composite system should be taken into account individually, because they are expected to effect on the R-curve in different ways. The effect of whisker size on the rising R-curve behavior has, first, been examined with Vw of 0.2 and a constant Aw of 8.7 resulting in the constant χ-value of 1.0, where the effect of whisker bridging on the toughening of the present composite system has been optimized, as well as demonstrated in Fig.4. The increase in rw and lw with a constant Aw enhances the rising R-curve behavior in the second stage, while the difference in KIc( α) in the first stage of R-curve is hardly detected owing to the insignificant effect of whisker size on the peak value of σb in FB. The effect of whisker size on the maximum σb in PB is also insignificant, because it is principally given in terms of χ, Vw and σw. The simulation reveals that the increase in lb with rw and lw at constant Aw is caused by the compensation of the increase in lw for the increase in δb at the trailing edge of the bridging zone. Therefore, the increase in whisker size with constant Aw increases lb, and results in the enhancement of rising R-curve behavior at the second stage in the present composite system. The effect of Aw on the rising R-curve behavior is, then, examined through the χ-value, because the use of χ, which is simply proportional to Aw, properly gives a general description of the change in R-curve behavior. The χ -value is given in terms of the ratio of lw to rw. Accordingly, we have employed rw as a variable of χ. R-curves simulated for various values of χ with Vw of 0.2 were depicted in Fig.5. It is found that the decrease in χ down to χ=1 remarkably enhances the rising R-curve behavior at the second stage. However, the KIc( α)-value at the bend in curve is very insusceptible owing to the insignificant dependence of χ on the peak value of σb in FB. The simulation of σb-values in PB for various values of χ with Vw of 0.2 reveals that both the maximum σb in PB and lb increase with the decrease in χ down to χ=1. The increase in the maximum σb is caused by the increase in the number of bridging whiskers intact at the transition from FB to PB process; the tensile stresses on bridging whiskers decreases with the decrease in χ. Moreover, the decrease in the tensile stress increases the pulled-out whisker length resulting in the increase in lb. We conclude that the decrease in Aw with the increase in rw at constant lw significantly enhances rising R-curve behavior at the second stage in the present composite system through the increase in both the maximum σb in PB and lb. A significant difference in rising gradient at the second stage of R-curve between Compo-sw and Compo-lw is attributed to the difference in whisker size as well as aspect ratio. 200 400 600 800 1000 5 10 15 20 0 rw=2.29μ m, lw =40μ m rw=1.72μ m, lw =30μ m rw =1.14μ m, lw =20μ m rw =0.57μ m, lw=10μ m Crack extension length /μ m Critical stress intensity factor /MPa√m Aw(≡lw/2rw)=8.7, χ=1 200 400 600 800 1000 5 10 15 0 χ =3.0 (rw =0.38μ m, lw =20μ m) Crack extension length /μ m Critical stress intensity factor /MPa√m χ =2.5 (rw =0.46μ m, lw =20μ m) χ =2.0 (rw =0.57μ m, lw =20μ m) χ =1.5 (rw =0.76μ m, lw =20μ m) χ =1.0 (rw =1.14μ m, lw =20μ m) Figure 4: R-curves simulated for various whisker sizes with a constant whisker aspect ratio of 8.7 resulting in the constant χ-value of 1.0 and whisker volume fraction of 20%. Figure 5: R-curves simulated for various values of χ with whisker volume fraction of 20%.
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