Availableonlineatwww.sciencedirect.com SCIENCE E噩≈S Journal of the European Ceramic Society 24(2004)2861-2868 www.elsevier.com/locate/jeurceramsoc The characterization and measurement of interfacial toughness for Si3N4/bn composites by the four-point bend test Linhua Zou", Yong Huang, Chang-an Wan State Key Laboratory of New Ceramics and Fine Processing, Tsinghua University, Beijing 100084, China Received 10 March 2003: received in revised form 30 July 2003; accepted 3 August 2003 Abstract The interfacial toughness of Si3 N4/BN composites with different interphase compositions has been characterized. A single-inter- layer type of sandwich material Si3N4/BN/Si3N4, with one preset crack path connecting directly to the bn interphase in the center of one side of the Si3 N4 matrix, was designed and fabricated. Sandwiched sample bars measuring 3 mmx 4 mmx50 mm were cut nd machined. The load-displacement curves for the samples were obtained using the four-point bend test, and the interfacial toughness was calculated, based on the model for a specimen with bimaterial interface. The interfacial toughness was measured for composites with interphases strengthened by Si3 N4 or Al2O3 modifiers. The method was proved to be viable. The effectiveness of the method was further discussed and the reasons for its effectiveness explained C 2003 Elsevier Ltd. All rights reserved Keywords: Composites; Interfaces: Testing: Si3N4-BN: Toughness 1. Introduction interfacial strain-energy release rate or interfacial frac- ture resistance. is used to characterize the interfacial Silicon nitride(Si3 N4) is a very promising, high-tem- combining strength. Unfortunately, data on the inter perature structural material, with excellent mechanical facial toughness of Si3 N4/BN composites with different strength; but brittleness limits its applications. Based interphase compositions have seldom been reported in on the structures of natural biomaterials such as mol he literature, especially for Si, N4 composites reinforced lusk shells, bamboos, trees, and bones. the idea of with Sic whiskers. Kovar et al. 2 measured the inter- biomimetic design has been introduced to materials facial toughness of Si3 N4/BN composites with different processing within the past 10 years. The principle of interphase compositions modified by Si3N4; in their structural design introduced by that idea is to decrease, experiment, a laminated sample with multiple inter- as much as possible, the dependence of the mechanical phases was notched at the middle position and then properties of a material on its original natural crack loaded, under four-point bending. However, the model population, by a mechanism of energy dissipation, thus with which the interfacial toughness was calculated was producing a material with flaw tolerance that of a bimaterial interface. Thus, the interphase Si3 N4/BN composites with multilayer laminates and crack-propagation behavior was not accurately reflec- in situ synthesized fibrous monolithic structures have ted. Based on the model of Charalambides et al., Phil- been fabricated according to the biomimetic lips et al. studied the fracture behavior of laminated principle. Such composites possess higher apparent SiC/C composites and measured the interfacial tough fracture toughness, and they also maintain a high level ness of the composites using an SiC/C/SiC sandwich of strength. The design of the interphase is the most sample with a single interlayer. However, the sample important factor in fabricating materials with such dimensions adopted by those researchers (3.5 mmx183 properties. Usually, the interfacial toughness, i.e., t mmx140 mm) and in another work by Howard et al. 7(3 mmx20 mmx 160 mm)were too large for the sample to be easily manufactured and machined, making it diffi cult to characterize the interfacial toughness and also 0955-2219S. see front matter C 2003 Elsevier Ltd. All rights reserved. doi: 10. 1016/j. jeurceramsoc 2003.08.006
The characterization and measurement of interfacial toughness for Si3N4/BN composites by the four-point bend test Linhua Zou*,Yong Huang,Chang-an Wang State Key Laboratory of New Ceramics and Fine Processing, Tsinghua University, Beijing 100084, China Received 10 March 2003; received in revised form 30 July 2003; accepted 3 August 2003 Abstract The interfacial toughness of Si3N4/BN composites with different interphase compositions has been characterized. A single-interlayer type of sandwich material Si3N4/BN/Si3N4,with one preset crack path connecting directly to the BN interphase in the center of one side of the Si3N4 matrix,was designed and fabricated. Sandwiched sample bars measuring 3 mm4 mm50 mm were cut and machined. The load–displacement curves for the samples were obtained using the four-point bend test,and the interfacial toughness was calculated,based on the model for a specimen with bimaterial interface. The interfacial toughness was measured for composites with interphases strengthened by Si3N4 or Al2O3 modifiers. The method was proved to be viable. The effectiveness of the method was further discussed and the reasons for its effectiveness explained. # 2003 Elsevier Ltd. All rights reserved. Keywords: Composites; Interfaces; Testing; Si3N4–BN; Toughness 1. Introduction Silicon nitride (Si3N4) is a very promising,high-temperature structural material,with excellent mechanical strength; but brittleness limits its applications. Based on the structures of natural biomaterials,such as mollusk shells,bamboos,trees,and bones,the idea of biomimetic design has been introduced to materials processing within the past 10 years. The principle of structural design introduced by that idea is to decrease, as much as possible,the dependence of the mechanical properties of a material on its original natural crack population,by a mechanism of energy dissipation,thus producing a material with flaw tolerance. Si3N4/BN composites with multilayer laminates and in situ synthesized fibrous monolithic structures have been fabricated according to the biomimetic principle.14 Such composites possess higher apparent fracture toughness,and they also maintain a high level of strength. The design of the interphase is the most important factor in fabricating materials with such properties. Usually,the interfacial toughness,i.e.,the interfacial strain–energy release rate or interfacial fracture resistance,is used to characterize the interfacial combining strength. Unfortunately,data on the interfacial toughness of Si3N4/BN composites with different interphase compositions have seldom been reported in the literature,especially for Si3N4 composites reinforced with SiC whiskers. Kovar et al.2 measured the interfacial toughness of Si3N4/BN composites with different interphase compositions modified by Si3N4; in their experiment,a laminated sample with multiple interphases was notched at the middle position and then loaded,under four-point bending. However,the model with which the interfacial toughness was calculated was that of a bimaterial interface.5 Thus,the interphase crack-propagation behavior was not accurately reflected. Based on the model of Charalambides et al.,5 Phillips et al.6 studied the fracture behavior of laminated SiC/C composites and measured the interfacial toughness of the composites using an SiC/C/SiC sandwich sample with a single interlayer. However,the sample dimensions adopted by those researchers (3.5 mm18.3 mm140 mm) and in another work by Howard et al.7 (3 mm20 mm160 mm) were too large for the sample to be easily manufactured and machined,making it diffi- cult to characterize the interfacial toughness and also 0955-2219/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jeurceramsoc.2003.08.006 Journal of the European Ceramic Society 24 (2004) 2861–2868 www.elsevier.com/locate/jeurceramsoc * Corresponding author. E-mail address: linhua_zou@hotmail.com (L. Zou).
2862 L Zou et al. / Journal of the European Ceramic Society 24(2004)2861-2868 limiting its flexibility. In addition, the sample was not- here, y is the displacement from the neutral axis, E o) ched and precracked under three-point bending, with a Youngs modulus at displacement y, and A the cross hort loading span, a process which is difficult to control sectional area of the beam. For a sandwiched sample with ceramic materials and which also makes it very dif- with a single, thin interlayer, the corresponding beam ficult to obtain a crack that reaches the interphase; the stiffness can be expressed approximately as sample tends to fracture directly instead of obtaining a precrack that reaches the interphase This is the most 2=mbE=lE 3) important thing that limits the application of the method Based on the above-mentioned previous work, we where h is the total thickness of the sample(mm), b the improved their methods by adopting a sandwich spe sample width(mm), E Youngs modulus for the si3N4 men of small size, and by introducing a weak crack path matrix(kgf/mm), and Ic the moment of inertia of the connecting to the interphase for solving the precrack sample (mm#). It implies that the Youngs modulus of problem, and used the improved method for character- the sample is approximately equal to that of the Si3 n4 izing and measuring the interfacial toughness of SigN matrix layer BN composites with Sic whisker toughened Si3N4 Substituting Eq. 3)into Eq (1)gives matrix. Interfacial toughness is measured for various P2S2 nterphase compositions strengthened by Si3N4 or Al2O3. Gi 2. Experimental where Is is the moment of inertia of the single-matrix beam contacting the two inner loading points(mm) 2. 1. Experimental principle When crack bursting occurs, the critical interfacial toughness, Gic, or critical load, Pc, corresponding to Usually, two types of crack propagation occur: (1) crack propagation, varies considerably with crack posi stable propagation, also known as crack creeping, and tion, and compliance increases quickly under the con (2)nonstable propagation, also called crack bursting. 6. 7 stant roller displacement, so that the applied load, P, What type of propagation will happen depends on the decreases with the crack advance. According to the variation of interfacial toughness with position(possibly crack-propagation criterion aused by microstructural inhomogeneities) and on fac- G> G crack propagation, interfacial toughness does not vary when Pc decreases more rapidly than P, unstable crack considerably along the interface. Under the displace- propagation occurs, and the interfacial toughness is ment control of four-point loading, stable crack prop- characterized by bursting initiation and termination agation occurs between two inner loading points after a loads critical load has been reached. 7 In such a case. the load almost constant, but displacement increases con- G:_ P2S2/1-L tinuously. For symmetrical propagation along both 8bE I expressed by the following equation>ughness can be sides of an interphase, interfacial to Here. Gic is the average value of critical interfacial P2S2 toughness and PI and P2 the bursting initiation and (1) termination loads, respectively(N). Pe is the effective load(N), i.e., the geometric mean of the initiation and termination loads [(P, P2)/2] where Gi is the interfacial toughness (J/m), P the load According to the sample dimensions, if it is in plane corresponding to crack propagation(N), b the sample strain condition, E in Eqs. (4)and(6) will be substituted width(mm), S the spacing between the inner and outer by the plane strain modulus E=E(1-v2) oading lines(mm), >s the beam stiffness of the single layer Si3 N4 matrix(N-mm), and >c the beam stiffness 2. 2. Sample design and material preparation of the single-interlayer sandwiched sample(N-mm) The interfacial toughness given by Eq ()is a transient A Si3 N4/BN/Si3 N4 sandwich sample with a single BN one, because the load P is not absolutely constant due to interlayer and the thickness of the upper and lower sides defined by the follows ity. The beam stiffness can be of the Si3N4 matrices as equal as possible was designed the interphase ununiform for the present study. On one side of the sandwich, a crack source directly connecting to the Bn interphase was ∑=|Ey2l4 (2) preset during material preparation. First, a-Si3N4 pow ders( Founder High Technology Ceramic Co., Beijing
limiting its flexibility. In addition,the sample was notched and precracked under three-point bending,with a short loading span,a process which is difficult to control with ceramic materials and which also makes it very dif- ficult to obtain a crack that reaches the interphase; the sample tends to fracture directly instead of obtaining a precrack that reaches the interphase. This is the most important thing that limits the application of the method. Based on the above-mentioned previous work,we improved their methods by adopting a sandwich specimen of small size,and by introducing a weak crack path connecting to the interphase for solving the precrack problem,and used the improved method for characterizing and measuring the interfacial toughness of Si3N4/ BN composites with SiC whisker toughened Si3N4 matrix. Interfacial toughness is measured for various interphase compositions strengthened by Si3N4 or Al2O3. 2. Experimental 2.1. Experimental principle Usually,two types of crack propagation occur: (1) stable propagation,also known as crack creeping,and (2) nonstable propagation,also called crack bursting. 6,7 What type of propagation will happen depends on the variation of interfacial toughness with position (possibly caused by microstructural inhomogeneities) and on factors dependent on the beam stiffness.7 During stable crack propagation,interfacial toughness does not vary considerably along the interface. Under the displacement control of four-point loading,stable crack propagation occurs between two inner loading points after a critical load has been reached.7 In such a case,the load is almost constant,but displacement increases continuously. For symmetrical propagation along both sides of an interphase,interfacial toughness can be expressed by the following equation,7 Gi ¼ P2S2 8b 1 P s 1 P c ð1Þ where Gi is the interfacial toughness (J/m2 ), P the load corresponding to crack propagation (N), b the sample width (mm),S the spacing between the inner and outer loading lines (mm), Ps the beam stiffness of the singlelayer Si3N4 matrix (N.mm2 ),and Pc the beam stiffness of the single-interlayer sandwiched sample (N.mm2 ). The interfacial toughness given by Eq. (1) is a transient one,because the load P is not absolutely constant due to the interphase ununiformity. The beam stiffness can be defined by the following integral: X ¼ ð E yð Þy2 dA ð2Þ here, y is the displacement from the neutral axis, E (y) Young’s modulus at displacement y,and A the crosssectional area of the beam. For a sandwiched sample with a single,thin interlayer,the corresponding beam stiffness can be expressed approximately as X ¼ 1 12 bh3 E ¼ IcE ð3Þ where h is the total thickness of the sample (mm), b the sample width (mm), E Young’s modulus for the Si3N4 matrix (kgf/mm2 ),and Ic the moment of inertia of the sample (mm4 ). It implies that the Young’s modulus of the sample is approximately equal to that of the Si3N4 matrix layer. Substituting Eq. (3) into Eq. (1) gives Gi ¼ P2S2 8bE 1 Is 1 Ic ð4Þ where Is is the moment of inertia of the single-matrix beam contacting the two inner loading points (mm4 ). When crack bursting occurs,the critical interfacial toughness, Gic,or critical load, Pc,corresponding to crack propagation,varies considerably with crack position,and compliance increases quickly under the constant roller displacement,so that the applied load, P, decreases with the crack advance. According to the crack-propagation criterion: Gi 5Gic ð5Þ when Pc decreases more rapidly than P,unstable crack propagation occurs,and the interfacial toughness is characterized by bursting initiation and termination loads:7 G ic ¼ P1P2S2 8bE 1 Is 1 Ic ð6Þ Here, G ic is the average value of critical interfacial toughness and P1 and P2 the bursting initiation and termination loads,respectively (N). Pe is the effective load (N),i.e.,the geometric mean of the initiation and termination loads [(P1P2) 1/2]. According to the sample dimensions,if it is in plane strain condition, E in Eqs. (4) and (6) will be substituted by the plane strain modulus E0 ¼ E 1 2 . 2.2. Sample design and material preparation A Si3N4/BN/Si3N4 sandwich sample with a single BN interlayer and the thickness of the upper and lower sides of the Si3N4 matrices as equal as possible was designed for the present study. On one side of the sandwich,a crack source directly connecting to the BN interphase was preset during material preparation. First, a-Si3N4 powders (Founder High Technology Ceramic Co.,Beijing, 2862 L. Zou et al. / Journal of the European Ceramic Society 24 (2004) 2861–2868
L. Zou et al. /Journal of the European Ceramic Society 24(2004)2861-2868 2863 China)combined with 8 wt %Y2O3(>9.99% purity, decreased, tending to level off as h1/h2-1. Thus, the Hokko Chemical Industry Co, Ltd, Tokyo, Japan), 2.5 ratio of shearing to opening stress-intensity factors wt%Al2O3(>99.9% Beijing Chemical Plant, tended to be constant(Fig. 1) Beijing), and 1.5 wt% >99.9% purity, Beijing Test errors resulting from fluctuation of the sample Hong Xing Chemical Plant, Beijing) were milled in an dimensions were reduced in the present study, to ethanol medium. Then, 20 wt SiC whiskers were dis- make the thicknesses of the upper and lower beams persed by ultrasonic in ethanol media (TwS-400, as identical as possible. In accordance with the four- Hokko Chemical Industry)and added to the mixture, point loading model proposed by Charalambides et and the milling step was repeated. The twice-milled al. and Cao and Evans, o the loading system illu- mixture was filtered and dried then sieved through a 60 strated in Fig. 2, with a 20 mm inner span and a 40 mm outer span, was adopted to conduct the tests a green body with a Si3 N4 matrix was obtained by die According to Charalambides et al., iI relatively small compaction. The bn interlayer was prepared by tape h/s values are preferred to minimize uncertainties casting. Mixed powders with different interfacial com- associated with unknown frictional effects, values in positions were prepared by incorporating BN(Com- the interval 0.25<(h/s)<0.5 seem practical. In this mercial Product, Chemical Reagent, average size I um, case, the current study is satisfied with the require- Hexagonal), with different amounts of a-Si3 N4(the ment due to h/s=0.3. In addition, one kind of alu same powder with the matrix, average size 0.69 um)or minum thin foil was employed as a media between AlO3(the same with the additive Al_O3, average size the specimen and the loading rollers to reduce the fric- 0.5 um) powders and by milling the mixtures in ethanol tion coefficient in the loading system. The sample was for 24 h, then filtering, drying, and sieving the milled notched along the preset source of crack to a certain depth mixtures through a 60-mesh screen. The sieved powders y using an inner round cutting machine, where it was were mixed with some water, glycerin, and paraffin, near the interphase. Three samples were tested for each milled, and incorporated into a 20 wt polyvinyl type of interphase composition. A universal material alcohol solution; this mixture was milled again and then degassed, under vacuum, at -1.013x10 Pa pressure The homogeneous slurry was used for tape casting, and green sheets 40-60 um thick were obtained Single- interphase samples were prepared by sand wiching two round green plates(diameter 70 mm) of the Si3 N4 matrix around a thinner bn interfacial sheet. The a=(E1-E2)/(E1+E2) samples then were stacked, placed in a graphite die, and sintered, by hot pressing, at 1820C for 1.5 h, under a Sic on ti pressure of 22 MPa and an atmosphere of N2. Initially, the heating rate was slow, to allow the binder in the interlayer tape to pyrolyze and burn out below 500oC. 30° Strict control of the heating rate was not necessary, because the interfacial layer was so thin. After sintering. h1/h2 mhom3mmm知pm 2.3. Experimental method Test samples measuring3mm×4mm×s0 mm were machined(the ratio of height to width is 0.75). For this kind of sample, plane strain condition was adopted Poissons ratio (v)of the Si3 N4 has been reported as 0. 27, here we used this value approximately. The mea sured interfacial toughness is an average value corres ponding to the average load in the stable propagation region for crack creeping and to the geometric mean of the initiation and termination loads for crack bursting Because the phase angle of loading, v, defined as the angle having a tangent equal to the ratio of the shearing Fig. 2. The loading schematic of four-point to the opening stress-intensity factors, was influenced through-thickness crack initiates in the center of th by sample dimensions, that value varied with the thick interfacial cracks propagate symmetrically from th ness ratio, h/h2. When h/h2 was increased gradually, y crack length is 2 a)
China) combined with 8 wt.% Y2O3 (>9.99% purity, Hokko Chemical Industry Co.,Ltd.,Tokyo,Japan),2.5 wt.% Al2O3 (>99.9% purity,Beijing Chemical Plant, Beijing),and 1.5 wt.% MgO (>99.9% purity,Beijing Hong Xing Chemical Plant,Beijing) were milled in an ethanol medium. Then,20 wt.% SiC whiskers were dispersed by ultrasonic in ethanol media (TWS-400, Hokko Chemical Industry) and added to the mixture, and the milling step was repeated. The twice-milled mixture was filtered and dried,then sieved through a 60- mesh screen. A green body with a Si3N4 matrix was obtained by die compaction. The BN interlayer was prepared by tape casting. Mixed powders with different interfacial compositions were prepared by incorporating BN (Commercial Product,Chemical Reagent,average size 1 mm, Hexagonal),with different amounts of a-Si3N4 (the same powder with the matrix,average size 0.69 mm) or Al2O3 (the same with the additive Al2O3,average size 0.5 mm) powders and by milling the mixtures in ethanol for 24 h,then filtering,drying,and sieving the milled mixtures through a 60-mesh screen. The sieved powders were mixed with some water,glycerin,and paraffin, milled,and incorporated into a 20 wt.% polyvinyl alcohol solution; this mixture was milled again and then degassed,under vacuum,at 1.013105 Pa pressure. The homogeneous slurry was used for tape casting,and green sheets 40–60 mm thick were obtained. Single-interphase samples were prepared by sandwiching two round green plates (diameter 70 mm) of the Si3N4 matrix around a thinner BN interfacial sheet. The samples then were stacked,placed in a graphite die,and sintered,by hot pressing,at 1820 C for 1.5 h,under a pressure of 22 MPa and an atmosphere of N2. Initially, the heating rate was slow,to allow the binder in the interlayer tape to pyrolyze and burn out below 500 C. Strict control of the heating rate was not necessary, because the interfacial layer was so thin. After sintering, the thickness of the interfacial layer was 15 to 30 mm. 2.3. Experimental method Test samples measuring 3 mm4 mm50 mm were machined (the ratio of height to width is 0.75). For this kind of sample,plane strain condition was adopted. Poisson’s ratio () of the Si3N4 has been reported as 0.27,2 here we used this value approximately. The measured interfacial toughness is an average value corresponding to the average load in the stable propagation region for crack creeping and to the geometric mean of the initiation and termination loads for crack bursting. Because the phase angle of loading, ,defined as the angle having a tangent equal to the ratio of the shearing to the opening stress–intensity factors,8 was influenced by sample dimensions,that value varied with the thickness ratio, h1/h2. When h1/h2 was increased gradually, decreased,tending to level off as h1/h2!1. Thus,the ratio of shearing to opening stress–intensity factors tended to be constant (Fig. 1).8,9 Test errors resulting from fluctuation of the sample dimensions were reduced in the present study,to make the thicknesses of the upper and lower beams as identical as possible. In accordance with the fourpoint loading model proposed by Charalambides et al.9 and Cao and Evans,10 the loading system illustrated in Fig. 2,with a 20 mm inner span and a 40 mm outer span,was adopted to conduct the tests. According to Charalambides et al.,11 relatively small h=s values are preferred to minimize uncertainties associated with unknown frictional effects,values in the interval 0.254ð Þ h=s 40.5 seem practical. In this case,the current study is satisfied with the requirement due to h=s ¼ 0:3. In addition,one kind of aluminum thin foil was employed as a media between the specimen and the loading rollers to reduce the friction coefficient in the loading system. The sample was notched along the preset source of crack to a certain depth by using an inner round cutting machine,where it was near the interphase. Three samples were tested for each type of interphase composition. A universal material Fig. 1. The dependence of phase angle on specimen size and Dundurs parameter in four-point bending test. Fig. 2. The loading schematic of four-point bending test (The through-thickness crack initiates in the center of the specimen and the interfacial cracks propagate symmetrically from the center,the total crack length is 2a.) L. Zou et al. / Journal of the European Ceramic Society 24 (2004) 2861–2868 2863
2864 L. Zou et al. Journal of the European Ceramic Society 24(2004)2861--2868 testing machine(model 2000, Shimadzu Corp, Kyoto, resistance at the interphase increased, making crack Japan)was used for the loading experiments deflection impossible. The measurement of Youngs s Samples that had the same composition as the matrix modulus of the Si3NA layer gives an average i3N4 were also prepared for measuring Youngs mod- value of 29 532 kgf /mn (4) was used to obtain the ulus by three-point bending test using the same method interfacial toughnes related to the different of fabricating the sandwich specimens. The sample is 4 interphase compositions(Table 1) mm wide and 20 ratio of span to thickness, the tests In the load-displacement curves of the Fig 3(b)and were conducted with 40 mm loading span. The average (c), there exist overloading phenomena. This is because value was obtained from the results of 20 samples the notch was somehow not deep enough, and preload ing process was also not enough for the crack initiated from the tip of the notch to reach the interphase. It still 3. Results and discussion had to propagate a short distance along the weak crack source preset beforehand to arrive at the interphase, The load-displacement curves of the samples with where it was then deflected and propagated within the pure Bn and BN+ Si3N4 interphases are shown in interphase. It was the propagation in that short distance Fig. 3. With pure BN and 15 vol % 25 vol. Si3N4 that led to the occurrence of overloading. Therefore, the modifier added interphases, stable crack propagation preset weak crack source made the initiated crack from occurred in the interphase. As the amount of Si3 N4 the tip of the notch easily propagate into the interface modifier was increased, the load corresponding to crack instead of a catastrophic fracture happening, which propagation increased [Fig 3(ac), and the interfacial occurs more often under the condition without the pre- toughness increased (Table 1). When the amount of set crack source. Although we have made our efforts to Si3 N4 added to the bn approached make sure that the notch must be deep enough to be crack propagation occurred in the BN+50% Si3 N4 near the interphase, our cut machine could not be pre- interphase: as in the case of monolithic ceramics, the cisely controlled with its cutting length. For the sake of sample fractured [Fig. 3(d)], and crack-propagation safety, several specimens were cut to a depth where it 200 b)160 60 .50.6 0.050.100.150.200.250.300.35040 Displacement, u(mm) Displacement, u(mm) 0.020.030.040.050.060.07 ment, u(mm Fig 3. The load-displacement curves of Si3 N4/BN/Si3 N4 sandwiching specimens with different composition of Si3N4 modifier(a)BN.(b)BN+15 vol %Si3 N4.(c)BN+ 25 vol %Si3 N4(d)BN+ 50 vol %Si3N4
testing machine (model 2000,Shimadzu Corp.,Kyoto, Japan) was used for the loading experiments. Samples that had the same composition as the matrix Si3N4 were also prepared for measuring Young’s modulus by three-point bending test using the same method of fabricating the sandwich specimens. The sample is 4 mm wide and 20 ratio of span to thickness,the tests were conducted with 40 mm loading span. The average value was obtained from the results of 20 samples. 3. Results and discussion The load–displacement curves of the samples with pure BN and BN+Si3N4 interphases are shown in Fig. 3. With pure BN and 15 vol.%,25 vol.% Si3N4 modifier added interphases,stable crack propagation occurred in the interphase. As the amount of Si3N4 modifier was increased,the load corresponding to crack propagation increased [Fig. 3(a)–(c)],and the interfacial toughness increased (Table 1). When the amount of Si3N4 added to the BN approached to 50 vol.%,no crack propagation occurred in the BN+50% Si3N4 interphase; as in the case of monolithic ceramics,the sample fractured [Fig. 3(d)],and crack-propagation resistance at the interphase increased,making crack deflection impossible. The measurement of Young’s modulus of the Si3N4 matrix layer gives an average value of 29 532 kgf/mm2 . Eq. (4) was used to obtain the interfacial toughness values related to the different interphase compositions (Table 1). In the load–displacement curves of the Fig. 3(b) and (c),there exist overloading phenomena. This is because the notch was somehow not deep enough,and preloading process was also not enough for the crack initiated from the tip of the notch to reach the interphase. It still had to propagate a short distance along the weak crack source preset beforehand to arrive at the interphase, where it was then deflected and propagated within the interphase. It was the propagation in that short distance that led to the occurrence of overloading. Therefore,the preset weak crack source made the initiated crack from the tip of the notch easily propagate into the interface instead of a catastrophic fracture happening,which occurs more often under the condition without the preset crack source. Although we have made our efforts to make sure that the notch must be deep enough to be near the interphase,our cut machine could not be precisely controlled with its cutting length. For the sake of safety,several specimens were cut to a depth where it Fig. 3. The load–displacement curves of Si3N4/BN/Si3N4 sandwiching specimens with different composition of Si3N4 modifier. (a) BN. (b) BN+15 vol.%Si3N4. (c) BN+25 vol.%Si3N4. (d) BN+50 vol.%Si3N4. 2864 L. Zou et al. / Journal of the European Ceramic Society 24 (2004) 2861–2868
L. Zou et al. /Journal of the European Ceramic Society 24 (2004)2861-2868 (b)160 200 20864 0.10.20.3040.50.60.7 0.3 Displacement, u(mm) Displacement, u(mm) 250 6420 0.10.20.30.40.50.60.70.8 0.020.040.060.080.10 Diaplacement, u(mm) Displacement, u(mm) Fig. 4. The load-displacement curves of Si3 N4/BN/Si3N4 sandwiching specimens with different composition of Al2O3 modifier.(a) BN+16 vol%AlO,(b)BN+36 vol %Al,O3(c)BN+63 voL %AlO3.-(d)100% Al,O3 that of the same sample with overloading. Even if over loading happened, as load increased to the maxim BN composites with different interphase composition mod- point, it yielded and finally fell down to a load corre- sponding to crack deflection and propagation in the interphase [Fig 3(b)and(c). According to Eq(4), the Parameter Interphases modified by different overloading will not influence the measured interfacial volume fraction of Si,N toughness. So for the samples with crack creeping, there 25% 50% was no need to ensure in the process of preloading that P(N) 74.79 10741 114.42 the crack reached the interphase and deflected there. Gi(/m-2) 117.76 The load-displacement curves of the Si3 N4/ BN/Si3N4 samples modified with different volume percentage of Al2O3 show that unstable crack propagation tended to occur when Al,O3 was the interphase modifier(Fig. 4) Similarly to addition of Si3 N4, as the amount of added was still a short distance away from the interphase. Al2O3 increased, the interphases were strengthened; the Nevertheless, we made preloading before every formal bursting initiation and termination loads increased and test to initiate the crack from the tip of the notch and to the interfacial toughness also increased gradually. In propagate it to the interphase On the other hand, in the Fig 4(a), there occurred one time of crack bursting with case of the crack creeping, the load corresponding to the the BN+ 16 vol %Al2O3 interphase. With the increase stable crack propagation should be the same with that of the modifier Al2O3, there occurred two times of crack of the sample without overloading, i.e., they should bursting with the BN+ 36 voL. Al2O3 interphase have the same plateau corresponding to stable crack [Fig. 4(b)]. Even as the amount of Al2O3 reaches 63 propagation whether there exists the overloading phe- vol % crack deflection and propagation still occurred nomenon or not. Only the slope in the elastic loading with the BN+63 vol. Al2O3 interphase, giving two region of the sample without overloading is lower than times of crack propagation, but different from the
was still a short distance away from the interphase. Nevertheless,we made preloading before every formal test to initiate the crack from the tip of the notch and to propagate it to the interphase. On the other hand,in the case of the crack creeping,the load corresponding to the stable crack propagation should be the same with that of the sample without overloading,i.e.,they should have the same plateau corresponding to stable crack propagation whether there exists the overloading phenomenon or not. Only the slope in the elastic loading region of the sample without overloading is lower than that of the same sample with overloading. Even if overloading happened,as load increased to the maximum point,it yielded and finally fell down to a load corresponding to crack deflection and propagation in the interphase [Fig. 3(b) and (c)]. According to Eq. (4),the overloading will not influence the measured interfacial toughness. So for the samples with crack creeping,there was no need to ensure in the process of preloading that the crack reached the interphase and deflected there. The load–displacement curves of the Si3N4/BN/Si3N4 samples modified with different volume percentage of Al2O3 show that unstable crack propagation tended to occur when Al2O3 was the interphase modifier (Fig. 4). Similarly to addition of Si3N4,as the amount of added Al2O3 increased,the interphases were strengthened; the bursting initiation and termination loads increased and the interfacial toughness also increased gradually. In Fig. 4(a),there occurred one time of crack bursting with the BN+16 vol.%Al2O3 interphase. With the increase of the modifier Al2O3,there occurred two times of crack bursting with the BN+ 36 vol.% Al2O3 interphase [Fig. 4 (b)]. Even as the amount of Al2O3 reaches 63 vol.%,crack deflection and propagation still occurred with the BN+63 vol.% Al2O3 interphase,giving two times of crack propagation,but different from the Table 1 Interfacial critical crack propagation loads and interfacial toughness of Si3N4/BN composites with different interphase composition modified by Si3N4 under four-point bending test Parameter Interphases modified by different volume fraction of Si3N4 0 15% 25% 50% P (N) 74.79 107.41 114.42 – Gi (J/m2 ) 37.16 90.58 117.76 – Fig. 4. The load–displacement curves of Si3N4/BN/Si3N4 sandwiching specimens with different composition of Al2O3 modifier. (a) BN+16 vol.%Al2O3. (b) BN+36 vol.%Al2O3. (c) BN+63 vol.%Al2O3. (d) 100% Al2O3. L. Zou et al. / Journal of the European Ceramic Society 24 (2004) 2861–2868 2865
L. Zou et al. Journal of the European Ceramic Society 24(2004)2861--2868 Table 2 interphase and deflected there instead of giving brittle Interfacial critical loads and interfacial toughness of SigNa/BN com- fracturing. The process was repeated for several cycles posites with different composition modified by Al2O under four-point until the expected results were obtained The interfacial toughness values for the bn+ Parameter Interphases modified by different and BN+ Al,O3 interphase systems are listed in Table 3, volume fraction of Al.O3 he results show that the values of the former system 16% 36% 63% was bigger than that of the later in the whole compos ition range(Fig. 5). The Si3N4 strengthened interphase Effective load 94.13 is much stronger than the Al,O3 strengthened inter (J/m2) 53.95 73.95 phase. This is in agreement with the three-point bending test results, II The above-mentioned results indicate that the method we used to characterize the interfacial toughness viable. The load-displacement curves corresponding to behavior of the former two interphases, in this case, first crack propagation in the interphase could be recorded occurred crack bursting, second a short period of crack during the bend test, because the interphase was still not creeping. This implies the interphase properties were much strengthened. Whether stable or unstable crack undergoing some transformation as it was strengthened propagation occurred, the initiating load related to by increasing amount of Al2O3 modifier gradually, and crack advance and the terminating load of crack burst tended to have some similar interfacial behavior with ing could be obtained from the curves. As the amount the bn interpase and interphases modified by Si3 N4. of interphase modifier increased, interfacial bonding When the interface consisted entirely of Al2O3, the was enhanced. Both the load corresponding to stable interfacial toughness was too high to allow interfacial crack propagation and the effective load of unstable crack advance, and the thickened crack crossed the crack bursting tended to increase rapidly, and the values nterphase directly, resulting in brittle fracture obtained for interfacial toughness followed the same The critical interfacial toughness of the Si3 N4/Bn trend composite with an Al2O3-modified interphase was In addition, the effect on the experimental results of obtained using Eq. (6) with crack bursting and (4) with residual stress resulting from the mismatch of two crack creeping. An average value was taken for each materials with different thermal expansion coeficients kind of interphase that produced two times of crack cannot be omitted with a multiple- interlayer laminated bursting or first crack bursting and second crack creep- sample On the other hand, this residual-stress effect can ing(Table 2). The interfacial toughness of the composite be eliminated for a sandwiched sample, because a BN with the pure Al_O3 interphase was not obtainable interlayer sandwiched between two thick Si3 N4 matrices because no crack propagation occurred along the inter- is much thinner. In Charalambides et al.'s work, they phase during loading [Fig. 4(d)], but the value could be thought that the residual stress existing in the thin bond deduced by extrapolation, after several values of the layer does not contribute to the mixed mode fracture Al2O3-modified BN interphase had been obtained resistance2Bn is highly anisotropic on thermal In this case, due to occurrence of the crack bursting, expansion. The thermal expansion coefficient along c interfacial toughness is influenced by the initiation load. direction is much bigger than that of along a direction We took measures to make sure that the crack reached During hot pressing, the bn plate grains are inclined to the interhpase and deflected there during the course of have an orientation parallel to Si3 N4 matrix layer, i.e preloading. Actually, after the weak crack source had the a axis is parallel to the matrix layer, and c axis is been preset, the precrack process was much easier to do perpendicular to it. Because the thermal expansio compared with that of Phillips et al. 9 the crack was coefficient of BN along c direction is also bigger than inclined to propagate along the crack source to the that of the Si3 N4 matrix, there exist residual tensile Table The interfacial toughness measured by four-point bending test for two interfacial modifier systems with different interphase compositions BN+ AlO3 Volume fraction of Si3 Na(vol % Volume fraction of Al,O3(vol % Comi 15 nterfacial toughness(/m-2) 37 90.58 11776 53.95 62
behavior of the former two interphases,in this case,first occurred crack bursting,second a short period of crack creeping. This implies the interphase properties were undergoing some transformation as it was strengthened by increasing amount of Al2O3 modifier gradually,and tended to have some similar interfacial behavior with the BN interpase and interphases modified by Si3N4. When the interface consisted entirely of Al2O3,the interfacial toughness was too high to allow interfacial crack advance,and the thickened crack crossed the interphase directly,resulting in brittle fracture. The critical interfacial toughness of the Si3N4/BN composite with an Al2O3-modified interphase was obtained using Eq. (6) with crack bursting and (4) with crack creeping. An average value was taken for each kind of interphase that produced two times of crack bursting or first crack bursting and second crack creeping (Table 2). The interfacial toughness of the composite with the pure Al2O3 interphase was not obtainable, because no crack propagation occurred along the interphase during loading [Fig. 4(d)],but the value could be deduced by extrapolation,after several values of the Al2O3-modified BN interphase had been obtained. In this case,due to occurrence of the crack bursting, interfacial toughness is influenced by the initiation load. We took measures to make sure that the crack reached the interhpase and deflected there during the course of preloading. Actually,after the weak crack source had been preset,the precrack process was much easier to do compared with that of Phillips et al.;9 the crack was inclined to propagate along the crack source to the interphase and deflected there instead of giving brittle fracturing. The process was repeated for several cycles until the expected results were obtained. The interfacial toughness values for the BN+Si3N4 and BN+Al2O3 interphase systems are listed in Table 3, the results show that the values of the former system was bigger than that of the later in the whole composition range (Fig. 5). The Si3N4 strengthened interphase is much stronger than the Al2O3 strengthened interphase. This is in agreement with the three-point bending test results.11 The above-mentioned results indicate that the method we used to characterize the interfacial toughness is viable. The load–displacement curves corresponding to crack propagation in the interphase could be recorded during the bend test,because the interphase was still not much strengthened. Whether stable or unstable crack propagation occurred,the initiating load related to crack advance and the terminating load of crack bursting could be obtained from the curves. As the amount of interphase modifier increased,interfacial bonding was enhanced. Both the load corresponding to stable crack propagation and the effective load of unstable crack bursting tended to increase rapidly,and the values obtained for interfacial toughness followed the same trend. In addition,the effect on the experimental results of residual stress resulting from the mismatch of two materials with different thermal expansion coefficients cannot be omitted with a multiple-interlayer laminated sample. On the other hand,this residual-stress effect can be eliminated for a sandwiched sample,because a BN interlayer sandwiched between two thick Si3N4 matrices is much thinner. In Charalambides et al.’s work,they thought that the residual stress existing in the thin bond layer does not contribute to the mixed mode fracture resistance.12 BN is highly anisotropic on thermal expansion. The thermal expansion coefficient along c direction is much bigger than that of along a direction. During hot pressing,the BN plate grains are inclined to have an orientation parallel to Si3N4 matrix layer,i.e., the a axis is parallel to the matrix layer,and c axis is perpendicular to it. Because the thermal expansion coefficient of BN along c direction is also bigger than that of the Si3N4 matrix,there exist residual tensile Table 2 Interfacial critical loads and interfacial toughness of Si3N4/BN composites with different composition modified by Al2O3 under four-point bending test Parameter Interphases modified by different volume fraction of Al2O3 16% 36% 63% 100% Effective load Pe (N) 80.14 86.08 94.13 G ic (J/m2 ) 53.95 73.95 83.62 – Table 3 The interfacial toughness measured by four-point bending test for two interfacial modifier systems with different interphase compositions Interface system BN+Si3N4 BN+Al2O3 Interphase Composition Volume fraction of Si3N4(vol.%) Volume fraction of Al2O3(vol.%) 0 15 25 50 16 36 63 100 Interfacial toughness (J/m2 ) 37.16 90.58 117.76 – 53.95 73.95 83.62 – 2866 L. Zou et al. / Journal of the European Ceramic Society 24 (2004) 2861–2868
L. Zou et al. /Journal of the European Ceramic Society 24(2004)2861-2868 2867 110 SiNA AL2O, Me 10203040 N, or Al,O3 (Vol%) Fig. 5. The dependence of interfacial toughness on volume fraction of Si3N4 or Al2O3 modifier. stresses in BN-containing interphase along c direction. dimensions during each stage of sample manufacturing This is beneficial for cleavage along the basal plane of and machining can be guaranteed, such influence BN. It is for this characteristic that bn is usually used dec as weak interface in composites. So even if there exists Compared with the method used by Phillips, the residual stress in BN-containing thin interphase, it was present method allowed us to measure the interfacial not considered in this case. Then, keeping the upper and toughness using smaller-sized samples, which were lower matrices the same height as possible h,/ much easier to obtain. Thus, the method of presetting h2>1, we can reduce the value of y and fix its effect on crack path directly connecting to the interphase is viable, interfacial toughness, decreasing measurement erro making the experimental testing simpler and more ver In our he top and bottom laye all satile. The measurement results under such a method are Si3N4 matrix reinforced by SiC whiskers with randomly credible, as long as the interphase is flat and the thickness orientation, which can be regarded as linear elastic of the upper and lower matrices almost the same homogeneous and isotropic layers. Usually, the com mon feature of sandwich specimens devised for experi mental determination of interfacial toughness is that 4. Conclusions m is homogeneous except for a very thi layer of second material which is sandwiched between the two halves comprising the bulk of the specimen, 3 Using a sandwich sample with small dimensions, According to Eqs. (4)and(6), the interfacial toughness and with a weak crack path preset, the method depends on the elastic modulus of the Si3N4 matrix used for measuring interfacial toughness of the layer. If the matrix layer is inhomogenous, it means the ceramic matrix composites was improved. The Youngs Modulus is dependent on the sample orient difficult point of precracking a crack in this kind ation. In this case, the interfacial toughness was strongly of measurement was successfully solved. nfluenced by the determination of e value, and an 2. The interfacial toughness of the interphases in interfacial toughness value that can reflect the real Si3N4/BN composites strengthened by Si3 N4 and properties of the interface will be not available Al2O3 was successfully characterized and mea- Eqs. (4 )and(6) indicate that Is has a significant effect sured by the improved method, making possible on Gic, because errors occurring during fabrication of the design of interfaces and model numerical the material and machining of the rectangular bars lead calculations for Si3 N4/BN composites to thickness fluctuations of the unnotched half-Si3 N4 3. The results showed that there exists difference of matrix. This also influences the accuracy of the mea interface fracture behavior between Si,N, and surements. When one of the Si3 N4 layers is much thin Al,O3 strengthened bn interp the former ner than 1.5 mm. the value obtained for the interfacial is characterized with crack creeping and the toughness corresponds to that of another phase angle later is mainly crack bursting which differs from the one of h1/2-1. If the specified 4. The measurement results showed that the inter
stresses in BN-containing interphase along c direction. This is beneficial for cleavage along the basal plane of BN. It is for this characteristic that BN is usually used as weak interface in composites. So even if there exists residual stress in BN-containing thin interphase,it was not considered in this case. Then,keeping the upper and lower matrices the same height as possible,i.e., h1/ h2!1,we can reduce the value of and fix its effect on interfacial toughness,decreasing measurement error. In our samples,the top and bottom layers are all Si3N4 matrix reinforced by SiC whiskers with randomly orientation,which can be regarded as linear elastic homogeneous and isotropic layers. Usually,the common feature of sandwich specimens devised for experimental determination of interfacial toughness is that each of them is homogeneous except for a very thin layer of second material which is sandwiched between the two halves comprising the bulk of the specimen,13 According to Eqs. (4) and (6),the interfacial toughness depends on the elastic modulus of the Si3N4 matrix layer. If the matrix layer is inhomogenous,it means the Young’s Modulus is dependent on the sample orientation. In this case,the interfacial toughness was strongly influenced by the determination of E value,and an interfacial toughness value that can reflect the real properties of the interface will be not available. Eqs. (4) and (6) indicate that Is has a significant effect on Gic,because errors occurring during fabrication of the material and machining of the rectangular bars lead to thickness fluctuations of the unnotched half-Si3N4 matrix. This also influences the accuracy of the measurements. When one of the Si3N4 layers is much thinner than 1.5 mm,the value obtained for the interfacial toughness corresponds to that of another phase angle, which differs from the one of h1/h2!1. If the specified dimensions during each stage of sample manufacturing and machining can be guaranteed,such influence is decreased. Compared with the method used by Phillips,9 the present method allowed us to measure the interfacial toughness using smaller-sized samples,which were much easier to obtain. Thus,the method of presetting a crack path directly connecting to the interphase is viable, making the experimental testing simpler and more versatile. The measurement results under such a method are credible,as long as the interphase is flat and the thickness of the upper and lower matrices almost the same. 4. Conclusions 1. Using a sandwich sample with small dimensions, and with a weak crack path preset,the method used for measuring interfacial toughness of the ceramic matrix composites was improved. The difficult point of precracking a crack in this kind of measurement was successfully solved. 2. The interfacial toughness of the interphases in Si3N4/BN composites strengthened by Si3N4 and Al2O3 was successfully characterized and measured by the improved method,making possible the design of interfaces and model numerical calculations for Si3N4/BN composites. 3. The results showed that there exists difference of interface fracture behavior between Si3N4 and Al2O3 strengthened BN interphases,the former is characterized with crack creeping and the later is mainly crack bursting. 4. The measurement results showed that the interFig. 5. The dependence of interfacial toughness on volume fraction of Si3N4 or Al2O3 modifier. L. Zou et al. / Journal of the European Ceramic Society 24 (2004) 2861–2868 2867
2868 L. Zou et al. Journal of the European Ceramic Society 24(2004)2861--2868 facial toughness of Si3 N/Bn composites Fibrous monolithic ceramics. J. Am. Ceram. Soc., 1997, 80(10) increases as the volume fraction of Si3N4 or 2471-2487. Al2O3 interphase modifier increases; the 5. Charalambides. P.G. Lund. J. Evans. A. G. and McMeeking improved method is proved to be effective. R M, A test specimen for determing the fracture resistance of bimaterial interfaces. J. Appl. Mech., 1989. 56(3), 77-82. 6. Phillips, A.J. Clegg. W.J. and Clyne, T.W., Fracture behavior of ceramic laminates in bending--l. Modelling of crack propa- gation. Acta Metall. Mater., 1993. 41(3). 805-817 Acknowledgements 7. Howard, S. J. Phillips, A. J. and Clyne, T.W., The inter- pretation of data from the four-point bend delamination test te easure interfacial fracture toughness. Composites, 1993. 24(2), The authe tefully acknowledge Professor ZD -112. Guan for his much help in conducting the four-point 8. Clyne, T. W. and Phillips, A J. Interfacial control and macro- bend tests. The project was supported by the national scopic failure in long-fiber-reinforced and laminated inorganic Natural Science Foundation of China under Grant No composites. Comp. Sci. Technol, 1994. 51, 271-282 59632090 9. Phillips, A J, Clegg, W.J. and Clyne, T.w., Fracture behavior of ceramic laminates in bending-ll. Comparison of model pre- dictions with experimental data. Acta Metall. Mater., 1993, 41(3) 819-827 10. Cao, H. C. and Evans, A. G, An experimental study of the fracture resistance of bimaterial interfaces. Mechanics of materi. References als,1989,7,295-304 I1. Linhua. Zou, Yong, Huang, Ruifeng. Chen, Chang'an. wang 1. Liu Haiyan, M. and Hsu, s, Fracture behavior of multilayer and Dong-Soo. Park, The measurement and characterization of Si3N4/BN ceramics.J. Am. Ceram Soc., 1996, 79(9), 2452-2457 2. Desiderio Kovar, M., Thouless, D. and Halloran, J. w., Crack bending test. J. Eur. Ceram. Soc., 2003, 23. 1987-1996 deflection and propagation in layered silicon nitride /boron nitride 12. Charal P G. Cao, H. C. Lund, J. and Evans, A.G. ceramics.J.A. Ceram. Soc., 1998, 81(4), 1004-1012. Development of a test method for measuring the mixed mode 3. Chang-an Wang, Yong Huang. Qingfeng Zan, Hai Guo, Shen- gyou Cai, Biomimetic structure design-a possible approach to als,1990,8 hange the brittleness of ceramics in nature. Materials science 3. Suo. Z. G. Itchinson, J. W, Sandwich test specimens for and Engineering: C, 11(1)9-12, 2000 measuring i时h crack toughness. Materials Science and 4. Kovar. D, King. B. H. Trice. R. W. and Halloran. J. w Engineering A,1989,107,135-143
facial toughness of Si3N4/BN composites increases as the volume fraction of Si3N4 or Al2O3 interphase modifier increases; the improved method is proved to be effective. Acknowledgements The authors gratefully acknowledge Professor Z.D. Guan for his much help in conducting the four-point bend tests. The project was supported by the National Natural Science Foundation of China,under Grant No. 59632090. References 1. Liu Haiyan,M. and Hsu,S.,Fracture behavior of multilayer Si3N4/BN ceramics. J. Am. Ceram. Soc.,1996, 79(9),2452–2457. 2. Desiderio Kovar,M.,Thouless,D. and Halloram,J. W.,Crack deflection and propagation in layered silicon nitride/boron nitride ceramics. J. Am. Ceram. Soc.,1998, 81(4),1004–1012. 3. Chang-an Wang,Yong Huang,Qingfeng Zan,Hai Guo,Shengyou Cai,Biomimetic structure design—a possible approach to change the brittleness of ceramics in nature. Materials Science and Engineering: C,11(1) 9–12,2000. 4. Kovar,D.,King,B. H.,Trice,R. W. and Halloran,J. W., Fibrous monolithic ceramics. J. Am. Ceram. Soc.,1997, 80(10), 2471–2487. 5. Charalambides,P. G.,Lund,J.,Evans,A. G. and McMeeking, R. M.,A test specimen for determing the fracture resistance of bimaterial interfaces. J. Appl. Mech.,1989, 56(3),77–82. 6. Philllips,A. J.,Clegg,W. J. and Clyne,T. W.,Fracture behavior of ceramic laminates in bending—I. Modelling of crack propagation. Acta Metall. Mater.,1993, 41(3),805–817. 7. Howard,S. J.,Phillips,A. J. and Clyne,T. W.,The interpretation of data from the four-point bend delamination test to measure interfacial fracture toughness. Composites,1993, 24(2), 103–112. 8. Clyne,T. W. and Phillips,A. J.,Interfacial control and macroscopic failure in long-fiber-reinforced and laminated inorganic composites. Comp. Sci. Technol.,1994, 51,271–282. 9. Phillips,A. J.,Clegg,W. J. and Clyne,T. W.,Fracture behavior of ceramic laminates in bending—II. Comparison of model predictions with experimental data. Acta Metall. Mater.,1993, 41(3), 819–827. 10. Cao,H. C. and Evans,A. G.,An experimental study of the fracture resistance of bimaterial interfaces. Mechanics of Materials,1989, 7,295–304. 11. Linhua,Zou,Yong,Huang,Ruifeng,Chen,Chang’an,Wang and Dong-Soo,Park,The measurement and characterization of interfacial toughness for Si3N4/BN composite by three-point bending test. J. Eur. Ceram. Soc.,2003, 23,1987–1996. 12. Charalambides,P. G.,Cao,H. C.,Lund,J. and Evans,A. G., Development of a test method for measuring the mixed mode fracture resistance of bimaterial interfaces. Mechanics of Materials,1990, 8,269–283. 13. Suo,Z. G. and Hutchinson,J. W.,Sandwich test specimens for measuring interface crack toughness. Materials Science and Engineering A,1989, 107,135–143. 2868 L. Zou et al. / Journal of the European Ceramic Society 24 (2004) 2861–2868
