the plastic strain through-the-thickness. ISO 10113:202

/ref> More recent studies have shown that the R-value of a material can depend strongly on the strain even at small strains . In practice, the R value is usually measured at 20% elongation in a
tensile test Tensile testing, also known as tension testing, is a fundamental materials science and engineering test in which a sample is subjected to a controlled tension until failure. Properties that are directly measured via a tensile test are ultimate ...
. For
sheet metal Sheet metal is metal formed into thin, flat pieces, usually by an industrial process. Thicknesses can vary significantly; extremely thin sheets are considered foil (metal), foil or Metal leaf, leaf, and pieces thicker than 6 mm (0.25  ...
s, the R values are usually determined for three different directions of loading in-plane (0^, 45^, 90^ to the rolling direction) and the normal R-value is taken to be the average : R = \cfrac\left(R_0 + 2~R_ + R_\right) ~. The planar anisotropy coefficient or planar R-value is a measure of the variation of R with angle from the rolling direction. This quantity is defined as : R_p = \cfrac\left(R_0 - 2~R_ + R_\right) ~.


Anisotropy of steel sheets

Generally, the Lankford value of
cold rolled steel Cold-formed steel (CFS) is the common term for steel products shaped by cold-working processes carried out near room temperature, such as rolling, pressing, stamping, bending, etc. Stock bars and sheets of cold-rolled steel (CRS) are common ...
sheet acting for deep-drawability shows heavy orientation, and such deep-drawability is characterized by R. However, in the actual press-working, the deep-drawability of steel sheets cannot be determined only by the value of R and the measure of planar anisotropy, R_p is more appropriate. In an ordinary cold rolled steel, R_ is the highest, and R_ is the lowest. Experience shows that even if R_ is close to 1, R_0 and R_ can be quite high leading to a high average value of R. In such cases, any press-forming process design on the basis of R_ does not lead to an improvement in deep-drawability.


See also

*
Yield surface A yield surface is a five-dimensional surface in the six-dimensional space of Stress (mechanics), stresses. The yield surface is usually convex polytope, convex and the state of stress of ''inside'' the yield surface is elastic. When the stress ...


References

{{DEFAULTSORT:Lankford Coefficient Plasticity (physics) Solid mechanics Metal forming