Average stiffness of fibre texture

This example shows how to compute the Voigt-Reuss-Hill average of crystals with perfect fibre texture.

Define fibre texture

We define the stiffness tensor for BCC austenite using its elastic constants. They are taken from the Materials Project (mp-13).

from elasticipy.tensors.elasticity import StiffnessTensor
C = StiffnessTensor.cubic(C11=274, C12=175, C44=89)

Create a gamma fibre texture

The gamma texture correspond to alignment of <1 1 1> with normal direction.

from elasticipy.crystal_texture import FibreTexture
gamma = FibreTexture.gamma()
print(gamma)

Fibre texture
<1. 1. 1.> || [0, 0, 1]

Plot the corresponding pole figure

The pole figure of uvw directions, defined with the help of orix, as pole figures. Eg.:

fig, ax = gamma.plot_as_pole_figure(uvw=[1,0,0])

Compute the Hill average

The Voigt-Reuss-Hill average of the polycrystal is:

Chill = C.Hill_average(orientations=gamma)
print(Chill)

Stiffness tensor (in Kelvin mapping):
[[310.73 164.6  148.67   0.     0.     0.  ]
 [164.6  310.73 148.67  -0.    -0.    -0.  ]
 [148.67 148.67 326.67  -0.     0.     0.  ]
 [  0.    -0.     0.   120.76   0.    -0.  ]
 [  0.    -0.    -0.    -0.   120.76   0.  ]
 [ -0.     0.    -0.    -0.     0.   146.13]]

Check transversely isotropy

The transversely isotropy, resulting from the fibre texture along ND, can be evidenced by looking at the Young modulus, which is constant along any direction in XY plane:

Chill.Young_modulus.plot3D()