calcTaylor edit page

compute Taylor factor and strain dependent orientation gradient

Syntax

[M,b,W] = calcTaylor(eps,sS)

Input

L velocityGradientTensor
sS slipSystem

Output

M taylor factor
b coefficients for the acive slip systems
W spinTensor

Example

% consider uniaxial tension in (100) direction about 30 percent
F = deformationGradientTensor.uniaxial(vector3d.X,1.3)
F = deformationGradientTensor (1)
  rank: 2 (3 x 3)
 
    1.3      0      0
      0 0.8771      0
      0      0 0.8771
% the corresponding rate of deformation tensor becomes
L = logm(F)
L = velocityGradientTensor (1)
  rank: 2 (3 x 3)
 
 *10^-2
  26.236       0       0
       0 -13.118       0
       0       0 -13.118
% define a crystal orientation
cs = crystalSymmetry('cubic')
ori = orientation.byEuler(0,30*degree,15*degree,cs)
cs = crystalSymmetry
 
  symmetry: m-3m   
  elements: 48     
  a, b, c : 1, 1, 1
 
 
ori = orientation (m-3m → xyz)
 
  Bunge Euler angles in degree
  phi1  Phi phi2 Inv.
     0   30   15    0
% define a slip system
sS = slipSystem.fcc(cs)
sS = slipSystem (m-3m)
 
  u    v    w  | h    k    l CRSS
  0    1   -1    1    1    1    1
% compute the Taylor factor
[M,b,spin] = calcTaylor(inv(ori)*L,sS.symmetrise)
M =
    0.6584
b =
  Columns 1 through 7
    0.0000    0.0000    0.0000    0.0000    0.0441    0.2008    0.0000
  Columns 8 through 14
    0.0000    0.0000    0.0000    0.2008    0.0441    0.0000    0.0441
  Columns 15 through 21
    0.0000    0.0402    0.0000    0.0000    0.0000    0.0441    0.0402
  Columns 22 through 24
    0.0000    0.0000    0.0000
 
spin = spinTensor (m-3m)
  rank: 2 (3 x 3)
 
 *10^-3
      0 -65.59      0
  65.59      0      0
      0      0      0