Lankford coefficient

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 formula_1 and formula_2 are the coordinate directions in the plane of rolling and formula_3 is the thickness direction, then the R-value is given by
where formula_5 is the in-plane plastic strain, transverse to the loading direction, and formula_6 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 formula_7 value is usually measured at 20% elongation in a tensile test.
For sheet metals, the formula_7 values are usually determined for three different directions of loading in-plane (formula_9 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 formula_7 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 formula_7. However, in the actual press-working, the deep-drawability of steel sheets cannot be determined only by the value of formula_7 and the measure of planar anisotropy, formula_15 is more appropriate.
In an ordinary cold rolled steel, formula_16 is the highest, and formula_17 is the lowest. Experience shows that even if formula_17 is close to 1, formula_19 and formula_16 can be quite high leading to a high average value of formula_7. In such cases, any press-forming process design on the basis of formula_17 does not lead to an improvement in deep-drawability.