compute Taylor factor and strain dependent orientation gradient
Syntax
[MFun,~,spinFun] = calcTaylor(eps,sS,'SO3Fun','bandwidth',32)
[M,b,W] = calcTaylor(eps,sS)Input
| eps | strainTensor list in crystal coordinates |
| sS | slipSystem list in crystal coordinates |
Output
| Mfun | SO3FunHarmonic (orientation dependent Taylor factor) |
| spinFun | SO3VectorFieldHarmonic |
| M | taylor factor |
| b | vector of slip rates for all slip systems |
| W | spinTensor |
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
symmetry: m-3m
elements: 48
a, b, c : 1, 1, 1
ori = orientation (m-3m → y↑→x)
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 w.r.t. the given orientation
[M,b,W] = calcTaylor(inv(ori)*eps,sS.symmetrise)M =
2.7187
b =
Columns 1 through 6
2.1058e-17 1.0668e-16 0.014162 0.033158 9.8911e-17 2.7042e-17
Columns 7 through 12
0.019786 1.2948e-16 2.3761e-17 3.156e-17 7.4774e-17 0.020425
Columns 13 through 18
4.8778e-17 2.007e-17 4.2509e-17 1.2248e-16 0.034477 0.0092782
Columns 19 through 24
2.0953e-17 0.029621 7.1262e-17 0.11096 2.332e-17 7.1768e-17
W = spinTensor (m-3m)
rank: 2 (3 x 3)
*10^-3
0 -20.77 31.63
20.77 0 -15.51
-31.63 15.51 0% update orientation
oriNew = ori .* orientation(-W)oriNew = orientation (m-3m → y↑→x)
Bunge Euler angles in degree
phi1 Phi phi2
356.003 29.6499 17.2781