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The influence of shape factors on the rigidity of fiber | fiber rigidity | fiber shape



The values of modulus obtained in tensile tests range from over 2,500 g-wt/tex for glass and about 1,800 The shape factor becomes greater, and the rigidity increases, the more distant the material is from the center.
g-wt/tex for the bast fibers and stretched rayons; through values of about 900 or less for Terylene, cotton viscose rayon, and silk; to values as low as 300 for wool, acetate and nylon. This has influence of about ten-fold range in stiffness.

It will be seen that with an asymmetrical shape there may be  a difference according to the direction of bending: in practice, the fibers will usually twist so as to bend about the easiest direction. For simple shapes, values   may be obtained by integration from a relation derived  For more complicated shapes, either numerical computation or experiment will be necessary. Table above gives some typical values.
As the fineness in as a squared term, and in view of the range of values occurring in practice – from 0.1 tex for a fine stretched rayon to 1 Tex for a coarse wool and higher for some hair fibers and man-made monofils – it will be the most important factor in determining the flexural rigidity. The choice of filament denier is thus important in deciding flexibility.

It is convenient to introduce a quantity which is independent of the fineness of the specimen. We may call this quantity the SPECIFIC FLEXURAL RIGIDITY, Rf; it is equal to the flexural rigidity of a filament of unit tex. It will be given by:
The values of Rf using values of the modulus obtained in tensile tests are given in table. They show the great flexibility of acetate filaments and the stiffness of stretched rayaon and glass.
It is convenient to introduce a quantity which is independent of the fineness of the specimen. We call this quantity the specific flexural rigidity, Rf ; it is equal to the flexural rigidity of filament of unit tex. It will be given by:  
 Rf   = [(1/4 Ï€ ) (η E/ r)] x 10-5   g-wt cm2 / tex2……+
The values of Rf, the specific flexural rigidity using values of the modulus obtained in tensile tests are given below:-
Fiber                 Specific Flexural Rigidity, Rf (g-wt cm2 / tex  x 10-4  )
Viscose                                                            1.94
Fortisan                                                           4.48
Acetate                                                            0.83
Wool                                                               1.99
Silk                                                                  1.89
Nylon                                                              1.42
Glass                                                               9.1
 

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