By P. W. R. Beaumont, Y. Shibuya

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**Example text**

The probabilistic expectation of axial tensile stress in the surviving fiber bundle at the position of macroscopic crack is the product of the axial tensile stress in the surviving fiber bundle at the position of macroscopic crack, e, and the survival probability of fiber bundle S. The probabilistic expectation of axial tensile stress in the pulling-out fiber bundle at the position of macroscopic crack is twice the product of the frictional stress T and the average embedded length of fiber bundlesle.

During the test, the load P and the crack mouth displacement VM were measured. The P-VM curves obtained are shown by dotted and dashed lines in Fig. 2. It can be seen from this figure that the load increases linearly to nearly 60 % of the maximum load and several load drops occur above 80 % of the maximum load. 02 GPa in -30 ply. The frictional stress T acting on the delaminated surfaces is taken as 50 MPa. 0, respectively. The tension-softening relation determined from Eq. 7 is depicted in Fig.

Then, bridging of the whiskers occurs, as shown in Fig. 1 (b). In this study, the micro-void is regarded as a pre-existing debond which extends in the whisker-matrix interface when the axial tensile stress in the bridging whisker at the position of the tip of debond attains the critical stress, i. , the debond stress d. Moreover, the frictional force acting on the debonding whisker-matrix interface is assumed to be negligibly small. Consider a bridging whisker with a pre-existing debond. When the strength distribution of whisker is given by the Weibull distribution, the survival probability of whisker S is written as m 2li exp 2li 1 l f 0 S m d 2l exp 2l 1 l f 0 0 d (1) d where 0 and m are the scale and shape parameters of Weibull moduli, respectively, li the length of pre-existing debond, l the length of debond and lf the length of whisker (see Fig.