Difference between revisions of "Yarnstrength"

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with
 
with
  
<math>k=\sqrt(dQ/\mu)</math>,
+
<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.
 
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:
 +
 +
{| border="1" cellspacing="0" cellpadding="5" align="center"
 +
!Quantity
 +
!Value
 +
|-
 +
|alpha
 +
|30deg
 +
|-
 +
|d
 +
|1nm
 +
|-
 +
|Q
 +
|30micron
 +
|-
 +
|mu
 +
|0.13
 +
|-
 +
|L
 +
|30micron
 +
|-
 +
|}

Revision as of 20:47, 19 March 2009

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