SUN and SINGH: MULTIPLE MATRIX CRACKING 12 o.- Crack Al …Crak E +一 Crack#10 已号 05010015020 250300350 plied Stress(MPa) Fig 10. The dependence of debond length on the applied stress different matrix cracks 4.2. Interfacial debonding and debond length and finally overlapped with their neighbors, as The initiation and propagation of interfacial shown in Fig. 6(e) bonding were the most prominent phenomena accompanying the multiple matrix cracking which length as a function of the external stress for differ were visually observed in this investigation. Figure 6 ent matrix cracks illustrated in Fig. 10. A close- shows the debonded regions (lengths) on either side to-linear relationship between the debond length and applied stress is observed before the matrix of the matrix cracks at five different load levels. crack saturation which is quite similar to the trend The measured FMC stress for this composite with a predicted by ACK [6], BHE [12], HJ [10] and LI[13] fiber volume fraction of 12% is 85 MPa, and the in- models. But, a suppression of debond length is also ial debond stress obtained from a fiber pushout observed before the saturation of the matrix crack how similar Therefore, upon FMC, the additional load which is debond lengths because they are from the same thrown onto the bridging fibers locally around the region of the sample and show similar crack spa- matrix crack is sufficiently large to initiate the lowever, cracks #9 and 12 differ greatly from debond as well. This is the reason why debonding other cracks in measured values of the debond was observed at the interface when the FMC length. This unusual behavior results from a non- occurred. This observation is even true for an uniform crack spacing and stress distribution along incompletely propagated crack #4 in Fig. 6(a). Such the length of the bend specimen after a large displa a weakly-bonded interface is desired for toughening cement upon matrix cracking brittle matrix materials. As expected, the debond Figure 11 shows a comparison of the calculated propagated further with an increase of applied load and measured dependencies of debond length on 12 #1Fd=1.2J/ * -Crack #2 Crack 30MPa C#2 Energy approach 少象=譬 = 100 200 250 Applied Stress(MP Fig. 11. Experimental and theoretical dependencies of debond length on the applied stress.4.2. Interfacial debonding and debond length The initiation and propagation of interfacial debonding were the most prominent phenomena accompanying the multiple matrix cracking which were visually observed in this investigation. Figure 6 shows the debonded regions (lengths) on either side of the matrix cracks at ®ve di€erent load levels. The measured FMC stress for this composite with a ®ber volume fraction of 12% is 85 MPa, and the in￾itial debond stress obtained from a ®ber pushout test [22] is about 55 MPa, as shown in Table 2. Therefore, upon FMC, the additional load which is thrown onto the bridging ®bers locally around the matrix crack is suciently large to initiate the debond as well. This is the reason why debonding was observed at the interface when the FMC occurred. This observation is even true for an incompletely propagated crack #4 in Fig. 6(a). Such a weakly-bonded interface is desired for toughening brittle matrix materials. As expected, the debond propagated further with an increase of applied load and ®nally overlapped with their neighbors, as shown in Fig. 6(e). The experimental data of measured debond length as a function of the external stress for di€er￾ent matrix cracks are illustrated in Fig. 10. A close￾to-linear relationship between the debond length and applied stress is observed before the matrix crack saturation which is quite similar to the trend predicted by ACK [6], BHE [12], HJ [10] and LI [13] models. But, a suppression of debond length is also observed before the saturation of the matrix crack￾ing. The cracks #1, 2, 3 and 10 show similar debond lengths because they are from the same region of the sample and show similar crack spa￾cing. However, cracks #9 and 12 di€er greatly from other cracks in measured values of the debond length. This unusual behavior results from a non￾uniform crack spacing and stress distribution along the length of the bend specimen after a large displa￾cement upon matrix cracking. Figure 11 shows a comparison of the calculated and measured dependencies of debond length on Fig. 10. The dependence of debond length on the applied stress for six di€erent matrix cracks. Fig. 11. Experimental and theoretical dependencies of debond length on the applied stress. SUN and SINGH: MULTIPLE MATRIX CRACKING 1665