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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^{[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

$R = \cfrac{1}{4}\left(R_0 + 2~R_{45} + R_{90}\right) ~.$

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

$R_p = \cfrac{1}{2}\left(R_0 - 2~R_{45} + R_{90}\right) ~.$

[edit] See also

[edit] References

^ 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).

[0] 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).

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