velocityGradientTensor.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);

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,W] = calcTaylor(inv(ori)*L,sS.symmetrise);

update orientation

oriNew = ori .* orientation(-W)
oriNew = orientation (m-3m → y↑→x)
 
  Bunge Euler angles in degree
         phi1         Phi        phi2
  1.54702e-10          30     11.2419