April 1998 Crack Deflection and Propagation in Layered Silicon Nitride/Boron Nitride Ceramics 10 layers that are oriented perpendicular or almost perpendicular to the interface. If these flaws are sufficiently large, they ca raw the delamination crack out of the interphase and into a n4 layer, which causes the delamination crack to kink 19A Crack Kinking heoretical treatment of such a problem has been previously 150 proposed by He et al. 24 and has been used here to predi ct the critical interfacial flaw size necessary to induce crack kinking He et al. 24 suggested that the driving force for crack kinking is provided by the in-plane stress(T-stress)that acts parallel to he interface at the delamination crack tip and is influenced by the size of interfacial flaws. This stress can result from the Delamination applied loads or from residual stresses that may be present due to thermal expansion mismatch between the layers. In the case of the SigN/BN system, extensive microcracking has been observed in the BN layers prior to testing.7 If the T-stress contributes to crack kinking in this material system, it must esult from the applied loads because microcracking should act to relieve most of the residual stress due to thermal mismatch between the sin, and the bn Ti/Tsin An analytical calculation of the T-stress caused by the a lied loads is quite complex for the delamination specimen Fig 14. Ratio of the resistance of the interphase to fracture used in the current study. However, it is possible to calculate an resistance of the Si na /TSin ) plotted versus the critical flaw upper-bound limit to the T-stress using simple beam-bending size necessary to induc quations. Because only the uncracked portion of the beam carries load, the normal stress in this portion of the beam ca be calculated from the moment necessary to propagate the de of the materials exhibited a combination of delamination crack- ack using Eq(1). To a first approximation, this ing and crack kinking(see Figs. 7 and 9(b)and(c). The plaI is the T-stress that results from the applied mo- probability that crack kinking occurred along a given inter- e, the T-stress, Oo, is given by phase increased as the interfacial fracture resistance increased The statistical nature of crack kinking is consistent with the 6T.E 0mhm-13m-m-301 notion that crack kinking is controlled by the probability encountering a suitable interfacial defect. Despite the qualitative agreement between the observed be- This is an approximation because, in reality, the uncracked havior and the crack kinking model that was presented, there portion of the beam also carries some load at a distance far are several reasons why caution should be taken in directly from the delamination crack tip. Thus, this calculation yields an applying this model to the Si3N4/BN system. For example, the upper bound to the T-stress. For this specimen geometry, the analysis of He et al. 2 that was used to calculate the conditions calculated value of the T-stress varies slightly with the position for crack kinking assumed that crack deflection occurs at the of the delamination crack within the specimen. However, given interface between two layers rather than within the in the nature of this calculation, this variation was neglected and as was observed in this system(see Fig. 8(a)); this the T-stress was calculated 0.5 that, in the sin,/bn system, crack deflection is not co Besides the T-stress, there are several other parameters that by the fracture resistance of the interface between SiN influence the critical flaw size for crack kinking. such as the bn, but rather by the weak bn interphase itself. The mismatch between the materials on either side of the interface. case are the ratio of the fracture resistance in the bn parallel to To simplify the calculation, it was assumed that all flaws were the interface, compared to the fracture resistance of the bn in oriented perpendicular to the interface. It was also necessary to a direction dicular to the interface. as well as the elastic compute the Dundurs parameters, a and B, from the Youngs anisotropy of BN in these directions. Based on SEM observa modulus(E) and Poissons ratios(v) of the individual layers. tions, the bn consists of well-aligned platelets that have a Previous measurements of E for this composition of Si3 N4 gave thickness of-0 1-0.5 um and a length and width of-5-10 um a value of 320 GPa, I and the value of v has been reported as Texture measurements on similar fibrous monolithic laminates being 0.27. Literature values of E and v for BN have been using XRD confirm that the bn is highly textured: 6 thus, it eported as 22 GPa and 0.32, respectively. 25 expected that there should be anisotropy in the fracture resis- The results of this calculation are plotted in Fig. 14 and show tance as well as in the elastic properties. Unfortunately, it is not the dependence of the critical flaw size required to cause crack possible to measure the fracture resistance of Bn perpendicular kinking on the interfacial fracture resistance. Based on the to the interface, because cracks that are driven in this direction strength(which, from Fig. 2, did not vary substantially as the inevitably deflect and grow parallel to the interface composition of the interphase was adjusted) and fracture resis- The fact that crack propagation occurs in the Bn interphase tance of the Si3 N4 layers, the maximum flaw size in these rather than at the Si3 N,/BN interface may also influence this layers is-45 um. At this critical flaw size, the transition from calculation. Although flaws in the Si3N4 layers can act to draw delamination cracking to crack kinking is predicted from Fig. the crack out of the interphase, it is also possible that local served crack deflection behavior shown in Figs. 4(aHd) seems (e.g, a Si3N4 particle or a misaligned BN platelet)may impede to agree well with this prediction. At very high values of frac ture resistance(T>80 J/m), no crack deflection was ob. trations of these two cases are shown in Fig. 15. Additional served. At moderate values of the interfacial fracture resistance complications also result if one considers the pre-existing (:=50-80 J/m), crack deflection occurred; however, most crocracks that have been observed in the bn layers?and their of the delamination crack lengths were very short due to crack influence on crack deflection and subsequent delamination. kinking. Extensive delamination cracking was only observed in These factors emphasize the need for the development of more- the materials that had very low interfacial fracture resistance realistic models that can account for interfacial defects as well alues(i= 30-50 J/m2). It is also important to note that sor as the anisotropy of the interphaslayers that are oriented perpendicular or almost perpendicular to the interface. If these flaws are sufficiently large, they can draw the delamination crack out of the interphase and into a Si3N4 layer, which causes the delamination crack to kink.19 A theoretical treatment of such a problem has been previously proposed by He et al.24 and has been used here to predict the critical interfacial flaw size necessary to induce crack kinking. He et al.24 suggested that the driving force for crack kinking is provided by the in-plane stress (T-stress) that acts parallel to the interface at the delamination crack tip and is influenced by the size of interfacial flaws. This stress can result from the applied loads or from residual stresses that may be present due to thermal expansion mismatch between the layers. In the case of the Si3N4/BN system, extensive microcracking has been observed in the BN layers prior to testing.7 If the T-stress contributes to crack kinking in this material system, it must result from the applied loads, because microcracking should act to relieve most of the residual stress due to thermal mismatch between the Si3N4 and the BN. An analytical calculation of the T-stress caused by the ap￾plied loads is quite complex for the delamination specimen used in the current study. However, it is possible to calculate an upper-bound limit to the T-stress using simple beam-bending equations. Because only the uncracked portion of the beam carries load, the normal stress in this portion of the beam can be calculated from the moment necessary to propagate the de￾lamination crack using Eq. (1). To a first approximation, this in-plane stress is the T-stress that results from the applied mo￾ment. Therefore, the T-stress, so, is given by so = F 6Gi E Hh~h − 1!~3h − h2 − 3!~1 − n2 ! G 1/2 (4) This is an approximation because, in reality, the uncracked portion of the beam also carries some load at a distance far from the delamination crack tip. Thus, this calculation yields an upper bound to the T-stress. For this specimen geometry, the calculated value of the T-stress varies slightly with the position of the delamination crack within the specimen. However, given the nature of this calculation, this variation was neglected and the T-stress was calculated assuming h 4 0.5. Besides the T-stress, there are several other parameters that influence the critical flaw size for crack kinking, such as the flaw orientation, with respect to the interface, and the elastic mismatch between the materials on either side of the interface. To simplify the calculation, it was assumed that all flaws were oriented perpendicular to the interface. It was also necessary to compute the Dundurs’ parameters, a and b, from the Young’s modulus (E) and Poisson’s ratios (n) of the individual layers. Previous measurements of E for this composition of Si3N4 gave a value of 320 GPa,11 and the value of n has been reported as being 0.27. Literature values of E and n for BN have been reported as 22 GPa and 0.32, respectively.25 The results of this calculation are plotted in Fig. 14 and show the dependence of the critical flaw size required to cause crack kinking on the interfacial fracture resistance. Based on the strength (which, from Fig. 2, did not vary substantially as the composition of the interphase was adjusted) and fracture resis￾tance of the Si3N4 layers, the maximum flaw size in these layers is ∼45 mm. At this critical flaw size, the transition from delamination cracking to crack kinking is predicted from Fig. 14 to occur when Gi /GSi3N4 4 0.4 or Gi 4 50 J/m2 . The ob￾served crack deflection behavior shown in Figs. 4(a)–(d) seems to agree well with this prediction. At very high values of frac￾ture resistance (Gi > 80 J/m2 ), no crack deflection was ob￾served. At moderate values of the interfacial fracture resistance (Gi 4 50–80 J/m2 ), crack deflection occurred; however, most of the delamination crack lengths were very short due to crack kinking. Extensive delamination cracking was only observed in the materials that had very low interfacial fracture resistance values (Gi 4 30–50 J/m2 ). It is also important to note that some of the materials exhibited a combination of delamination crack￾ing and crack kinking (see Figs. 7 and 9(b) and (c)). The probability that crack kinking occurred along a given inter￾phase increased as the interfacial fracture resistance increased. The statistical nature of crack kinking is consistent with the notion that crack kinking is controlled by the probability of encountering a suitable interfacial defect. Despite the qualitative agreement between the observed be￾havior and the crack kinking model that was presented, there are several reasons why caution should be taken in directly applying this model to the Si3N4/BN system. For example, the analysis of He et al.24 that was used to calculate the conditions for crack kinking assumed that crack deflection occurs at the interface between two layers rather than within the interphase, as was observed in this system (see Fig. 8(a)); this suggests that, in the Si3N4/BN system, crack deflection is not controlled by the fracture resistance of the interface between Si3N4 and BN, but rather by the weak BN interphase itself. The appro￾priate material properties that control crack deflection in this case are the ratio of the fracture resistance in the BN parallel to the interface, compared to the fracture resistance of the BN in a direction perpendicular to the interface, as well as the elastic anisotropy of BN in these directions. Based on SEM observa￾tions, the BN consists of well-aligned platelets that have a thickness of ∼0.1–0.5 mm and a length and width of ∼5–10 mm. Texture measurements on similar fibrous monolithic laminates using XRD confirm that the BN is highly textured;26 thus, it is expected that there should be anisotropy in the fracture resis￾tance as well as in the elastic properties. Unfortunately, it is not possible to measure the fracture resistance of BN perpendicular to the interface, because cracks that are driven in this direction inevitably deflect and grow parallel to the interface. The fact that crack propagation occurs in the BN interphase rather than at the Si3N4/BN interface may also influence this calculation. Although flaws in the Si3N4 layers can act to draw the crack out of the interphase, it is also possible that local regions of high interfacial resistance within the BN interphase (e.g., a Si3N4 particle or a misaligned BN platelet) may impede the delamination crack and cause it to kink. Schematic illus￾trations of these two cases are shown in Fig. 15. Additional complications also result if one considers the pre-existing mi￾crocracks that have been observed in the BN layers7 and their influence on crack deflection and subsequent delamination. These factors emphasize the need for the development of more￾realistic models that can account for interfacial defects as well as the anisotropy of the interphase. Fig. 14. Ratio of the fracture resistance of the interphase to fracture resistance of the Si3N4 layer (Gi /GSi3N4 ), plotted versus the critical flaw size necessary to induce crack kinking (a). April 1998 Crack Deflection and Propagation in Layered Silicon Nitride/Boron Nitride Ceramics 1011