Lankford coefficient
Encyclopedia
The Lankford coefficient (also called Lankford value or R-value) is a measure of the plastic
anisotropy
of a rolled
sheet metal
. This scalar
quantity is used extensively as an indicator of the formability
of recrystallized
low-carbon steel sheets.
and 
are the coordinate directions in the plane of rolling and 
is the thickness direction, then the R-value is given by
where
is the plastic strain in-plane and 
is the plastic strain through-the-thickness.
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
value is usually measured at 20% elongation in a tensile test.
For sheet metal
s, the
values are usually determined for three different directions of loading in-plane (
to the rolling direction) and the normal R-value is taken to be the average
The planar anisotropy coefficient or planar R-value is a measure of the variation of
with angle from the rolling direction. This quantity is defined as
shows heavy orientation, and such deep-drawability is characterized by
. However, in the actual press-working, the deep-drawability of steel sheets cannot be determined only by the value of 
and the measure of planar anisotropy, 
is more appropriate.
In an ordinary cold rolled steel,
is the highest, and 
is the lowest. Experience shows that even if 
is close to 1, 
and 
can be quite high leading to a high average value of 
. In such cases, any press-forming process design on the basis of 
does not lead to an improvement in deep-drawability.
Plasticity (physics)
In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the...
anisotropy
Anisotropy
Anisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material's physical or mechanical properties An example of anisotropy is the light...
of a rolled
Rolling (metalworking)
In metalworking, rolling is a metal forming process in which metal stock is passed through a pair of rolls. Rolling is classified according to the temperature of the metal rolled. If the temperature of the metal is above its recrystallization temperature, then the process is termed as hot rolling...
sheet metal
Sheet metal
Sheet metal is simply metal formed into thin and flat pieces. It is one of the fundamental forms used in metalworking, and can be cut and bent into a variety of different shapes. Countless everyday objects are constructed of the material...
. This scalar
Scalar
Scalar may refer to:*Scalar , a quantity used to multiply vectors in the context of vector spaces*Scalar , a quantity which is independent of specific classes of coordinate systems...
quantity is used extensively as an indicator of the formability
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....
of recrystallized
Recrystallization
Recrystallization may refer to:*Recrystallization *Recrystallization *Recrystallization...
low-carbon steel sheets.
Definition
If and are the coordinate directions in the plane of rolling and is the thickness direction, then the R-value is given bywhere
is the plastic strain in-plane and is the plastic strain through-the-thickness.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
value is usually measured at 20% elongation in a tensile test.For sheet metal
Sheet metal
Sheet metal is simply metal formed into thin and flat pieces. It is one of the fundamental forms used in metalworking, and can be cut and bent into a variety of different shapes. Countless everyday objects are constructed of the material...
s, the
values are usually determined for three different directions of loading in-plane ( to the rolling direction) and the normal R-value is taken to be the averageThe planar anisotropy coefficient or planar R-value is a measure of the variation of
with angle from the rolling direction. This quantity is defined asAnisotropy of steel sheets
Generally, the Lankford value of cold rolled steel sheet acting for deep-drawabilityDeep drawing
Deep drawing is a sheet metal forming process in which a sheet metal blank is radially drawn into a forming die by the mechanical action of a punch. It is thus a shape transformation process with material retention. The process is considered "deep" drawing when the depth of the drawn part exceeds...
shows heavy orientation, and such deep-drawability is characterized by
. However, in the actual press-working, the deep-drawability of steel sheets cannot be determined only by the value of and the measure of planar anisotropy, is more appropriate.In an ordinary cold rolled steel,
is the highest, and is the lowest. Experience shows that even if is close to 1, and can be quite high leading to a high average value of . In such cases, any press-forming process design on the basis of does not lead to an improvement in deep-drawability.