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 or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adaptab ...

anisotropy Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...

of a

rolled Rolling is a Motion (physics)#Types of motion, type of motion that combines rotation (commonly, of an Axial symmetry, axially symmetric object) and Translation (geometry), translation of that object with respect to a surface (either one or the ot ...

sheet metal Sheet metal is metal formed into thin, flat pieces, usually by an industrial process. Sheet metal is one of the fundamental forms used in metalworking, and it can be cut and bent into a variety of shapes. Thicknesses can vary significantly; ex ...

. 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 ...

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 experienc ...

of recrystallized

low-carbon steel Carbon steel is a steel with carbon content from about 0.05 up to 2.1 percent by weight. The definition of carbon steel from the American Iron and Steel Institute (AISI) states: * no minimum content is specified or required for chromium, cobalt ...

sheets.Ken-ichiro Mori, ''Simulation of Materials Processing: Theory, Methods and Applications'', (), p. 436

Definition

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 ultimat ...

. For

s, the

R

values are usually determined for three different directions of loading in-plane (

0^, 45^, 90^

to the

rolling direction Rolling is a Motion (physics)#Types of motion, type of motion that combines rotation (commonly, of an Axial symmetry, axially symmetric object) and Translation (geometry), translation of that object with respect to a surface (either one or the ot ...

) 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.

References

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

Definition

Anisotropy of steel sheets

See also

References