Lankford coefficient

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The Lankford coefficient or R-value [1] 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 [2]. 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}\right) ~.

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}\right) ~.
  1. ^ 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).
  2. ^ Citation needed.