Lankford coefficient or R-value from orientations or ODF
Description
The R-value, is the ratio of the true width strain to the true thickness strain at a particular value of length strain.
The normal anisotropy ratio (Rbar, or Ravg, or rm) defines the ability of the metal to deform in the thickness direction relative to deformation in the plane of the sheet. For Rbar values >= 1, the sheet metal resists thinning, improves cup drawing, hole expansion, and other forming modes where metal thinning is detrimental. For Rbar < 1, thinning becomes the preferential metal flow direction, increasing the risk of failure in drawing operations.
A related parameter is the planar anisotropy parameter (deltaR) which is an indicator of the ability of a material to demonstrate non-earing behavior. A deltaR value = 0 is ideal for can-making or deep drawing of cylinders, as this indicates equal metal flow in all directions; thus eliminating the need to trim ears during subsequent processing.
Syntax
[R, minM, M] = calcRValue(ori,sS,theta,RD,ND)Input
| ori | orientation |
| sS | slipSystem |
| theta | angle of the tensial direction with respect to RD, default 0,5,10,..,90 degree |
| RD | vector3d - rolling direction, default - x - used as reference tension direction |
| ND | vector3d - normal direction, default - z |
Output
| R | plastic anisotropy ratio (R-value) with minimum Taylor factor as a function of theta |
| M | Taylor factor as a function of theta and R |
| minM | minimum Taylor factor as a function of theta |
Options
| verbose | show summary |
| weights | @double, containing texture information |
Authors
- Dr. Azdiar Gazder, 2023
- Dr. Manasij Kumar Yadava, 2023