Yarnstrength

Tensile Strength Formula from M. Zhang et al. (2004)

The formula for the tensile strength <math>\sigma_y</math> of the yarn relative to the tensile strength <math>\sigma_f</math> of the fiber given in M. Zhang et al. (2004) is:

<math>\sigma_y/\sigma_f = \cos^2 \alpha (1 - k/\sin\alpha)</math>,

with

<math>k=\sqrt(dQ/\mu)/3L</math>,

where <math>\alpha</math> is the tilt of the fibers to the yarn axis, d the fiber diameter, Q the 'migration length', that is the length scale on which a fiber goes from the yarn's surface to the interior, L is the length of the fibers, and <math>\mu</math> the friction coefficient between the fibers.

If we enter the following values:

Quantity	Value
alpha	30deg
d	1nm
Q	30micron
mu	0.13
L	30micron