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), a conventional indicator of the fourfold earing tendency. A value near zero suppresses this contribution but does not imply equal flow at every angle or guarantee an ear-free cup.

Syntax

[R, M, minM] = calcLankford(ori,sS,theta,RD,ND)

Input

`ori`	`orientation`
`sS`	`slipSystem`
`theta`	`angle of the tensile direction with respect to RD, default 0,5,10,..,90 degrees`
`RD`	`vector3d - rolling direction, default - x - used as reference tension direction`
`ND`	`vector3d - normal direction, default - z`

Output

`R`	`plastic anisotropy ratio at minimum plastic work for each theta`
`M`	`normalized plastic work as a function of theta and rho`
`minM`	`minimum normalized plastic work as a function of theta`

Options

`verbose`	`show summary`
`weights`	`double, containing texture information`
`rho`	`width-contraction fraction between 0 and 1`

Authors

Dr. Azdiar Gazder, 2023
Dr. Manasij Kumar Yadava, 2023

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/calcLankford.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.