Syntax

[M,b,eps] = calcInvTaylor(mori,sS)

Input

`mori`	`misorientation`
`sS`	`slipSystem list in crystal coordinates`

Output

`M`	`taylor factor`
`b`	`coefficients for the acive slip systems`
`eps`	`strain tensor list in crystal coordinates`

Example

define 10 percent strain

eps = 0.1 * strainTensor(diag([1 -0.75 -0.25]))

eps = strainTensor (y↓→x)
  type: Lagrange 
  rank: 2 (3 x 3)
 
 *10^-2
   10    0    0
    0 -7.5    0
    0    0 -2.5

define a crystal orientation

cs = crystalSymmetry('cubic')
ori = orientation.byEuler(0,30*degree,15*degree,cs)

cs = crystalSymmetry (⊙c→a)
 
  symmetry: m3̅m   
  elements: 48     
  a, b, c : 1, 1, 1
 
 
ori = orientation (m3̅m → y↓→x)
 
  Bunge Euler angles in degree
  phi1  Phi phi2
     0   30   15

define a slip system

sS = slipSystem.fcc(cs)

sS = slipSystem (m3̅m)
 
  u    v    w  | h    k    l CRSS
  0    1   -1    1    1    1    1

compute the Taylor factor

[M,b,mori] = calcTaylor(inv(ori)*eps,sS.symmetrise)

M =
    2.7187
b =
  Columns 1 through 7
    0.0000    0.0000    0.0142    0.0332    0.0000    0.0000    0.0198
  Columns 8 through 14
    0.0000    0.0000    0.0000    0.0000    0.0204    0.0000    0.0000
  Columns 15 through 21
    0.0000    0.0000    0.0345    0.0093    0.0000    0.0296    0.0000
  Columns 22 through 24
    0.1110    0.0000    0.0000
 
mori = spinTensor (crystal)
  rank: 2 (3 x 3)
 
 *10^-3
      0 -20.77  31.63
  20.77      0 -15.51
 -31.63  15.51      0

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/orientation.calcInvTaylor.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.