Page 302 - Fiber Fracture
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284                                                           J.W.S. Hearle












                Force
                 Po












                                                      h
                        D,                   Amplitude, y
                         Fig.  18. Force-amplitude  plot for elasto-plastic buckling, from Hobbs et al. (2000).

                circumstances,  the  plot  follows  the  line DIC. If  plastic  yield  occurs  at  Hg,  this  will
                give an unstable plastic solution and there will be snap to the rising part of  the curve.
                However, if point E is reached before plastic buckling occurs, the decreasing portion of
                the curve will lead to snap in the elastic regime, which will subsequently give the plastic
                hinge.
                   A computer program has been written and used to calculate a solution for an aramid
                rope subject to tension-tension  cycling at 38f24% of  break  load. Although  there is
                uncertainty in the values chosen for the defining parameters,  particularly  the bending
                stiffness and  plastic  moment  of  the  yarn,  the  predictions  were  of  the  same order  of
                magnitude as the examples of failures in ropes, which are shown in Fig. 19.
                   The sensitivity analysis in Table 4 shows the effect of the fibre modulus E, the lateral
                pressure p and the coefficient of friction p on the buckle dimensions. The solid rod case


                Table 4. Sensitivity predictions, from Hobbs et al. (2000)

                Input values       Solid rod case             Free sliding case
                E  (GPa)           52.3   26.2   52.3   52.3   52.3   26.2   52.3   52.3
                P  (GPa)            0.1    0.1    0.1   0.1    0.1     0.1    0.05   0.1
                w                   0.15   0.15   0.15   0.1   0.15    0.15   0.15   0.1
                Calculated
                Half-wave length (mm)   8.75   6.76   10.2   8.98   0.296   0.25   0.346   0.31
                Buckle amplitude (mm)   1.85   1.63   1.77   2.18   0.03   0   0.03   0
                Slip length (mm)   19.7    9.79   24.1   35.3   1.84   1.48   2.21   3.18
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