October 1997 Fibrous monolithic ceramics 2481 tively a crack also can kink if the interfacial fracture resistance suddenly increases along a local region of the interface 50% 哥/ purpose of this discussion, no distinction is made weak regions in the Sig N4 cells and strong regions in 10% The orientation and size of the flaw necessary to draw a delamination crack out of interface and kink through a cell is determined by the interfacial fracture resistance, elastic mis match between the cell and cell boundary, and the residual stresses present in the layers. The specimen geometry also is important, because the driving force for a kink to grow is provided by the in-plai ane stresses(T-stress) parallel to the in- (Es-EB/(Es EB or because of residual stresses from thermal expansion mis match. However, in the Si3NaBN system, the spontaneous microcrack at Is observed in the bn interphase would be Fig. 15. Ratio of the fracture resistance of the interphase to that of expected to dissipate most of the in-plane residual stress be- the cell is plotted as a function of the elastic mismatch between the - v kinking it is expected that the primary driving force for crack cause of thermal mismatch between the sin, and the bn.a flection should or should not occur based on the analysis of He Hutchinson. 33 Points indicate experimental data for Si, N, layers sepa- inking would be provided by the applied load rated by Si3N-BN interphases with the volume fraction of Si3N4 in A simple model based on the analysis of He et al, as de- the interphase shown next to the datum point. Crack deflection is scribed elsewhere, 5 has been constructed to predict when observed in all of the experiments crack kinking occurs. A map of crack propagation behavior is plotted in Fig. 18 based system, the predicted critical flaw size(either in the cell or in he cell boundary)to induce crack kinking is of the order of 100 um. Because it is unlikely that flaws of such a large size woule SigNa be present, crack kinking is not anticipated in Si3 N4 with a BN interphase. Thus, it is likely that a delamination crack continues to propagate until it reaches the end of the inner loading span, creases. The applied load must then increase until the stress on the outermost layers of uncracked cells reaches the strength of he cells. At this point, a through-thickness crack initiates in his layer of cell If the interfacial fracture resistance is increased (for ex ample, by adding Si N4 to the BN interphase ), the critical flaw BN size to induce kinking decreases. If a delamination crack does encounter a flaw greater than the critical flaw size, the delani- nation crack kinks at the flaw and the delamination crack ceases to propagate. The result is that the delamination crack engths are significantly shorter when crack kinking occurs Extensive crack deflection is observed only when the interfa cial fracture resistance is very low(<50 J/m). As the interfa SiaN 15 um cial fracture is increased by adding SiaN4 to the interphase, the extent of delamination cracking is reduced as an increasing number of delamination cracks kink Fig. 16. SEM micrograph showing a crack growing within the BN Theoretical arguments suggest that a delamination crack will rack Kinking kink out of an interface if a suitably oriented flaw larger than a critical flaw size in the cell is encountered. as shown sche matically in Fig. 17. Kinking due to a flaw in the strong phase (Si N4) has been considered by several authors 40-42 Alterna Delamination 00.10.2030.40506 TUTe Fig. 18. Critical flaw size predicte kink out of the Bn interphase is plotted versus the facial fracture Fig. 17. Schematic showing a delamination crack growing in resistance to the fracture resistance of e delamination interphase and encountering a flaw in the surrounding Si,N laye cracking occurs only when the interfacial fracture resistance is very causes the crack to kink out of the interphase and into the Si, N A low or when the flaw size in the Si,N4 layers is smallTheoretical arguments suggest that a delamination crack will kink out of an interface if a suitably oriented flaw larger than a critical flaw size in the cell is encountered, as shown sche￾matically in Fig. 17. Kinking due to a flaw in the strong phase (Si3N4) has been considered by several authors.40–42 Alterna￾tively, a crack also can kink if the interfacial fracture resistance suddenly increases along a local region of the interface. For the purpose of this discussion, no distinction is made between weak regions in the Si3N4 cells and strong regions in the BN interphase, and both are considered to act as flaws that promote crack kinking. The orientation and size of the flaw necessary to draw a delamination crack out of interface and kink through a cell is determined by the interfacial fracture resistance, elastic mis￾match between the cell and cell boundary, and the residual stresses present in the layers.41 The specimen geometry also is important, because the driving force for a kink to grow is provided by the in-plane stresses (T-stress) parallel to the in￾terface. These stresses can result because of the applied loads or because of residual stresses from thermal expansion mis￾match. However, in the Si3N4–BN system, the spontaneous microcracking that is observed in the BN interphase would be expected to dissipate most of the in-plane residual stress be￾cause of thermal mismatch between the Si3N4 and the BN. As a result, it is expected that the primary driving force for crack kinking would be provided by the applied load. A simple model based on the analysis of He et al., as de￾scribed elsewhere,35 has been constructed to predict when crack kinking occurs. A map of crack propagation behavior is plotted in Fig. 18 based on this analysis. For the Si3N4–BN system, the predicted critical flaw size (either in the cell or in the cell boundary) to induce crack kinking is of the order of 100 mm. Because it is unlikely that flaws of such a large size would be present, crack kinking is not anticipated in Si3N4 with a BN interphase. Thus, it is likely that a delamination crack continues to propagate until it reaches the end of the inner loading span, where the driving force for continued crack propagation de￾creases. The applied load must then increase until the stress on the outermost layers of uncracked cells reaches the strength of the cells. At this point, a through-thickness crack initiates in this layer of cells. If the interfacial fracture resistance is increased (for ex￾ample, by adding Si3N4 to the BN interphase), the critical flaw size to induce kinking decreases. If a delamination crack does encounter a flaw greater than the critical flaw size, the delami￾nation crack kinks at the flaw and the delamination crack ceases to propagate. The result is that the delamination crack lengths are significantly shorter when crack kinking occurs. Extensive crack deflection is observed only when the interfa￾cial fracture resistance is very low (<50 J/m2 ). As the interfa￾cial fracture is increased by adding Si3N4 to the interphase, the extent of delamination cracking is reduced as an increasing number of delamination cracks kink. Fig. 15. Ratio of the fracture resistance of the interphase to that of the cell is plotted as a function of the elastic mismatch between the cell and cell boundary. Solid line separates the regions where crack de￾flection should or should not occur based on the analysis of He and Hutchinson.33 Points indicate experimental data for Si3N4 layers sepa￾rated by Si3N4–BN interphases with the volume fraction of Si3N4 in the interphase shown next to the datum point. Crack deflection is observed in all of the experiments. Fig. 16. SEM micrograph showing a crack growing within the BN cell boundary. Fig. 17. Schematic showing a delamination crack growing in the BN interphase and encountering a flaw in the surrounding Si3N4 layer that causes the crack to kink out of the interphase and into the Si3N4 layer. Fig. 18. Critical flaw size predicted to cause a crack to kink out of the BN interphase is plotted versus the ratio of the interfacial fracture resistance to the fracture resistance of Si3N4. Extensive delamination cracking occurs only when the interfacial fracture resistance is very low or when the flaw size in the Si3N4 layers is small. October 1997 Fibrous Monolithic Ceramics 2481