# Yarnstrength

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

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

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

with

$k=\sqrt(dQ/\mu)/3L$,

where $\alpha$ 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 $\mu$ 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