DISCUSSION Effects of whisker volume fraction on R-curve The distribution of σb has been calculated for various values of Vw using the same whisker dimensions as TWS-400, as shown in Figs.3(a) and 3(b). As shown in Fig.3(a) where the relations of σb in the vicinity at a crack tip are demonstrated , the peak value of σb in Frictional Bridging (FB) [3,8] increases with Vw simply owing to the increase in the number of whiskers bridging a crack in FB. That is the main reason why KIc( α) at the bend of R-curve of the present composite system increases with Vw, as shown in Fig.1. In Fig.3(b) where a wide range view of bridging is depicted, the maximum σb in Pull-out Bridging (PB) [3,8] increases but the zone length lb decreases with the increase in Vw. The former is also due to the increase in the number of whiskers bridging a crack in PB. In order to investigate the latter, we take δb into consideration, because lb, which significantly affects KIc( α) at the second stage of R-curve as much as σb does, is geometrically determined through the combination of lw and δb at the trailing edge of a bridging zone under crack propagation. The δb-values within the zone for various values of Vw have been calculated for the same whisker dimensions as TWS-400 in terms of the distance from crack tip. It is found that there is almost no difference in δb with various Vw at very close range from the tip; however, the δb-value of the composite with high Vw increases more progressively with the increase in the distance from the tip than that of the composite with low Vw. The progressive increase in δb is caused by the increase in nominal KIc( α) with Vw due to the stress shielding effect of σb, and results in the decrease in lb with the increase in Vw at a constant lw. The negative effect of the decrease in lb on toughening is entirely overcome by the positive effect of the increase in σb with Vw. As a result, the minute increase in rising R-curve gradient at the second stage with Vw has been observed, as shown in Fig.1. We conclude that the increase in Vw is fairly effective for toughening the present composite system. 50 100 150 200 100 200 300 400 500 600 700 0 Distance from crack tip / μ m Crack closure stress /MPa TWS400-20vol.% TWS400-15vol.% TWS400-10vol.% TWS400-5vol.% 1000 2000 3000 4000 5000 20 40 60 80 100 0 Distance from crack tip / μ m Crack closure stress /MPa TWS400-20vol.% TWS400-15vol.% TWS400-10vol.% TWS400-5vol.% (a) (b) Figure 3: Distribution of crack closure stresses in the composite for various whisker volume fractions in the vicinity of a crack tip (a) and throughout bridging zone (b). Effects of whisker dimensions on R-curve As shown in Fig.2, there is a negligible small discrepancy in KIc( α) at the bend in R-curve between Compo-sw and Compo-lw, because of the insignificant difference between their peak values of σb. The simulation reveals that much larger values of σb and lb in PB of Compo-lw than those of Compo-sw cause the significant difference in the rising behavior at the second stage of their R-curves. In order to examine the difference in R-curve between Compo-sw and Compo-lw in detail, the effect of the size and the aspect ratio Aw of whiskers on the R-curve behavior of the present
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