Lankford coefficient

The Lankford coefficient or R-value [Lankford, W. T., Snyder, S. C., Bausher, J. A.: "New criteria for predicting the press performance of deep drawing sheets." Trans. ASM, 42, 1197–1205 (1950).] is a measure of the plastic anisotropy of a rolled metal sheet. 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:$R\; =\; cfrac\{epsilon^p\_\{xy\{epsilon^p\_z\}$where $epsilon^p\_\{xy\}$ is the plastic strain in-plane and $epsilon^p\_z$ 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 [Citation needed.] . 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 ($0^\{circ\},\; 45^\{circ\},\; 90^\{circ\}$ to the rolling direction) and the normal R-value is taken to be the average :$R\; =\; cfrac\{1\}\{4\}left(R\_0\; +\; 2~R\_\{45\}\; +\; R\_\{90\}\; ight)\; ~.$

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:$R\_p\; =\; cfrac\{1\}\{4\}left(R\_0\; -\; 2~R\_\{45\}\; +\; R\_\{90\}\; ight)\; ~.$