82 C.Wu et al. Fig. 11.4 Development of TSRs: traction versus end-displacement ( D26.97ı) Fig. 11.5 Toughness versus phase angle the epoxy interphase being oriented normal to the interface as the loading is increased. The normal traction reached its peak at a normal separation of approximately 130 nm which was very close to the values found in previous work [1], albeit with a different epoxy. The peak strength was about 48 MPa which was at the elastic limit of the epoxy used in present study. After the peak, the normal traction dropped suddenly and eased into a plateau with an average strength of 2 MPa, which ended at a normal separation of 2.5 m. The descending traction also followed a power-law type function of separation, with a steeper decay than has been previously described by exponential functions. The shear TSR had an essentially linear response till the shear traction reached its peak. After the peak, the traction dropped very rapidly to zero with very small increase in separation for a shear interaction range of 0.7 m, much smaller than the range of the normal interaction. The development of the tractions were considered in detail (Fig. 11.4). Between zero and point ①, the response is linear for both tractions near the original crack front. After point ①, the normal traction increases much more rapidly than the linearly increasing shear traction. After point ②, the normal traction decreases sharply while the shear traction maintains its constant growth rate. However, after point ③, the shear traction rapidly decayed to zero simultaneously with the normal traction. The implication of this sequence of events is that damage in each response is not coupled as is commonly assumed. The obtained toughness versus the mode-mix phase angle was plotted in Fig. 11.5. As shown, the variation of toughness with mode-mix can be approximated using a 4th order polynomial function. The toughness increased with increasing phase
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