Page 301 - Fiber Fracture
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FRACTURE OF HIGHLY ORIENTED, CHAIN-EXTENDED POLYMER FIBRES           283
























                                                                     (b)
                                                                     Axial force
                                                                     distribution
                          Fig.  16. Slip lengths and force distribution, from Hobbs et al. (2000).

                                                I







                                       I
                     -               LP         iv  Mode 4
                                                I
                     k
                       I     4                 4
                 0.608Lp                        I
              4            m
                        Fig. 17. Form of kinking due to plastic yielding, from Hobbs et al. (2000).


             resistance to axial slip. In order to apply this to the kinking of yams within ropes, it was
             necessary to introduce appropriate forms for the transverse and axial resistances. The
             more important difference is the plastic yielding of the fibres, which transforms smooth
             buckles into sharp kinks. As an approximation, the fibres are assumed to show ideal
             elastic-plastic  behaviour, so that the plastic bending moment has to be introduced as
             well as the initial flexural rigidity. The predicted form of buckling is shown in Fig. 17. It
             is assumed that elastic buckling occurs first and determines the form and dimensions of
             buckles. The plastic solution peels off the elastic solution as shown in Fig. 18.
               The ideal solution for perfectly straight rods is the line AC with the plastic solutions
             coming off at HI to &. However, there are both theoretical and practical problems with
             this ideal case. Realistically there will be initial imperfections in the fibre paths. In these
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