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.

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 where is the in-plane plastic strain, transverse to the loading direction, 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 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 ( 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 R with angle from the rolling direction. This quantity is defined as

Anisotropy of steel sheets

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.