SUN and SINGH: MULTIPLE MATRIX CRACKING 100 1门2 Error Bar 06185109132156179217245307 Applied Stress(MP Fig. 8. A dependence of matrix crack density on the applied stress. sponding to the first matrix cracking), and cracks distribution of the normalized crack spacing. For 15, 16 were generated at a load of 46 N(217 MPa, Fig. 9, the scatter of the crack spacing is from corresponding to the saturation of matrix cracking). 0.66mm to 2.53 mm, and the probability ranged No more matrix cracks were generated between the from 1. 2 to 19.8%. Figure 9 is obtained from a sum inside two pins after the saturation load of 46 N. of data from 10 samples with 164 cracks(7 samples Figure 8 shows the influence of the applied stress with 16 cracks, 2 samples with 17 cracks, and I on the crack density. The crack density was sample with 18 cracks). The predicted matrix crack obtained as the ratio of the number of cracks at a spacing calculated from equation (7)with statistical certain stress level to the total number of cracks at modification is about 0.65 mm by taking the inter- saturation. The saturation stress is about twice as face as a frictional case with a value of tr equal much as the FMC stress for this composite. This 30 MPa [22]. The experimental average crack range of stress is much larger than Zok's model [7, spacing value is much higher than the calculated in which the saturation stress was about 30% crack spacing value because firstly the real interface higher than the FMC stress. This difference can be of the composite shows debonding rather than explained by the fact that Zok,s model is valid purely frictional coupling, and secondly the statisti- Inder the assumption of a frictionally-coupled cal modification parameter a may not be equal to fiber-matrix interface. But, the current composite 1.34 in the case of a partially-bonded and debonded shows a higher interfacial shear strength (a large interface. In the present study, a is experimentally debond initiation stress aa)as shown in Table 2. found to be 2, and the overlap of debonded zone ccording to equation(17). the saturation stress for was not commonly observed in those composites a bonded interface will be higher than the friction- The non-uniformly distributed cracks implies that ally-coupled interface(aa>slide) provided other the matrix cracks and crack spacing are dependent roperties remain the same. Another explanation on the distribution of flaw and flaw size in the from Weitsman and Zhu [8] and LI [13] is that the matrix. amount of mechanical energy absorbed during the multiple fracture will be larger because of the appearance of an additional interfacial debond energy Ia term for a bonded interface. Therefore, the saturation stress will be higher because of the ontribution from interfacial debonding Another interesting phenomenon was the non- 8 uniformity of matrix crack distribution. The crack =10 spacing did not follow equation(7)strictly. The ex perimental average value from 10 specimens was E bout 1. I mm. The ratio of a particular crack spa- cing to the average crack spacing was taken as the normalized crack spacing. The statistical distri 聊] bution of matrix crack spacing was then obtained 06070.91.11.2151.82.3 by sorting the crack spacing, counting the number of their appearance, and calculating their prob- ability of occurrence. Figure 9 shows the statistical Fig 9 Histogram of matrix crack spacingsponding to the ®rst matrix cracking), and cracks 15, 16 were generated at a load of 46 N (217 MPa, corresponding to the saturation of matrix cracking). No more matrix cracks were generated between the inside two pins after the saturation load of 46 N. Figure 8 shows the in¯uence of the applied stress on the crack density. The crack density was obtained as the ratio of the number of cracks at a certain stress level to the total number of cracks at saturation. The saturation stress is about twice as much as the FMC stress for this composite. This range of stress is much larger than Zok's model [7], in which the saturation stress was about 30% higher than the FMC stress. This di€erence can be explained by the fact that Zok's model is valid under the assumption of a frictionally-coupled ®ber±matrix interface. But, the current composite shows a higher interfacial shear strength (a large debond initiation stress sd) as shown in Table 2. According to equation (17), the saturation stress for a bonded interface will be higher than the friction￾ally-coupled interface (sa>sslide) provided other properties remain the same. Another explanation from Weitsman and Zhu [8] and LI [13] is that the amount of mechanical energy absorbed during the multiple fracture will be larger because of the appearance of an additional interfacial debond energy Gd term for a bonded interface. Therefore, the saturation stress will be higher because of the contribution from interfacial debonding. Another interesting phenomenon was the non￾uniformity of matrix crack distribution. The crack spacing did not follow equation (7) strictly. The ex￾perimental average value from 10 specimens was about 1.1 mm. The ratio of a particular crack spa￾cing to the average crack spacing was taken as the normalized crack spacing. The statistical distri￾bution of matrix crack spacing was then obtained by sorting the crack spacing, counting the number of their appearance, and calculating their prob￾ability of occurrence. Figure 9 shows the statistical distribution of the normalized crack spacing. For Fig. 9, the scatter of the crack spacing is from 0.66 mm to 2.53 mm, and the probability ranged from 1.2 to 19.8%. Figure 9 is obtained from a sum of data from 10 samples with 164 cracks (7 samples with 16 cracks, 2 samples with 17 cracks, and 1 sample with 18 cracks). The predicted matrix crack spacing calculated from equation (7) with statistical modi®cation is about 0.65 mm by taking the inter￾face as a frictional case with a value of tf equal to 30 MPa [22]. The experimental average crack spacing value is much higher than the calculated crack spacing value because ®rstly the real interface of the composite shows debonding rather than a purely frictional coupling, and secondly the statisti￾cal modi®cation parameter a may not be equal to 1.34 in the case of a partially-bonded and debonded interface. In the present study, a is experimentally found to be 2, and the overlap of debonded zones was not commonly observed in those composites. The non-uniformly distributed cracks implies that the matrix cracks and crack spacing are dependent on the distribution of ¯aw and ¯aw size in the matrix. Fig. 8. A dependence of matrix crack density on the applied stress. Fig. 9. Histogram of matrix crack spacing. 1664 SUN and SINGH: MULTIPLE MATRIX CRACKING