Page 294 - Handbook of Properties of Textile and Technical Fibres
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268                             Handbook of Properties of Textile and Technical Fibres

         Table 7.4 Typical values of tenacity, breaking elongation, and work of
         rupture for open-end spun carded yarns (Elmogahzy and
         Chewning, 2001) (Uster Tensorapid)
                                               Breaking
                          Tenacity (cN/tex)  elongation (%)
          Count range                                       Work of rupture
          (Ne) (s)       Mean     CV%      Mean    CV%      (cN$cm)
          6e10           12.5e12  6e7.2    8e7.2   5e5.8    3000e1450
          10e20          12       7.2e8.7  7.2e6.4  5.8e7.0  1450e600
          20e40          12e11.5  8.7e10.2  6.4e5.8  7.0e8.0  600e250




         Table 7.5 Typical values of tenacity, breaking elongation, and work of
         rupture for ring-spun combed yarns (Elmogahzy and Chewning,
         2001) (Uster Tensorapid)

                                            Breaking
                         Tenacity (cN/tex)  elongation
          Count range                                     Work of rupture
          (Ne)          Mean    CV%     Mean     CV%      (cN$cm)
          20e40         17.5    6.5e8.5  6.2e5.4  6e7.5   800e400
          50e100        22e20   9e13    5.6e5.2  7.5e10.5  350e160



         where E y is yarn modulus, E f is fiber modulus, a is the twist angle, and k is expressed
         by the following equation:
                 p
                          1=2
                   ffiffiffi
                   2 aQ
             k ¼
                 3L f  m
         where L f is the fiber length, a is the fiber radius, Q is the migration period, and m is the
         coefficient of friction.
            The above equation indicates that there are two basic components determining yarn
         strengthetwist relationship for a given fiber strength: the cos a (Elmogahzy,
         December, 2015) (which is the only component needed in case of continuous filament
         yarn) and the (1 k$cosec a) required to adjust for spun yarn structure. The former
         component yields a decreasing strength with the increase in twist angle and the latter
         yields an increasing strength with twist, which is largely dependent on the k value
         (higher k values will result in lower strength ratios). Fiber properties reflected in this
         equation are fiber length and fiber fineness (or fiber diameter). As fiber length increases
         k decreases, leading to higher yarn strength; as the fiber diameter, a, increases k
         increases, leading to lower yarn strength. The equation also indicates that the increase
         in friction results in a decrease in k value or an increase in yarn strength.
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