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
0 30 15% 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 =
2.2034
b =
Columns 1 through 7
0.0000 0.0000 0.1244 0.0000 0.0803 0.0000 0.1244
Columns 8 through 14
0.0803 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Columns 15 through 21
0.0000 0.0000 0.0803 0.0039 0.0000 0.0039 0.0000
Columns 22 through 24
0.0803 0.0000 0.0000
spin = spinTensor (m-3m)
rank: 2 (3 x 3)
*10^-3
0 98.39 0
-98.39 0 0
0 0 0