Optimal projection equations

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

$R=\frac{{ϵ}_{\mathrm{x}\mathrm{y}}^p}{{ϵ}_{\mathrm{z}}^p}$

where ${ϵ}_{\mathrm{x}\mathrm{y}}^p$ is the plastic strain in-plane and ${ϵ}_{\mathrm{z}}^p$ 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 Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. . 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

$R=\frac{1}{4}(R_0+2R_{45}+R_{90}).$

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

$R_p=\frac{1}{2}(R_0-2R_{45}+R_{90}).$

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.

See also

• Yield surface

References

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