1988 L Zou et al. Journal of the European Ceramic Society 23(2003)1987-1996 directly. Meanwhile, the reliability of the SENB method symmetrically from the centre, also a debonded layer is influenced by notch retard effect and the highly ani- between the through-thickness crack and the tip of an sotropy in composite due to the existence of multi weak interfacial crack cannot undertake load. The com- interfaces. So the interfacial toughness, i.e. the inter- pliance corresp onding to the loading stage is calculated facial strain-energy release rate or interfacial resistance, according to the remained section as shown in Fig. 1. In was proposed for characterizing the interfacial bonding addition, it was assumed that the value of the critical strength. Unfortunately, data on interfacial toughness interfacial toughness Gic is a constant, uniform of the composite have been seldom reported in litera- throughout the specimen. 1. tures. In addition. so far. there are few relia ble methods From Fig. 1. the formula for calculating the inter for measuring interfacial toughness. Although Kovar et facial toughness can be deduced. Because the interlay alo gave a method for measuring the interfacial tough- is just in the middle of the upper and lower Si3N4 ness, the specimens they used were different with what matrixes, it is exact the position of the neutral axis. In the model based on, with which interfacial toughness region ( the beam can carry stress, there exists corre- was calculated, o and the method was not so reliable. sponding deflection curve equation Based on the model of Charalambides et al., Phillips et al. II measured the interfacial toughness of a lam d-y1 Px nated SiC/C composite using an SiC/C/Sic sandwich dx2 (1) sample with a single interphase. However, the sample mensions ado pted by those researchers were too large where yi is the displacement from the neutral axis and (3.5×18×140mm3) for the sample to be easily man-∑ the beam stifness of region① ufactured and machined, making the method incon In region 2, only the half side Si3 N4 matrix layer is venient for characterizing interfacial toughness and also assumed to carry the applied stress, so it is related with limiting its flexibility. Besides the big size, the sample the following equatio was notched and precracked under three-point bending, with a short loading span, before the test, but that pro- dy2=-2Es cess is difficult to control and also makes it very difficult to obtain a crack starting from the tip of the notch and just exactly reaches the interphase or deflects toward where y2 the displacement from the neutral axis of the wo sides a little there lower Si3N4 matrix, Es the beam stifness of the matrix In this paper, we improved the method used by Phil- layer in region(2 lips et al., and gave a method that is suitable for mea There exist the following boundary conditions suring and characterizing interfacial toughness of the Si3/BN composite, which is simple and easy to be )ilr=0 extended. By using this method the interfacial toughness of the BN interphase systems strengthend by Si3 N4 and Al2O3 respectively was measured and characterized dx l=) d 2. Experimental d d 2. 1. Experiment prIne According to the partial differential equations of (1)and Based on the model of the fracture of laminated(2), and the earlier-mentioned boundary conditions, we composites under three-point bending given by Phillips can obtain the relationship between the displacement of et al., 2 a single- interlayer type of sandwiching material, the central loading point and the propagating crack with one preset crack source connecting directly to a bn length interphase in the middle of a single half-Si3 N4 matrix acterizing interfacial toughness. The upper and lower P PL+6Ee Es)(L-a was designed and fabricated for measuring and char- Si3N4 matrixes height were kept as equal as possible to fix the effect of h/h2 on the phase angle v, i.e. to make since y= CP, hence the ratio of shearing to opening stress-intensity factors tended to be constant. 3, 4 The three-point loading system of the sample is shown in Fig. 1. According to the model, 2 the through-thickness cracks occur in the centre of the beam and the interfacial cracks propagate so the crack length can be expressed by compliancedirectly. Meanwhile,the reliability of the SENB method is influenced by notch retard effect and the highly ani￾sotropy in composite due to the existence of multi weak interfaces. So the interfacial toughness,i.e. the inter￾facial strain–energy release rate or interfacial resistance, was proposed for characterizing the interfacial bonding strength. Unfortunately,data on interfacial toughness of the composite have been seldom reported in litera￾tures. In addition,so far,there are few reliable methods for measuring interfacial toughness. Although Kovar et al 6 gave a method for measuring the interfacial tough￾ness,the specimens they used were different with what the model based on,with which interfacial toughness was calculated,10 and the method was not so reliable. Based on the model of Charalambides et al.,10 Phillips et al.11 measured the interfacial toughness of a lami￾nated SiC/C composite using an SiC/C/SiC sandwich sample with a single interphase. However,the sample dimensions adopted by those researchers were too large (3.5
18
140 mm3 ) for the sample to be easily man￾ufactured and machined,making the method incon￾venient for characterizing interfacial toughness and also limiting its flexibility. Besides the big size,the sample was notched and precracked under three-point bending, with a short loading span,before the test,but that pro￾cess is difficult to control and also makes it very difficult to obtain a crack starting from the tip of the notch and just exactly reaches the interphase or deflects toward two sides a little there. In this paper,we improved the method used by Phil￾lips et al.,11 and gave a method that is suitable for mea￾suring and characterizing interfacial toughness of the Si3N4/BN composite,which is simple and easy to be extended. By using this method,the interfacial toughness of the BN interphase systems strengthend by Si3N4 and Al2O3 respectively was measured and characterized. 2. Experimental 2.1. Experiment principle Based on the model of the fracture of laminated composites under three-point bending given by Phillips et al.,12 a single-interlayer type of sandwiching material, with one preset crack source connecting directly to a BN interphase in the middle of a single half-Si3N4 matrix, was designed and fabricated for measuring and char￾acterizing interfacial toughness. The upper and lower Si3N4 matrixes height were kept as equal as possible to fix the effect of h1/h2 on the phase angle ,i.e. to make the ratio of shearing to opening stress-intensity factors tended to be constant.11,13,14 The three-point loading system of the sample is shown in Fig. 1. According to the model,12 the through-thickness cracks occur in the centre of the beam and the interfacial cracks propagate symmetrically from the centre,also a debonded layer between the through-thickness crack and the tip of an interfacial crack cannot undertake load. The com￾pliance corresponding to the loading stage is calculated according to the remained section as shown in Fig. 1. In addition,it was assumed that the value of the critical interfacial toughness Gic is a constant,uniform throughout the specimen.11,12 From Fig. 1,the formula for calculating the inter￾facial toughness can be deduced. Because the interlayer is just in the middle of the upper and lower Si3N4 matrixes,it is exact the position of the neutral axis. In region ,the beam can carry stress,there exists corre￾sponding deflection curve equation: d2y1 dx2 ¼ Px 2Sc ð1Þ where y1 is the displacement from the neutral axis and c the beam stiffness of region . In region ,only the half side Si3N4 matrix layer is assumed to carry the applied stress,so it is related with the following equation: d2y2 dx2 ¼ Px 2Ss ð2Þ where y2 the displacement from the neutral axis of the lower Si3N4 matrix, s the beam stiffness of the matrix layer in region . There exist the following boundary conditions: y1jx¼0 ¼ 0 dy1 dx jx¼ð Þ La ¼ dy2 dx jx¼ð Þ La y1jx¼ð Þ La ¼ y2jx¼ð Þ La dy2 dx jx¼L¼ 0 According to the partial differential equations of (1) and (2),and the earlier-mentioned boundary conditions,we can obtain the relationship between the displacement of the central loading point and the propagating crack length. y ¼ P 6Ss L3 þ P 6 1 Sc 1 Ss
ð Þ L a 3 ð3Þ since y ¼ CP,hence C ¼ 1 6Ss L3 þ 1 6 1 Sc 1 Ss
ð Þ L a 3 ð4Þ so the crack length can be expressed by compliance. 1988 L. Zou et al. / Journal of the European Ceramic Society 23 (2003) 1987–1996