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 {\displaystyle x} and y {\displaystyle y} are the coordinate directions in the plane of rolling and z {\displaystyle z} is the thickness direction, then the R-value is given by
R = ϵ x p ϵ z p {\displaystyle R={\cfrac {\epsilon _{\mathrm {x} }^{p}}{\epsilon _{\mathrm {z} }^{p}}}}
where ϵ x p {\displaystyle \epsilon _{\mathrm {x} }^{p}} is the in-plane plastic strain, transverse to the loading direction, and ϵ z p {\displaystyle \epsilon _{\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 . In practice, the R {\displaystyle R} value is usually measured at 20% elongation in a tensile test. For sheet metals, the R {\displaystyle R} values are usually determined for three different directions of loading in-plane ( 0 ∘ , 45 ∘ , 90 ∘ {\displaystyle 0^{\circ },45^{\circ },90^{\circ }} to the rolling direction) and the normal R-value is taken to be the average
R = 1 4 ( R 0 + 2 R 45 + R 90 ) . {\displaystyle 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 {\displaystyle R} with angle from the rolling direction. This quantity is defined as
R p = 1 2 ( R 0 − 2 R 45 + R 90 ) . {\displaystyle R_{p}={\cfrac {1}{2}}\left(R_{0}-2~R_{45}+R_{90}\right)~.}
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