polytex.misc

Module contents

polytex.misc.cai_berdichevsky(vf, rf, packing='Quad', tensorial=False)

Calculate the fiber tow permeability for a given fiber packing pattern according to cai’s model.

\[\begin{split}K_L = & 0.211 r^2\left(\left(V_a-0.605\right)\left(\frac{0.907 V_f}{V_a}\right)^{(-0.181)} *\left(\frac{1-0.907 V_f}{V_a}\right)^{(2.66)}\right. \\ & \left.+0.292\left(0.907-V_a\right)\left(V_f\right)^{(-1.57)}\left(1-V_f\right)^{(1.55)}\right) \\ K_T = & 0.229 r^2\left(\frac{1.814}{V_a}-1\right)\left(\frac{\left(1-\sqrt{\frac{V_f}{V_a}}\right)}{\sqrt{\frac{V_f}{V_a}}}\right)^{2.5}\end{split}\]

Parameters

vffloat or array_like

Fiber volume fraction.

rffloat or array_like

Fiber radius (m). If vf and rf are arrays, they must have the same shape.

packingstring

Fiber packing pattern. Valid options are “Quad” and “Hex”.

tensorialbool

If True, return the permeability tensor (a list with 9 elements). Otherwise, return the permeability components that parallel and perpendicular to the fiber tow as a list of 3 floats. The default is False.

Returns

karray-like

Fiber tow permeability. If tensorial is True, return a list with 9 elements. Otherwise, return a list of 3 floats (k11, k22, k33), corresponding to the permeability components that parallel and perpendicular to the fiber tow. The units are m^2. Note that the principal permeability components k22 and k33 are equal.

References

Cai, Z. and A. Berdichevsky, An improved self‐consistent method for estimating the permeability of a fiber assembly. Polymer composites, 1993. 14(4): p. 314-323

Examples

>>> rf = 6.5e-6
>>> k = cai_berdichevsky(vf=0.3, rf=rf, packing='Hex')
>>> k / rf**2
array([[0.04415829, 0.10741589, 0.10741589]])
>>> k = cai_berdichevsky(vf=0.7, rf=rf, packing='Hex')
>>> k / rf**2
array([[0.00604229, 0.00162723, 0.00162723]])
>>> k = cai_berdichevsky(vf=0.3, rf=rf, packing='Hex', tensorial=True)
>>> k / rf**2
array([[0.04415829, 0.        , 0.        , 0.        , 0.10741589,
        0.        , 0.        , 0.        , 0.10741589]])

polytex.misc.compress_file(zipfilename, dirname)

Compresses all files and subdirectories in the specified directory.

Parameters

zipfilenamestr

The name of the zip file, including the path.

dirnamestr

The name of the directory to be compressed, including the path.

Returns

int

1 if the compression is successful, otherwise 0.

Examples

>>> compress_file("test.zip", "./test")

polytex.misc.drummond_tahir(vf, rf, packing='Quad', tensorial=False)

Calculate the fiber tow permeability for a given fiber packing pattern according to Drummond and Tahir’s model.

\[\begin{split}K_l & = \frac{r^2}{4V_f}\left(-lnV_f-1.476+2V_f-0.5V_f^2\right) \\ K_{tQuad} & =\frac{r^2}{8V_f}\left(-lnV_f-1.476+\frac{2V_f-0.796V_f}{1+0.489V_f-1.605{V_f}^2}\right) \\ K_{tHex} & =\frac{r^2}{8V_f}\left(-lnV_f-1.497+2V_f-\frac{V_f^2}{2}-0.739V_f^4+\frac{2.534V_f^5}{1+1.2758V_f}\right)\end{split}\]

Parameters

vffloat or array_like

Fiber volume fraction.

rffloat or array_like

Fiber radius (m). If vf and rf are arrays, they must have the same shape.

packingstring

Fiber packing pattern. Valid options are “Quad” and “Hex”.

tensorialbool

If True, return the permeability tensor (a list with 9 elements). Otherwise, return the permeability components that parallel and perpendicular to the fiber tow as a list of 3 floats. The default is False.

Returns

karray-like

Fiber tow permeability. If tensorial is True, return a list with 9 elements. Otherwise, return a list of 3 floats (k11, k22, k33), corresponding to the permeability components that parallel and perpendicular to the fiber tow. The units are m^2. Note that the principal permeability components k22 and k33 are equal.

References

Drummond J E, Tahir M I. Laminar viscous flow through regular arrays of parallel solid cylinders[J]. International Journal of Multiphase Flow, 1984, 10(5): 515-540..

Examples

>>> rf = 6.5e-6
>>> k = drummond_tahir(vf=0.3, rf=rf, packing='Hex')
>>> k / rf**2
array([[0.23581067, 0.10851671, 0.10851671]])
>>> k = drummond_tahir(vf=0.7, rf=rf, packing='Hex')
>>> k / rf**2
array([[0.01274105, 0.01110984, 0.01110984]])
>>> k = drummond_tahir(vf=0.3, rf=rf, packing='Hex', tensorial=True)
>>> k / rf**2
array([[0.23581067, 0.        , 0.        , 0.        , 0.10851671,
        0.        , 0.        , 0.        , 0.10851671]])

polytex.misc.gebart(vf, rf, packing='Quad', tensorial=False)

Calculate the fiber tow permeability for a given fiber packing pattern according to Gebart’s model.

\[\begin{split}k_l & = \frac{8 r_f^2}{c} \frac{(1 - V_f)^3}{V_f^2} \\ k_t & = c_1 r_f^2 \sqrt{\left(\sqrt{\frac{V_{f_{max}}}{V_f}} - 1\right)^5}\end{split}\]

Parameters

vffloat or array_like

Fiber volume fraction.

rffloat or array_like

Fiber radius (m). If vf and rf are arrays, they must have the same shape.

packingstring

Fiber packing pattern. Valid options are “Quad” and “Hex”.

tensorialbool

If True, return the permeability tensor (a list with 9 elements). Otherwise, return the permeability components that parallel and perpendicular to the fiber tow as a list of 3 floats. The default is False.

Returns

karray-like

Fiber tow permeability. If tensorial is True, return a list with 9 elements. Otherwise, return a list of 3 floats (k11, k22, k33), corresponding to the permeability components that parallel and perpendicular to the fiber tow. The units are m^2. Note that the principal permeability components k22 and k33 are equal.

References

Gebart BR. Permeability of Unidirectional Reinforcements for RTM. Journal of Composite Materials. 1992;26(8):1100-33.

Examples

>>> print(gebart(vf=0.5, rf=1.7e-5, packing="Quad", tensorial=False))
[2.02807018e-11 3.73472833e-12 3.73472833e-12]
>>> print(gebart(vf=0.5, rf=1.7e-5, packing="Quad", tensorial=True))
[2.02807018e-11 0.00000000e+00 0.00000000e+00 0.00000000e+00
 3.73472833e-12 0.00000000e+00 0.00000000e+00 0.00000000e+00
 3.73472833e-12]
>>> print(gebart(vf=0.5, rf=1.7e-5, packing="Hex", tensorial=False))
[2.18113208e-11 4.72786599e-12 4.72786599e-12]
>>> print(gebart(vf=0.5, rf=1.7e-5, packing="Hex", tensorial=True))
[2.18113208e-11 0.00000000e+00 0.00000000e+00 0.00000000e+00
 4.72786599e-12 0.00000000e+00 0.00000000e+00 0.00000000e+00
 4.72786599e-12]

polytex.misc.perm_rotation(permeability, orientation, inverse=False, disable_tqdm=True)

Rotate the permeability tensor according to the yarn orientation in the world coordinate system.

Parameters

permeability: ndarray

The principal permeability tensor of the yarn in the local coordinate system of the yarn. Shape: (n, 9)

orientation: ndarray

The orientation of the yarn in the world coordinate system. Shape: (n, 3)

inverse: bool

If True, the inverse of permeability tensor is returned.

Returns

perm_rot: ndarray

The rotated permeability tensor. Shape: (n, 9)

Dndarray

The inverse of the rotated permeability tensor. Shape: (n, 9)

polytex.misc.porosity_tow(rho_lin, area_xs, rho_fiber=2550, fvf=False)

Calculate local porosity of a tow based on its cross-sectional area and linear density.

Parameters

rho_lin: float

Linear density of the tow. Unit: Tex (g/1000m)

area_xs: array-like

Cross-sectional area of the tow. Unit: m^2. Shape: (n cross-sections, 1).

rho_fiber: float

Volume density of the fiber. Unit: kg/m^3. Default: 2550 (glass fiber).

fvf: bool

Whether to return fiber volume fraction. Default: False. If True, return fiber volume fraction instead of porosity.

Returns

porosity: array-like

Local porosity of the tow. Shape: (n cross-sections, 1). Unit: 1. The fiber volume fraction is returned if fvf is True.

Examples

>>> rho_lin = 275 # 275 Tex
>>> area_xs = np.array([0.16, 0.22, 0.15])/1e6 # mm^2 to m^2
>>> rho_fiber = 2550 # kg/m^3
>>> porosity = porosity_tow(rho_lin, area_xs, rho_fiber, fvf=True)
>>> print(porosity)
[0.67401961 0.49019608 0.71895425]