3242 HSUEH and BECHER INTERFACIAL SHEAR DEBONDING Ef/em=5 3目oz 0.4 =0.5 5 Fig. 2. The normalized axial stress, ar/ard, along the fiber in the effective defect-free region for are used in the following figures. To normalize the quickly along the fiber length(within a distance of debond stress, ts is sufficient in the strength cri- about four times the fiber diameter when the fiber terion; however, Ti Youngs modulus, and a spatial and the matrix have similar Youngs modulus)to dimension are required in the energy criterion zero. Lower ratios of E Em require a shorter length When a uniform shear stress is applied at the to reach zero stress. This indicates that low ratios nterface in the effective defect region, the calcu- of ErEm are more effective in load transfer from lated normalized axial stress, o ard, along the fiber the fiber to the matrix n the defect-free region is shown in Fig. 2 for The calculated normalized initial debond stresses rla=100 at different ratios of Er/Em. The results od/ts and da/(ETio\y normalized initial 62. as functions of the are not sensitive to i/a when t/a>30. The axial Y oung's modulus ratio stress in the fiber, ar. is ord at z=t and decreases both criteria show that th 6 30 10 10 Youngs modulus ratio, Ef/ em Fig. 3. The normalized initial debond stresses, Oats and a/(ET/a) as functions of the Young's modulus ratio, Er/Em, for vr=Vm=0.25. b/a=10 and t/aare used in the following ®gures. To normalize the debond stress, ts is sucient in the strength cri￾terion; however, Gi, Young's modulus, and a spatial dimension are required in the energy criterion. When a uniform shear stress is applied at the interface in the e€ective defect region, the calcu￾lated normalized axial stress, sf/sfd, along the ®ber in the defect-free region is shown in Fig. 2 for t/a = 100 at di€erent ratios of Ef/Em. The results are not sensitive to t/a when t/a>30. The axial stress in the ®ber, sf, is sfd at z = t and decreases quickly along the ®ber length (within a distance of about four times the ®ber diameter when the ®ber and the matrix have similar Young's modulus) to zero. Lower ratios of Ef/Em require a shorter length to reach zero stress. This indicates that low ratios of Ef/Em are more e€ective in load transfer from the ®ber to the matrix. The calculated normalized initial debond stresses, sd/ts and sd/(E*Gi/a) 1/2, as functions of the Young's modulus ratio, Ef/Em, are shown in Fig. 3. Both criteria show that the normalized initial Fig. 2. The normalized axial stress, sf/sfd, along the ®ber in the e€ective defect-free region for nf=nm=0.25, b/a = 10 and t/a = 100 when the interface in the e€ective defect region is subjected to a uniform shear stress. Fig. 3. The normalized initial debond stresses, sd/ts and sd/(E*Gi/a) 1/2, as functions of the Young's modulus ratio, Ef/Em, for nf=nm=0.25, b/a = 10 and t/a 4 1. 3242 HSUEH and BECHER: INTERFACIAL SHEAR DEBONDING