September 1999 MATERIALS LETTE.S ELSEVIER Materials Letters 40(1999)280-284 ww.elsevier. com/locate/mallet fracture toughness of multilayer silicon nitride with crack deflection Tatsuki Ohji Yasuhiro Shigegaki Naoki Kondo, Yoshikazu Suzuki National Industrial Research Institute of Nagoya, Nagoya, 462-851 b Synergy Ceramics Laboratory, Fine Ceramics Research Association, Nagoya, 462-8510, Japan Received 15 October 1998; received in revised form 26 January 1999, accepted 24 February 1999 Abstract The fracture resistance of a multilayer silicon nitride consisting of alternate dense and porous layers was investigated by a single-edge-V-notched beam(SEVNB) technique. Since silicon nitride whiskers were aligned parallel to the laminar direction in the porous layer, the crack deflected macroscopically along the whiskers, resulting in high apparent KI values 15-25 MPa m/. The crack then propagated in mode L, and was arrested when K, was reduced to the fracture resistance without the crack deflection effects. These fracture resistance behaviors were well-explained in terms of the notch-insensitiv ity and the shielding effects of pull-out of the aligned whiskers. o 1999 Elsevier Science B v. All rights reserved Keywords: Fracture resistance; Fracture toughness; Silicon nitride; Multilayer, Whisker 1. Introduction um thick. While the dense layer was produced by a normal process (with sintering additives and no Ceramic composites with laminar structures have whiskers), a large amount of silicon nitride whiskers been considered as one of the most effective ap- was added to silicon nitride powders without sinter proaches for giving damage-tolerance ability to brit- ing additives in the porous layer [13, 14]. Since the tle ceramic materials. A number of studies have been layers are formed by a tape-casting method, the made so far in several systems including added silicon nitride whiskers of the porous layer are alumina/zirconia[1-4), alumina/aluminium titanate aligned in the casting direction B], mullite/alumina [6], silicon carbide/aluminium The present study is aimed at investigating frac nitride [7], silicon carbide[8], silicon nitride /boron ture resistance behavior of this material by a single nitride 9, 10], and silicon carbide/carbon [11, 12] edge-V-notched beam(SEVNB) technique [15]. The Recently, Shigegaki et al. [13 have developed a aligned silicon nitride whiskers in the porous layer silicon nitride with a laminar structure of alternate attract a crack to extend along them, even when dense layers about 70 um thick and porous layers 50 propagates in the direction normal to the er axis. The crack deflection induced by the d whiskers results in very high fracture resis Corresponding author. Fax: +81-52-9162802 tance in the sevnb tests 00167-577X/99/ssee front matter o 1999 Elsevier Science B.V. All rights reserved Pl:S0167-577X(99)000907
September 1999 Materials Letters 40 1999 280–284 Ž . www.elsevier.comrlocatermatlet Fracture toughness of multilayer silicon nitride with crack deflection Tatsuki Ohji a,), Yasuhiro Shigegaki b , Naoki Kondo a , Yoshikazu Suzuki a a National Industrial Research Institute of Nagoya, Nagoya, 462-8510, Japan b Synergy Ceramics Laboratory, Fine Ceramics Research Association, Nagoya, 462-8510, Japan Received 15 October 1998; received in revised form 26 January 1999; accepted 24 February 1999 Abstract The fracture resistance of a multilayer silicon nitride consisting of alternate dense and porous layers was investigated by a single-edge-V-notched beam SEVNB technique. Since silicon nitride whiskers were aligned parallel to the laminar Ž . direction in the porous layer, the crack deflected macroscopically along the whiskers, resulting in high apparent K values, I 15–25 MPa m1r2 . The crack then propagated in mode I, and was arrested when K was reduced to the fracture resistance I without the crack deflection effects. These fracture resistance behaviors were well-explained in terms of the notch-insensitivity and the shielding effects of pull-out of the aligned whiskers. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Fracture resistance; Fracture toughness; Silicon nitride; Multilayer; Whisker 1. Introduction Ceramic composites with laminar structures have been considered as one of the most effective approaches for giving damage-tolerance ability to brittle ceramic materials. A number of studies have been made so far in several systems including aluminarzirconia 1–4 , alumina w x raluminium titanate wx wx 5 , mulliteralumina 6 , silicon carbideraluminium nitride 7 , silicon carbide 8 , silicon nitride wx wx rboron nitride 9,10 , and silicon carbide wx w x rcarbon 11,12 . Recently, Shigegaki et al. 13 have developed a w x silicon nitride with a laminar structure of alternate dense layers about 70 mm thick and porous layers 50 ) Corresponding author. Fax: q81-52-9162802 mm thick. While the dense layer was produced by a normal process with sintering additives and no Ž whiskers , a large amount of silicon nitride whiskers . was added to silicon nitride powders without sintering additives in the porous layer 13,14 . Since the w x layers are formed by a tape-casting method, the added silicon nitride whiskers of the porous layer are aligned in the casting direction. The present study is aimed at investigating fracture resistance behavior of this material by a singleedge-V-notched beam SEVNB technique 15 . The Ž . w x aligned silicon nitride whiskers in the porous layer attract a crack to extend along them, even when a crack propagates in the direction normal to the whisker axis. The crack deflection induced by the aligned whiskers results in very high fracture resistance in the SEVNB tests. 00167-577Xr99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0167- 577X 99 00090-7 Ž
T. Ohji et al/ Materials Letters 40(1999/280-284 2. Experimental Flexural test specimens with nominal dimensions of 4.0 mm height, 3.0 mm width, and 35 mm length The fabrication procedures for the multilayer sili- were cut from the sintered billets so that the tensile con nitride composite(hereafter denoted by MlSn) axis and tensile surface were parallel to the casting has been reported in detail by Shigegaki et al. [13, direction and the layer plane, respectively. AV but are briefly described here. Starting powders for shaped notch with a crack depth of 2 mm was the dense layers were a-silicon nitride powders with introduced by a tapered diamond wheel [15]. The tip sintering additives of 5 wt. yttria and 2 wt. radius then was reduced to less than 10 um by alumina. To produce the porous layers 70 vol. scrubbing the tip using a razor blade with diamond B-silicon nitride whiskers are added to the a-silicon paste of I um. The fracture testing was carried out at nitride powders without sintering additives. The green room temperature in a three-point bending loading sheets which were formed by tape-casting methods with a lower span of 30 mm at a cross-head speed of are stacked alternating the dense and porous layers. 0.01 mm/min. The bending fixture of silicon car- intering was carried out at 1850.C under a nitrogen bide was used to realize high rigidity of the testing pressure of 1 MPa. The obtained multilayered struc- system. The true load-displacement(L-D)curve ture which was observed normal to the casting direc- was determined by subtracting the compliance of the tion and parallel to the layer plane, is shown in Fig. testing machine and the fixture, which was obtained The thickness ranged from 60 to 80 um for the in advance by an independent calibration, from the dense layer and from 40 to 60 um for the porous experimentally observed curve ayer, with average values of 73 and 52 um, respec tively. The silicon nitride whiskers were well-aligned parallel to the casting direction in the porous layer, 3. Results and discussion whose porosity was 32.9%. For the comparison, the fracture resistance behavior of a reference material A typical example of the L-d curve for the (hereafter RSN), which was fabricated under the mLSn by the SEVNb technique is shown in Fig. 2 same conditions using sheets to obtain the in comparison with that of the rsn. The Rsn dense layers, was characterized by the same testing showed a linear elastic fashion until final failure as procedures. The mLSn has demonstrated a high expected. On the other hand, the mlsn was de- strength in spite of the low elastic modulus, the formed in a linear manner until Li, at which the three-point bending strength was 930 MPa while the crack began to grow. Li is lower than the failure elastic modulus was 238 GPa[14] load of the rsn. which is discussed later. when the crack entered the adjacent porous layer after running the dense layer, it deflected along the whiskers resulting in the delamination(Fig. 3(a)). This al lowed furthe load increased less steeply than before crack exten- sion began, and reached L2. At this point, the crack started to propagate in mode I manner across the following several dense and porous layers, accompa ed by an abrupt decrease of the load. When the load decreased sufficiently (L,), the crack was ar- rested, and deflected along the whiskers leading to process of the load increase and decrease was re peated several times until final failure, resulting in a looum sawtooth appearance The crack depth ratio a/w(a is the crack depth Fig. 1. Microstructure of the mlsn and n ight, 4 mm)at the load
T. Ohji et al.rMaterials Letters 40 1999 280–284 ( ) 281 2. Experimental The fabrication procedures for the multilayer silicon nitride composite hereafter denoted by MLSN Ž . has been reported in detail by Shigegaki et al. 13 , w x but are briefly described here. Starting powders for the dense layers were a-silicon nitride powders with sintering additives of 5 wt.% yttria and 2 wt.% alumina. To produce the porous layers 70 vol.% b-silicon nitride whiskers are added to the a-silicon nitride powders without sintering additives. The green sheets which were formed by tape-casting methods are stacked alternating the dense and porous layers. Sintering was carried out at 18508C under a nitrogen pressure of 1 MPa. The obtained multilayered structure which was observed normal to the casting direction and parallel to the layer plane, is shown in Fig. 1. The thickness ranged from 60 to 80 mm for the dense layer and from 40 to 60 mm for the porous layer, with average values of 73 and 52 mm, respectively. The silicon nitride whiskers were well-aligned parallel to the casting direction in the porous layer, whose porosity was 32.9%. For the comparison, the fracture resistance behavior of a reference material Ž . hereafter RSN , which was fabricated under the same conditions using green sheets to obtain the dense layers, was characterized by the same testing procedures. The MLSN has demonstrated a high strength in spite of the low elastic modulus; the three-point bending strength was 930 MPa while the elastic modulus was 238 GPa 14 . w x Fig. 1. Microstructure of the MLSN. Flexural test specimens with nominal dimensions of 4.0 mm height, 3.0 mm width, and 35 mm length were cut from the sintered billets so that the tensile axis and tensile surface were parallel to the casting direction and the layer plane, respectively. A Vshaped notch with a crack depth of 2 mm was introduced by a tapered diamond wheel 15 . The tip w x radius then was reduced to less than 10 mm by scrubbing the tip using a razor blade with diamond paste of 1 mm. The fracture testing was carried out at room temperature in a three-point bending loading with a lower span of 30 mm at a cross-head speed of 0.01 mmrmin. The bending fixture of silicon carbide was used to realize high rigidity of the testing system. The true load–displacement Ž . L–D curve was determined by subtracting the compliance of the testing machine and the fixture, which was obtained in advance by an independent calibration, from the experimentally observed curve. 3. Results and discussion A typical example of the L–D curve for the MLSN by the SEVNB technique is shown in Fig. 2, in comparison with that of the RSN. The RSN showed a linear elastic fashion until final failure as expected. On the other hand, the MLSN was deformed in a linear manner until L , at which the 1 crack began to grow. L is lower than the failure 1 load of the RSN, which is discussed later. When the crack entered the adjacent porous layer after running the dense layer, it deflected along the whiskers, resulting in the delamination Fig. 3 a . This al- Ž Ž .. lowed further increase of the measured load. The load increased less steeply than before crack extension began, and reached L2 . At this point, the crack started to propagate in mode I manner across the following several dense and porous layers, accompanied by an abrupt decrease of the load. When the load decreased sufficiently Ž . L , the crack was ar- 3 rested, and deflected along the whiskers leading to another. Then, the load again increased to L . The 4 process of the load increase and decrease was repeated several times until final failure, resulting in a sawtooth appearance. The crack depth ratio arW aŽ is the crack depth and W is the specimen height, 4 mm at the load
T. Ohji et al/ Materials Letters 40(1999/280-284 o values for L2, L4, and L6(Table 1)all agree well with the real bending strength, 926 MPa(the fracture defects of the bending tests exclusively ex isted in the outermost dense layers, as earlier noted) MLSN [14]. This supports the above speculation; when the delamination occurred in the porous layer, the adja- cent dense layer behaved independently of the crack 100 and fractured from some defect within the layer RSN The K at L,(or crack initiation toughness), 5.8 was lower than Ki of RsW.7.4 MPa m/, because of the difference of Young's modulus The modulus of the dense layer of the mlsn is identical with that of the rsn. 325 GPa. while the Displacement mLSN as a bulk has the modulus of 238 GPa [14 Fig. 2. Load-displacement diagrams of the sevnb bend tests for Then, the local stress at the dense layer in the mlsn the mlsn and rsn is 1.36 times higher than that in the rsn. The K,at L estimated from 7. 4 MPa m/2 using this relation points, L1-L6, of Fig. 2, was determined from frac tography. Using the a/w, the tensile stress at the outermost dense layer, o, and stress intensity factor, Ki, were calculated for the load points, L1-L6 which are listed in Table 1. The o was estimated by assuming an unnotched flexural beam with a respective remaining thickness(W-a). For the KI a shape factor given by Rawley and Gross [18] was used. The sawtooth appearance of Fig. 2 has very frequently observed in fracture mechanics of laminar ceramic composites with sufficiently interfaces [10-12], and has been analytically mod- eled [17, 18]. For example, Clegg et al. [11] and Clegg [12] reported a similar appearance in the L-D 50m curve of a notched-beam three point flexure test for laminated silicon carbide-graphite composites. In their study, during load increases from the sawtooth minima to the maxima, a crack deflected along weak graphite interfaces(delamination), without growing across the lamina. It was observed that the failure of the next lamina normally occurred well-behind the tip of the delamination crack and the crack had grown from some defect within the lamina In addi- tion. the tensile stress in the lamina calculated from the load was identical with the strength of an un- notched bar with the remaining thickness. In the present study, extensive crack deflection and delani- 5Hm nation were observed in the porous layers. This (b) suggests that the adjacent dense layer can fracture Fig. 3.(a)SEM micrograph of the crack deflection; (b) high independently of the crack. In reality, the estimated agnification of the porous layer indicated by the arrow in (a)
282 T. Ohji et al.rMaterials Letters 40 1999 280–284 ( ) Fig. 2. Load–displacement diagrams of the SEVNB bend tests for the MLSN and RSN. points, L –L , of Fig. 2, was determined from frac- 1 6 tography. Using the arW, the tensile stress at the outermost dense layer, s , and stress intensity factor, o K , were calculated for the load points, L –L , I 16 which are listed in Table 1. The so was estimated by assuming an unnotched flexural beam with a respective remaining thickness Ž . Wya . For the K ,I a shape factor given by Srawley and Gross 18 was w x used. The sawtooth appearance of Fig. 2 has been very frequently observed in fracture mechanics tests of laminar ceramic composites with sufficiently weak interfaces 10–12 , and has been analytically mod- w x eled 17,18 . For example, Clegg et al. 11 and w x wx Clegg 12 reported a similar appearance in the w x L–D curve of a notched-beam three point flexure test for laminated silicon carbide–graphite composites. In their study, during load increases from the sawtooth minima to the maxima, a crack deflected along weak graphite interfaces delamination , without growing Ž . across the lamina. It was observed that the failure of the next lamina normally occurred well-behind the tip of the delamination crack and the crack had grown from some defect within the lamina. In addition, the tensile stress in the lamina calculated from the load was identical with the strength of an unnotched bar with the remaining thickness. In the present study, extensive crack deflection and delamination were observed in the porous layers. This suggests that the adjacent dense layer can fracture independently of the crack. In reality, the estimated s values for L , L , and L Ž . Table 1 all agree o 24 6 well with the real bending strength, 926 MPa the Ž fracture defects of the bending tests exclusively existed in the outermost dense layers, as earlier noted. w x 14 . This supports the above speculation; when the delamination occurred in the porous layer, the adjacent dense layer behaved independently of the crack, and fractured from some defect within the layer. The KI 1 at L Ž . or crack initiation toughness , 5.8 MPa m1r2 , was lower than K of RSW, 7.4 MPa IC m1r2 , because of the difference of Young’s modulus. The modulus of the dense layer of the MLSN is identical with that of the RSN, 325 GPa, while the MLSN as a bulk has the modulus of 238 GPa 14 . w x Then, the local stress at the dense layer in the MLSN is 1.36 times higher than that in the RSN. The K at I L estimated from 7.4 MPa m1r2 1 using this relation Fig. 3. a SEM micrograph of the crack deflection; b high Ž. Ž. magnification of the porous layer indicated by the arrow in a . Ž
T. Ohji et al/ Materials Letters 40(1999/280-284 Table I extend macroscopically in the mode I without deflec Tensile stress at the outermost dense layer, "o, and stress intensity tions due to the notch configuration [19). It was factor, KI at Li of the MLSN, and at fracture of the RSN revealed that the fracture resistance increased by Load(N) a/W a(MPa) K,(MPa m/2) pull-out effects of the aligned whiskers, similar to MLSN the present study Assuming the Dugdale model with uniform shielding stress, U, over the entire crack wake region, Os, was estimated to be about 90 MPa from the R-curve behavior. Since the present SEVNB specimen has the same geometry and dimensions as 945 the CNB specimens, except for the notch geometry, it is reasonable to assume that o is equivalent to each other. The R-curve with uniform sh stress. o. in the sevnb tests can be estimated as 5.5 MPa m/, which agrees well with 5. 8 MPa K,=Ko+AK=Ko+2(a/T)' As already noted, the applied load increased whe the crack deflected in the porous layer. The apparent where Ko is the crack initiation toughness, 5. 8 MPa K, values calculated from the loads at L,, L4 and m/ 2, AK is the toughness increase, and ao is the L, are apparently high, 15-25 MPa m 2, due to the initial crack depth, 2.0 mm. By substituting 0=90 notch insensitivity of the adjacent dense layer, and MPa to Eq (2), we can obtain the R-curve corre- tend to decrease with increasing the crack depth. sponding to the sawtooth minima of Fig. 2(without Thus, the K values corresponding to the sawtooth toughening of the macroscopic crack deflection) maxima of Fig. 2 can be determined from a, W, and Fig. 4 shows the R-curves estimated by Eqs. (1)and g. as follows (2), in comparison with the R-curve which w determined from the results of Table l. The experi K=P/BW/Y(a/w) mental R-curve also exhibited a sawtooth appear =2(H-a)2aY(a/W)/3sH1/2 ance.When the crack deflected macroscopically in where P is the load, B is the specimen width, 3.0 mm,y(a/w)is the shape factor given by Ref [16] and S is the span length, 30.0 mm. Note that this K E 、L2 an apparent value without physical meaning in A terms of fracture mechanics 4Eq.(1) On the other hand, the Ki values for Li, L, and Ls where the crack was arrested, are the values without effects of the macroscopic crack deflections, and tend to increase with increasing the crack depth This is due to pull-out of the aligned whiskers in the a 10 porous layer. The magnified view for the porous yer(indicated in Fig 3(a))shows the pulling-out of whisker, as shown in Fig 3(b). The whisker align ment is beneficial to the crack growth resistance, eater number of the whiskers are involved with the toughening. The authors previously investi- gated the R-curve for the mlsn by chevron-notched Fig 4. R-curves estimated by Eqs. (1)and (2), in comparison wit beam(CNB) tests. where a crack was forced to the r-curve which was determined from the results of Table I
T. Ohji et al.rMaterials Letters 40 1999 280–284 ( ) 283 Table 1 Tensile stress at the outermost dense layer, so , and stress intensity factor, KI at Li of the MLSN, and at fracture of the RSN 1r2 Load NŽ. Ž . Ž . ar W so I MPa K MPa m MLSN L1 52 0.50 5.8 L2 180 0.57 925 24.6 L3 47 0.69 10.7 L4 82 0.71 903 20.6 L5 19 0.84 11.6 L6 23 0.85 945 15.0 RSN 66 0.50 7.4 is 5.5 MPa m1r2 , which agrees well with 5.8 MPa m1r2 . As already noted, the applied load increased when the crack deflected in the porous layer. The apparent KI 24 values calculated from the loads at L , L and L are apparently high, 15–25 MPa m1r2 , due to the 6 notch insensitivity of the adjacent dense layer, and tend to decrease with increasing the crack depth. Thus, the KI values corresponding to the sawtooth maxima of Fig. 2 can be determined from a, W, and s , as follows. o K sPrBW 1r2 I Y aŽ . rW s 2 1r2 2Ž . Ž . Ž. Wya soY arW r3SW 1 where P is the load, B is the specimen width, 3.0 mm, Y aŽ . rW is the shape factor given by Ref. 16 , w x and S is the span length, 30.0 mm. Note that this KI is an apparent value without physical meaning in terms of fracture mechanics. On the other hand, the KI 13 values for L , L and L where the crack was arrested, are the values 5 without effects of the macroscopic crack deflections, and tend to increase with increasing the crack depth. This is due to pull-out of the aligned whiskers in the porous layer. The magnified view for the porous layer indicated in Fig. 3 a shows the pulling-out of Ž Ž .. whisker, as shown in Fig. 3 b . The whisker align- Ž . ment is beneficial to the crack growth resistance, since a greater number of the whiskers are involved with the toughening. The authors previously investigated the R-curve for the MLSN by chevron-notched beam CNB tests, where a crack was forced to Ž . extend macroscopically in the mode I without deflections due to the notch configuration 19 . It was w x revealed that the fracture resistance increased by pull-out effects of the aligned whiskers, similar to the present study. Assuming the Dugdale model with uniform shielding stress, ss, over the entire crack wake region, s , was estimated to be about 90 MPa s from the R-curve behavior. Since the present SEVNB specimen has the same geometry and dimensions as the CNB specimens, except for the notch geometry, it is reasonable to assume that ss is equivalent to each other. The R-curve with uniform shielding stress, s , in the SEVNB tests can be estimated as s follows: 1r2 KI0 0 s sK qDKsK q 2Ž . arp s =arccosŽ . Ž. a0ra 2 where K is the crack initiation toughness, 5.8 MPa 0 m1r2 , DK is the toughness increase, and a is the 0 initial crack depth, 2.0 mm. By substituting sss90 MPa to Eq. 2 , we can obtain the Ž . R-curve corresponding to the sawtooth minima of Fig. 2 without Ž toughening of the macroscopic crack deflection .. Fig. 4 shows the R-curves estimated by Eqs. 1 and Ž . Ž . 2 , in comparison with the R-curve which was determined from the results of Table 1. The experimental R-curve also exhibited a sawtooth appearance. When the crack deflected macroscopically in Fig. 4. R-curves estimated by Eqs. 1 and 2 , in comparison with Ž. Ž. the R-curve which was determined from the results of Table 1
T. Ohji et al/ Materials Letters 40(1999/280-284 the porous layers, the fracture resistance steeply [21 D.B. Marshall, J.J. Ratto, E.F. Lange, J Am Ceram Soc. 74 increased up to the curve estimated from Eq. ( (1991)2979 After the mode I crack propagation started, the resis [3] J. Requena, R. Moreno, J.S. Moya, J.Am.Ceram. Soc. 72 (1989)151 tance dropped to the curve estimated from Eq.(2) [4]K P. Plucknett, C H. Caceres, C. Hughers, D.S. Wilkinson, J Thus. the sawtooth maxima and minima of the r- Am. Ceram.Soc.77(1994)2145 curve can be well-predicted by Eqs. (1)and(2), [5] C.J. Russo, M.P. Harmer, H.M. Chan, G.A. Miller, Design of respectively. In summary, it should be pointed out laminated ceramic composite for improved strength and layer had two benefits, one is to induce macrosc t that the aligned silicon nitride whiskers in the porou toughness, J. Am. Ceram Soc. 75(1992)3396 [6] H. Katsuki, Y. Hirata, Coat of alumina sheet with needle-like mullite, J. Ceram. Soc. Jpn. 98(1990)1114. crack deflections and the other is to increase effects [7]R Sathyamoorthy, AV.Virker, RA.Cutler,J.Am. Ceram of the pulling-out. The former contributes to the Soc.75(1992)1136 awtooth maxima of the r-curve and the latter to the [8]N P. Padture, D.C. Pender, S. Wuttiphan, B.R. Lawn, J.Am sawtooth minima Ceram.Soc.78(1995)3160. [9] H. Liu, B R. Lawn, S M. Hsu, J. Am. Ceram. Soc. 79(1996) [10] H Liu, S M. Hsu, J. Am. Ceram Soc. 79(1996)2452. Acknowledgements [11] W.J. Clegg, K. Kendall, N.M. Alford, T W.Button, JD Birchall Nature(London)347(1990)455 This work has been promoted by AIST, MITl [12] WJ. Clegg, Acta Metall (1992)3085 Japan as a part of the Synergy Ceramics Project [13]Y. Shigegaki, M.E. Brito 10, M. Toriyama, S. Kan- under the Industrial Science and Technology Frontier [14] Y. Shigegaki, M.E. Brito, K Hirao, M. Toriyama, Ceram (ISTF)Program. Under this program, part of the Sci.17(1996)l3l work has been supported by NEDO. The authors are [15] H. Awaji, Y Sakaida, J. Am. Ceram. Soc. 73(1990)3522 members of the Joint Research Consortium of Syn- [16] A.J. Phillips, W.J. Clegg, T W. Clyne, Acta Metall. Mater ergy Ceramics 41(1993)805 [17 C.A. Folsom, F w. Zok, FF. Lange, J. Am. Ceram. Soc. 77 994)68 [18]J E. Srawley, B. Gross, in: Cracks and Fracture, STM STP References 601, American Society for Testing and Materials, PA, 1976, 559 [1 P Sarkar, XHaung, P.S. Nicholson, J. Am. Ceram Soc. 75 [19] T. Ohji, Y. Shigegaki, T. Miyajima,S.Kanzaki,J.Am (1992)2907 Ceram.Soc.80(1997)991
284 T. Ohji et al.rMaterials Letters 40 1999 280–284 ( ) the porous layers, the fracture resistance steeply increased up to the curve estimated from Eq. 1 . Ž . After the mode I crack propagation started, the resistance dropped to the curve estimated from Eq. 2 . Ž . Thus, the sawtooth maxima and minima of the Rcurve can be well-predicted by Eqs. 1 and 2 , Ž. Ž. respectively. In summary, it should be pointed out that the aligned silicon nitride whiskers in the porous layer had two benefits; one is to induce macroscopic crack deflections and the other is to increase effects of the pulling-out. The former contributes to the sawtooth maxima of the R-curve and the latter to the sawtooth minima. Acknowledgements This work has been promoted by AIST, MITI, Japan as a part of the Synergy Ceramics Project under the Industrial Science and Technology Frontier Ž . ISTF Program. Under this program, part of the work has been supported by NEDO. The authors are members of the Joint Research Consortium of Synergy Ceramics. References w x 1 P. Sarkar, X. Haung, P.S. Nicholson, J. Am. Ceram. Soc. 75 Ž . 1992 2907. w x 2 D.B. Marshall, J.J. Ratto, F.F. Lange, J. Am. Ceram. Soc. 74 Ž . 1991 2979. w x 3 J. Requena, R. Moreno, J.S. Moya, J. Am. Ceram. Soc. 72 Ž . 1989 1511. w x 4 K.P. Plucknett, C.H. Caceres, C. Hughers, D.S. Wilkinson, J. Am. Ceram. Soc. 77 1994 2145. Ž . w x 5 C.J. Russo, M.P. Harmer, H.M. Chan, G.A. Miller, Design of laminated ceramic composite for improved strength and toughness, J. Am. Ceram. Soc. 75 1992 3396. Ž . w x 6 H. Katsuki, Y. Hirata, Coat of alumina sheet with needle-like mullite, J. Ceram. Soc. Jpn. 98 1990 1114. Ž . w x 7 R. Sathyamoorthy, A.V. Virker, R.A. Cutler, J. Am. Ceram. Soc. 75 1992 1136. Ž . w x 8 N.P. Padture, D.C. Pender, S. Wuttiphan, B.R. Lawn, J. Am. Ceram. Soc. 78 1995 3160. Ž . w x 9 H. Liu, B.R. Lawn, S.M. Hsu, J. Am. Ceram. Soc. 79 1996 Ž . 1009. w x 10 H. Liu, S.M. Hsu, J. Am. Ceram. Soc. 79 1996 2452. Ž . w x 11 W.J. Clegg, K. Kendall, N.M. Alford, T.W. Button, J.D. Birchall, Nature London 347 1990 455. Ž . Ž. w x 12 W.J. Clegg, Acta Metall. Mater. 40 1992 3085. Ž . w x 13 Y. Shigegaki, M.E. Brito, K. Hirao, M. Toriyama, S. Kanzaki, J. Am. Ceram. Soc. 79 1996 2197. Ž . w x 14 Y. Shigegaki, M.E. Brito, K. Hirao, M. Toriyama, Ceram. Eng. Sci. 17 1996 131. Ž . w x 15 H. Awaji, Y. Sakaida, J. Am. Ceram. Soc. 73 1990 3522. Ž . w x 16 A.J. Phillips, W.J. Clegg, T.W. Clyne, Acta Metall. Mater. 41 1993 805. Ž . w x 17 C.A. Folsom, F.W. Zok, F.F. Lange, J. Am. Ceram. Soc. 77 Ž . 1994 689. w x 18 J.E. Srawley, B. Gross, in: Cracks and Fracture, STM STP 601, American Society for Testing and Materials, PA, 1976, p. 559. w x 19 T. Ohji, Y. Shigegaki, T. Miyajima, S. Kanzaki, J. Am. Ceram. Soc. 80 1997 991. Ž
