calcTaylor

(method of tensor)

compute Taylor factor and strain dependent orientation gradient

Syntax

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

Input

eps

strain tensor list in crystal coordinates

sS

slipSystem list in crystal coordinates

Output

M

taylor factor

b

coefficients for the acive slip systems

mori

misorientation

Example

% define 10 percent strain
eps = 0.1 * tensor(diag([1 -0.75 -0.25]),'name','strain')
 
eps = strain tensor  
  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('Euler',0,30*degree,15*degree,cs)
 
cs = crystalSymmetry  
 
  symmetry: m-3m   
  a, b, c : 1, 1, 1
 
 
ori = orientation  
  size: 1 x 1
  crystal symmetry : m-3m
  specimen symmetry: 1
 
  Bunge Euler angles in degree
  phi1  Phi phi2 Inv.
     0   30   15    0
 
 
% define a slip system
sS = slipSystem.fcc(cs)
 
sS = slipSystem  
 symmetry: m-3m
 CRSS: 1
 size: 1 x 1
  u   v   w | h   k   l
  0   1  -1   1   1   1
% compute the Taylor factor
[M,b,mori] = calcTaylor(inv(ori)*eps,sS.symmetrise)
M =
    0.2719
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    0.0204    0.0000    0.0000    0.0000
  Columns 15 through 21
    0.0000    0.0345    0.0093    0.0000    0.0000    0.0296    0.0000
  Columns 22 through 24
    0.0000    0.0000    0.1110
 
mori = misorientation  
  size: 1 x 1
  crystal symmetry : m-3m
  crystal symmetry : m-3m
 
  Bunge Euler angles in degree
     phi1     Phi    phi2    Inv.
  64.4732  2.0184 296.717       0