The Lankford coefficient (also called Lankford value, R-value, or plastic strain ratio) 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.
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 = ϵ x y p ϵ z p where ϵ x y p is the plastic strain in-plane and ϵ z p 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 R value is usually measured at 20% elongation in a tensile test.
For sheet metals, 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 = 1 4 ( R 0 + 2 R 45 + R 90 ) . 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 = 1 2 ( R 0 − 2 R 45 + R 90 ) . Generally, the Lankford value of cold rolled steel 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 90 is the highest, and R 45 is the lowest. Experience shows that even if R 45 is close to 1, R 0 and R 90 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 45 does not lead to an improvement in deep-drawability.
