《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_Al2O3-SiC-8

e 1996 Elsevier Science Printed in Great Britain. All rights 0955-2219(95)00163-8 955-22199631500 Fatigue Crack Growth Rate and Fracture Toughness of 25 wt% Silicon Carbide Whisker Reinforced Alumina Composite with Residual porosity AK.Ray, E.R. Fuller&S. Banerjeec "National Metallurgical Laboratory, Jamshedpur-831007, Bihar, India National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Research and Development Centre for Iron and Steel, SAIL, Ranchi-834002, Bihar, India (Received 8 December 1994; revised version received 20 July 1995; accepted 28 August 1995) Abstract and cyclic loading which produces crack extension Accordingly, in the present investigation, the fatigue The main purpose of this study was to determine the crack growth bchaviour(FCGR) and the fracture fracture toughness and the fatigue crack growth toughness(K,c) of a high density, 25 wt% silicon rate behaviour of 25 wt%o silicon carbide whisker carbide whisker reinforced alumina composite reinforced alumina ceramic composite. The fracture have been studied toughness values determined using the indentation In general, the determination of FCGR and kic technique depended significantly on the crack length of such ceramic materials is difficult since the produced at the corners of the indentation which, in specimens are small, Young's modulus of such turn, depended on the load used for the indentation materials is rather high and the material is brittle and anisotropy in orientation of whiskers in the Consequently, the load, displacement and crack matrix. However, the fracture toughness values length which are all required to be measured determined using the precracked four-point bend for the determination of Kic and FCGR--are specimens were in general higher than that obtained very small and their precise measurement poses by the indentation technique and the value was some problems. In addition, the permissible 596+0. 15 MPa m. The fatigue crack growth dimcnsional tolerance of the specimens and those behaviour in this material was similar to that in of the grips and fixtures used to test the speci the case of metals. However, the exponent for the mens, have to be very close. Particularly difficult is fatigue crack growth rate was 15.5, significantly the precracking of ceramic specimens since these higher than that usually observed in metals. The materials have very low toughness. Moreover, the likely micromechanism of crack growth under crack initiation in such materials often requires a monotonic and cyclic loading in this composite has load which is higher than that required for crack been identified from fractography of fatigue failed extension. Therefore specimens fail before crack samples. growth is achieved in a controlled manner, because he precision and dimensional tolerance of the fixture used to precrack the specimens are not 1 Introduction adequate to avoid spurious loading, that is load ing in modes other than in mode I Silicon carbide whiskers have been incorporated in such ceramic materials as alumina to improve the general mechanical propertiesand the resis- 2 Material and Specimen Orientation ce to catastrophic failure in particular. These ceramic composite materials have potential appli- The ceramic composite material was prepared by cation in the production of structural components mixing a-alumina powder of particle size l um used at elevated temperatures, 0-12i e in high effi- with 25 wt% B-silicon carbide whiskers the aver- cy heat engines and heat recovery systems, age whisker diameter was 0.45-065 um and the and for making cutting tools to machine special length ranged from 10 to 80 um. This mixture materials. When used in such applications, these was hot-pressed at 1700 to 1850 C under a pressure ceramic components often encounter monotonic of 25 MPa for 30 min to produce a preformed billet

Journul (I/ the Europcw~ Ckrwi~ SocictJ: 16 ( 1996) 503-5 13 0 1996 Elsevier Science Limited 0955-2219(95)00163-8 Printed in Great Britain. All rights reserved 0955-2219/96/$15.00 Fatigue Crack Growth Rate and Fracture Toughness of 25 wt% S:ilicon Carbide Whisker Reinforced Alumina Composite with Residual Porosity A. K. Ray,” E. R. Fullerb & S. Banerjee” “National Metallurgical Laboratory, Jamshedpur-831007, Bihar, India ‘National Institute of Standards and Technology, Gaithersburg, MD 20899, USA “Research and Development Centre for Iron and Steel, SAIL, Ranchi-834002, Bihar, India (Received 8 December 1994; revised version received 20 July 1995; accepted 28 August 1995) Abstract The main purpose of this study was to determine the fracture toughness and the fatigue crack growth rate behaviour of 25 wt% silicon carbide whisker reinforced alumina ceramic composite. The fracture toughness values determined using the indentation technique depended sign$cantly on the crack length produced at the corners of the indentation which, in turn, depended on the load used for the indentation and anisotropy in orientation of whiskers in the matrix. However, the fracture toughness values determined using the precracked four-point bend specimens were in general higher than that obtained by the indentation technique and the value was 5.96 f 0.15 MPa m ‘I2 . The fatigue crack growth behaviour in this material was similar to that in the case of metals. How(ever, the exponent for the fatigue crack growth rate was 15.5, sigru~cantly higher than that usually observed in metals. The likely micromechanism of crack growth under monotonic and cyclic loading in this composite has been identtjied from fractography of fatigue failed samples. 1 Introduction Silicon carbide whiskers, have been incorporated in such ceramic materials as alumina to improve the general mechanical properties’-’ and the resis￾tance to catastrophic failure in particular. These ceramic composite materials have potential appli￾cation in the production of structural components used at elevated tempera.tures,‘@i2 i.e. in high effi￾ciency heat engines and heat recovery systems, and for making cutting tools to machine special materials. When used in such applications, these ceramic components 0fl:en encounter monotonic and cyclic loading which produces crack extension. Accordingly, in the present investigation, the fatigue crack growth behaviour (FCGR) and the fracture toughness (K,,) of a high density, 25 wt% silicon carbide whisker reinforced alumina composite have been studied. In general, the determination of FCGR and K,, of such ceramic materials is difficult since the specimens are small, Young’s modulus of such materials is rather high and the material is brittle. Consequently, the load, displacement and crack length - which are all required to be measured for the determination of K,, and FCGR - are very small and their precise measurement poses some problems. In addition, the permissible dimensional tolerance of the specimens and those of the grips and fixtures used to test the speci￾mens, have to be very close. Particularly difficult is the precracking of ceramic specimens since these materials have very low toughness. Moreover, the crack initiation in such materials often requires a load which is higher than that required for crack extension. Therefore specimens fail before crack growth is achieved in a controlled manner, because the precision and dimensional tolerance of the fixture used to precrack the specimens are not adequate to avoid spurious loading, that is load￾ing in modes other than in mode I. 2 Material and Specimen Orientation The ceramic composite material was prepared by mixing a-alumina powder of particle size < 1 pm with 25 wt% p-silicon carbide whiskers. The aver￾age whisker diameter was 0~450.65 pm and the length ranged from 10 to 80 pm.8 This mixture was hot-pressed at 1700 to 1850°C under a pressure of 25 MPa for 30 min to produce a preformed billet. 503

A.K. Ray, E.R. Fuller, S. Banerjee The grain size of the matrix varied between I and 4 um. Details of fabrication, processing and micro- structural characterization are reported elsewhere. s The composite material had a porosity of 89%, Youngs modulus of 340 GPa, fracture strength of 559 MPa and a hardness of 20 GPa,as determined by National Institute of Standards and Technology(NIST), USA, and has been Ref. 8 mm×4mm×50mm, were sliced from the pre- formed billet and were supplied to us(National Metallurgical Laboratory, NML, India) by nist. a sketch of the billet showing the longitudinal (L), long transverse(LT)and the short transverse Hot (ST) planes is presented in Fig. 1(a). Opposite sides of the four-point flexure specimens were dia mond-ground fat and parallel with a 30 um dia- mond wheel, and the prospective tensile surface was polished with 9 um diamond paste. The specimens were soaked and rinsed in ethyl alcohol ALL DIMENSIONS ARE IN MM to remove the wax needed to mount them for pol ishing, and then dried in a hot air flow The location and orientation of the flexure mens in the billet is shown in Fig. 1(a). The 3 mm X 50 mm faces of the specimen were parallel to the st plane. The crack plane introduced later in the specimen was parallel to the lt plane and the crack propagation direction was parallel to the 4 mm dimension of the specimen. Thus the direction of crack propagation was perpendicular to the hot-pressing direction. Accordingly, the crack front was parallel to the hot-pressing direction [se Fig. 1(a)]. On the other hand, in the R-curve studies undertaken earlier by one of the authors while the plane of crack propagation was parallel to the lt plane like in the present investigation, the direction of crack propagation was parallel to HoT PTESSING the 3 mm dimension A montage of the microstructures of the 25 wt% silicon carbide whisker reinforced alumina ceramic composite, as shown in Fig. 1(b), revealed a three Fig. 1.(a) Billet p dimensional 3D distribution pattern of the whisker reinforce whiskers in the L, the Lt and the st planes of the microstructures she billet. As can be seen from Fig. 1(b), the distribu the three planes tion of the whiskers in the l plane was non-uni- form and heterogeneous. The cross-section of of the whiskers seemed to be embedded with ran these whiskers measured -0.45 um in diameter. dom orientation; and the others were observed to During hot-pressing, the whiskers which were not be embedded normal to this plane. Probably, the normal to the longitudinal plane became further friction of the walls, which in the ST planes were clined and therefore some of the whiskers very close to each other, prevented easy material appeared to be randomly oriented in the l plane flow and the alignment of all the whiskers normal [Fig. 1(b). However, a majority of the whiskers to the ST plane. tended to be oriented normal to the hot-pressing According to Becher and Wei, 3 whisker orien direction. Since the material flow along this plane tation during processing of hot-pressed Sic was high, whiskers were aligned normal to this whisker reinforced alumina leads to anisotropy in plane. On the other hand, in the St plane, a few both fracture toughness and fracture strength of

504 A. K. Ray, E. R. The grain size of the matrix varied between 1 and 4 pm. Details of fabrication, processing and micro￾structural characterization are reported elsewhere.* Fuller, S. Banerjee The composite material had a porosity of 4.89%, Young’s modulus of 340 GPa, fracture strength of 559 MPa and a hardness of 20 GPa, as determined by National Institute of Standards and Technology (NIST), USA, and has been reported in Ref. 8. Four-point flexure specimens, of dimensions 3 mm X 4 mm X 50 mm, were sliced from the pre￾formed billet and were supplied to us (National Metallurgical Laboratory, NML, India) by NIST. A sketch of the billet showing the longitudinal (L), long transverse (LT) and the short transverse (ST) planes is presented in Fig. l(a). Opposite sides of the four-point flexure specimens were dia￾mond-ground flat and parallel with a 30 pm dia￾mond wheel, and the prospective tensile surface was polished with 9 pm diamond paste.* The specimens were soaked and rinsed in ethyl alcohol to remove the wax needed to mount them for pol￾ishing, and then dried in a hot air flow. The location and orientation of the flexure spec￾imens in the billet is shown in Fig. l(a). The 3 mm X 50 mm faces of the specimen were parallel to the ST plane. The crack plane introduced later in the specimen was parallel to the LT plane and the crack propagation direction was parallel to the 4 mm dimension of the specimen. Thus the direction of crack propagation was perpendicular to the hot-pressing direction. Accordingly, the crack front was parallel to the hot-pressing direction [see Fig. l(a)]. On the other hand, in the R-curve studies’ undertaken earlier by one of the authors, while the plane of crack propagation was parallel to the LT plane like in the present investigation, the direction of crack propagation was parallel to the 3 mm dimension. A montage of the microstructures of the 25 wt% silicon carbide whisker reinforced alumina ceramic composite, as shown in Fig. l(b), revealed a three￾dimensional 3D distribution pattern of the whiskers in the L, the LT and the ST planes of the billet. As can be seen from Fig. l(b), the distribu￾tion of the whiskers in the L plane was non-uni￾form and heterogeneous. The cross-section of these whiskers measured -0.45 pm in diameter. During hot-pressing, the whiskers which were not normal to the longitudinal plane became further inclined and therefore some of the whiskers appeared to be randomly oriented in the L plane [Fig. l(b)]. However, a majority of the whiskers tended to be oriented normal to the hot-pressing direction. Since the material flow along this plane was high, whiskers were aligned normal to this plane. On the other hand, in the ST plane, a few Fig. 1. (a) Billet prepared from the 25 wt% silicon carbide whisker reinforced alumina composite; (b) montage of the microstructures showing the distribution of the SIC whiskers along the three planes. of the whiskers seemed to be embedded with ran￾dom orientation; and the others were observed to be embedded normal to this plane. Probably, the friction of the walls, which in the ST planes were very close to each other, prevented easy material flow and the alignment of all the whiskers normal to the ST plane. According to Becher and Wei,13 whisker orien￾tation during processing of hot-pressed SiC￾whisker reinforced alumina leads to anisotropy in both fracture toughness and fracture strength of ALL DIMENSlONS ARE IN MM (a) (b)

FCGR and fracture toughness of 25 wt% SiC /Al2O, composite these composites. In other words, their fracture 3.2 Crack length measurement strengths are limited by the non-unifor The crack starter indentation at the mid-point of tribution of the whiskers, i.e. by the ability to dis- the upper face of the specimen had cracks at all erse the Sic whiskers. They also found that four of its corners(Fig. 2). During precracking, dispersion of the whiskers was improved by using the crack length of the two corner cracks growing finer alumina powder, resulting in an increase in the thickness of the specimen, which is of he fracture strength of the composite Neverthe- prime importance for the present investigation less, they have clearly observed 3, 4 that, similar to was measured using the micron marker in the our composite under investigation [Fig. 1(b), the SEM at a magnification of 40x. The tip of the whiskers were preferentially aligned perpendicular crack was located through observation at higher to the hot-pressing axis. this type of distribution magnification, which often showed evidence of of whiskers suggests that a great deal of rear- crack branching. The branch extending the fur- rangement of whiskers and powders occurred in thest was considered to be the crack tip and the the initial stage of densification of the composites crack length was measured accordingly and/or the matrix material underwent consider. At first, the crack length of these two crack able deformation or creep during hot-pressing growing on the tensile (3 mm X 50 mm) surface of the specimen from the two opposite corners of the indentation as crack starter, was monitored during 3 Experimental Procedure precracking. Later, after these two cracks had spanned right across the specimen thickness, the 3.1 Precracking of the specimens crack lengths were measured on both the side The standard bridge technique is normally used surfaces(4 mm X 50 mm planes)from the respec for precracking four-point bend specimens. How- tive upper edges. The average of the crack length ever, it did not produce satisfactory precracking measured on the side surfaces gave the crack and all the specimens loaded for precracking in length a this fixture(24 out of the 30 specimens supplied) The crack length a was measured in this manner were lost due to premature crack extension. This during the precracking and also during the FCGR is probably related to fixture stiffness more than determination which preceded the Kic testing. anything else. An examination of the changing After the crack had advanced with regular incre- crack path trajectory on the fractured surfaces of ments of number of cycles, the specimen was these lost specimens showed that, instead of pure unloaded from the MTS-880 servohydraulic test mode I loading, the specimens experienced a com- machinc, and the current crack length was mca bined mode loading with mode III loading playing sured using the SEM. Since the determination of a significant role in the crack extension. The FCGr required precise measurement of au, bridge technique was, therefore, modified to avoid the crack length during FCGR studies was mea mode III loading during precracking. Accordingly, sured with special care taken in locating the crack new articulated precracking bridge fixtures were tip. designed and fabricated. These fixtures gave excel lent results--achieving 100% success in precrack- ing. The articulated bridge fixtures have been Extemal span described elsewhere A Vicker's indentation was produced at 0.8 kN pad at the mid-point of the upper face (3 X 50 mm surface) of the four-point bend specimen which acted as the crack starter, Bcforc indention all the specimens were coated with aluminium in a acuum evaporator by physical vapour deposition technique to -0-03 um thickness, to facilitate loca- tion of the crack tip in scanning electron microscope. Precracking was accomplished using the articulated bridge fixture at a force of 4 to 5 kN, load ratio(R)of 0.1 and frequency () of 20 Hz. The crack growth was measured at first on the top surface, and later on the two side surfaces ALL DIMENSIONS ARE N MK of the four-point bend specimen using the micron Fig. 2. Indented and precracked specimen for four-point marker in a Jeol JSM 840A scanning electron micro- bend loading. Cracks are located at the four corners of the scope(SEM)

FCGR and fracture toughness of 25 wt% SiC,,/Alz03 composite 505 these composites. In olther words, their fracture strengths are limited by the non-uniformity of dis￾tribution of the whiskers, i.e. by the ability to dis￾perse the SIC whiskers. They also found that dispersion of the whiskers was improved by using finer alumina powder, resulting in an increase in the fracture strength of the composite. Neverthe￾less, they have clearly observed’3s’4 that, similar to our composite under investigation [Fig. l(b)], the whiskers were preferentially aligned perpendicular to the hot-pressing axis. This type of distribution of whiskers suggests that a great deal of rear￾rangement of whiskers and powders occurred in the initial stage of densification of the composites and/or the matrix material underwent consider￾able deformation or creep during hot-pressing. 3 Experimental Procedure 3.1 Precracking of the specimens The standard bridge technique is normally used for precracking four-point bend specimens. How￾ever, it did not produce satisfactory precracking and all the specimens loaded for precracking in this fixture (24 out of the 30 specimens supplied) were lost due to premature crack extension. This is probably related to fixture stiffness more than anything else. An examination of the changing crack path trajectory on the fractured surfaces of these lost specimens showed that, instead of pure mode I loading, the specimens experienced a com￾bined mode loading with mode III loading playing a significant role in the crack extension. The bridge technique was, therefore, modified to avoid mode III loading during precracking. Accordingly, new articulated precracking bridge fixtures were designed and fabricated. These fixtures gave excel￾lent results-achieving 100% success in precrack￾ing. The articulated bridge fixtures have been described elsewhere.15 A Vicker’s indentation was produced at 0.8 kN load at the mid-point of the upper face (3 X 50 mm surface) of the flour-point bend specimen, which acted as the crack starter. Before indention, all the specimens were coated with aluminium in a vacuum evaporator by Iphysical vapour deposition technique to -0.03 pm thickness, to facilitate loca￾tion of the crack tip in the scanning electron microscope. Precracking was accomplished using the articulated bridge hxture at a force of 4 to 5 kN, load ratio (R) of 01.1 and frequency u> of 20 Hz. The crack growth was measured at first on the top surface, and later on the two side surfaces, of the four-point bend specimen using the micron marker in a Jeol JSM 841DA scanning electron micro￾scope @EM). 3.2 Crack length measurement The crack starter indentation at the mid-point of the upper face of the specimen had cracks at all four of its corners (Fig. 2). During precracking, the crack length of the two corner cracks growing across the thickness of the specimen, which is of prime importance for the present investigation, was measured using the micron marker in the SEM at a magnification of 40X. The tip of the crack was located through observation at higher magnification, which often showed evidence of crack branching. The branch extending the fur￾thest was considered to be the crack tip and the crack length was measured accordingly. At first, the crack length of these two cracks growing on the tensile (3 mm X 50 mm) surface of the specimen from the two opposite corners of the indentation as crack starter, was monitored during precracking. Later, after these two cracks had spanned right across the specimen thickness, the crack lengths were measured on both the side surfaces (4 mm X 50 mm planes) from the respec￾tive upper edges. The average of the crack length measured on the side surfaces gave the crack length a. The crack length a was measured in this manner during the precracking and also during the FCGR determination which preceded the K,, testing. After the crack had advanced with regular incre￾ments of number of cycles, the specimen was unloaded from the MTS-880 servohydraulic test machine, and the current crack length was mea￾sured using the SEM. Since the determination of FCGR required precise measurement of Au, the crack length during FCGR studies was mea￾sured with special care taken in locating the crack tip. ALL DIMENSIONS ARE Y MM. Fig. 2. Indented and precracked specimen for four-point bend loading. Cracks are located at the four corners of the indentation

A.K. Ray, E.R. Fuller, S. Banerjee 3.3 Determination of fatigue crack growth rate monotonic loading; the ramp rate was 0.25 N s FCGR The load value corresponding to the onset of fast FCGR was determined after the crack had grown fracture was used in eqn (1)to obtain the K ignificantly on the side surfaces during precrack value. Since four- point bend specimens were used 0.05 to 0. 1. The four-point bend specimen is not to the mcthod givcn clscwhcrc 6/S in all respects ing and achieved length a equivalent to a/w Kic testing followed here conforme recommended in Astm Standard E647 and In addition to this procedure, the indentation therefore, the k values of the specimen were cal- fracture toughness Kc of this material was deter culated using the standard formula reported else- mined from the indentation technique at various (referred to as the ASTM STP 410 loads(0 63, 0-8, 1-0 and 1.2 kN using the follow method). Except for this aspect and the use of an ing equation proposed by anstis et al. 8 indentation as a crack starter, the procedure used here to determine fcgr conformed to the recom- K=0061E.P h a mendations given in ASTM Standard E647 The tests were conducted in an MTS-880 servo- where E is the Young's modulus, H is the hardness, hydraulic test machine using a I kN load cell P is the load and a the crack length. Many emper- under four-point bend loading, in laboratory cal expressions to evaluate indentation fracture atmosphere and at ambient temperature. The toughness have been reported in the literature. 19 loading rate was 0.25 s. The frequency wa However, in the case of toughened Hz and r= 01. Typically, the specimens were adial cracks are emanating at the four corners of cycled within the load range between 11 and 11 the Vickers indentation, 9 the above model [eqn(2)1 N, when a/w=0-1. The crack lengths were mes has been used by Anstis et al. to determine Ko sured at regular increments of number of cycles giving 0-05 to 0.1 mm of crack growth. While 3.5 SEM studies measuring the crack length, the specimen was first The fracture surfaces of the test specimens were unloaded from the servohydraulic machine and coated with a thin film of gold (thickness 0-02 um) the current crack length was measured with the and then examined g the scanning electron help of the micron marker in the SEM. Thus the microscope to identify the characteristic fracto fatigue cracking was interrupted after a predeter- graphic features of the fatigue and fast fracture mined number of load cycles. This was continued regions in this material. The identification of these until the crack length increased to a value giving features gives a clue as to the likely mechanisms of a/W-045to0.5 fracture for this material The test data of crack length were plotted in At first, the SEM examination of the fatigue tcrms of crack length a vS. numbcr of cycles N. fracture and fast fracture zones was carried out at The values of da/dN were generated from the a vs low magnification of 30X. Thereafter, each of N plot at any given a and plotted against AK these zones was scanned at 4500x and 7500x (stress intensity range). With load and a known, The fatigue crack growth at the low AK region K values were calculated from and the fast fracture region(due to monotonic K - Y3P(L L,)v/2bw () tify and distinguish between the characteristic where fractographic features Y=199-247(a/W)+1297(a/W) 2317(a/W)3+2480(a/W 4 Results P=load; L, external span; L2 internal span b= thickness of specimen;W= depth or width 4.1 Fracture toughness data of specimen; a= crack length. The values of Kmax Fracture toughness values determined in this pro and Kmin were calculated using eqn(1). The AK ject, using both the indentation technique as well value is given by kmax -kmi as the ASTM STP 410 method with precracked specimens, are reported in Table 1. Indentation 3.4 Fracture toughness(Kic) testing fracture toughness test data determincd with a After the FCGr determination was complete and Vickers indentation at various loads of 0-63,0-80, he crack had grown to a level of a/w =0-45 1- 0 and 1. 2 kN yielded Kc values of 537, 5 45, 5.5 0.5, Kc was determined by subjecting the pre- and 5 6 MPa m", respectively. Figure 3 shows the variation of indentation fracture to oughness values loading. The test record of load vs. mid-point dis- with the square root of the corresponding crack placement of the specimen was obtained during lengths. It was observed (see Fig. 3)that the

506 A. K. Ray, E. R. Fuller, S. Banerjee 3.3 Determination of fatigue crack growth rate (FCGR) FCGR was determined after the crack had grown significantly on the side surfaces during precrack￾ing and achieved length a equivalent to a/W = 0.05 to 0.1. The four-point bend specimen is not recommended in ASTM Standard E647 and, therefore, the K, values of the specimen were cal￾culated using the standard formula reported else￾where’6,‘7 (referred to as the ASTM STP 410 method). Except for this aspect and the use of an indentation as a crack starter, the procedure used here to determine FCGR conformed to the recom￾mendations given in ASTM Standard E647. The tests were conducted in an MTS-880 servo￾hydraulic test machine using a 1 kN load cell under four-point bend loading, in laboratory atmosphere and at ambient temperature. The loading rate was 0.25 N s?. The frequency was 1 Hz and R = 0.1. Typically, the specimens were cycled within the load range between 11 and 111 N, when a/W = 0.1. The crack lengths were mea￾sured at regular increments of number of cycles giving - 0.05 to 0.1 mm of crack growth. While measuring the crack length, the specimen was first unloaded from the servohydraulic machine and the current crack length was measured with the help of the micron marker in the SEM. Thus the fatigue cracking was interrupted after a predeter￾mined number of load cycles. This was continued until the crack length increased to a value giving a/W = 0.45 to 0.5. The test data of crack length were plotted in terms of crack length a vs. number of cycles N. The values of da/dN were generated from the a vs. N plot at any given a and plotted against AK (stress intensity range). With load and a known, KI values were calculated from16,‘7 KI= Y3P(L,-L,)da/2bW2 (1) where Y = 1.99 - 2.47 (a/W) + 12.97 (a/v2 - 23.17 (alW’j3 + 24.80 (a/w4 P = load; L1 = external span; L, = internal span; b = thickness of specimen; W = depth or width of specimen; a = crack length. The values of Km,, and Kmin were calculated using eqn (I). The AK value is given by Km,, - Kmi,. 3.4 Fracture toughness (K,,) testing After the FCGR determination was complete and the crack had grown to a level of a/W = 0.45 to 0.5, K,, was determined by subjecting the pre￾cracked four-point bend specimens to monotonic loading. The test record of load vs. mid-point dis￾placement of the specimen was obtained during monotonic loading; the ramp rate was 0.25 N ss’. The load value corresponding to the onset of fast fracture was used in eqn (1) to obtain the K,, value. Since four-point bend specimens were used, K,, testing followed here conformed in all respects to the method given elsewhere.‘6,‘7 In addition to this procedure, the indentation fracture toughness Kc of this material was deter￾mined from the indentation technique at various loads (0.63, 0.8, 1 .O and 1.2 kN) using the follow￾ing equation proposed by Anstis et al.‘* Kc = 0.016 1/ $. -$ where E is the Young’s modulus, H is the hardness, P is the load and a the crack length. Many emper￾ical expressions to evaluate indentation fracture toughness have been reported in the literature.]’ However, in the case of toughened ceramics where radial cracks are emanating at the four corners of the Vickers indentation,” the above model [eqn (2)] has been used by Anstis et al.‘* to determine Kc. 3.5 SEM studies The fracture surfaces of the test specimens were coated with a thin film of gold (thickness 0.02 pm) and then examined using the scanning electron microscope to identify the characteristic fracto￾graphic features of the fatigue and fast fracture regions in this material. The identification of these features gives a clue as to the likely mechanisms of fracture for this material. At first, the SEM examination of the fatigue fracture and fast fracture zones was carried out at a low magnification of 30X. Thereafter, each of these zones was scanned at 4500X and 7500X. The fatigue crack growth at the low AK region and the fast fracture region (due to monotonic loading) were carefully examined in order to iden￾tify and distinguish between the characteristic fractographic features. 4 Results 4.1 Fracture toughness data Fracture toughness values determined in this pro￾ject, using both the indentation technique as well as the ASTM STP 410 method with precracked specimens, are reported in Table 1. Indentation fracture toughness test data determined with a Vickers indentation at various loads of 0.63, 0.80, 1.0 and 1.2 kN yielded Kc values of 5.37, 5.45, 5.5 and 5.6 MPa m1’2, respectively. Figure 3 shows the variation of indentation fracture toughness values with the square root of the corresponding crack lengths. It was observed (see Fig. 3) that the

FCGR and fracture toughness of 25 wt% SiC., composite Table 1. Fracture toughness determined by indentation and by using precracked specimen for 25 wt% SiC reinforced 01.f=1H ughness(MPu m) TM STP 410 60 Average:596±015 548±0-08 12.64S/C-AlO, [21 Stress Intensity Range, AK(MP a/M) 5 Fig. 4. Fatigue crack propagation rate data 0521215222252323.524245 Square Root of (rock Length, va Ivpm) Fig. 3. Dependence of indentation fracture toughness Ke on re root of crack length Fig. 5. At low AK(0-8 to 1.8 MPa m")region, a majority of indentation fracture toughness of this composite the whiskers failed with a square fracture without evidence of when determined using the indentation technique large-scale pull-out increased as a function of the square root of the crack length 4.2 FCGR studies Fatigue crack propagation behaviour of this ceramic material is reported in Fig 4. The FCGR data of this material were fitted to the usual paris equation da/dN= A(4K,20-22 and the fatigue crack growth rate da/dN (in m/cycle) increased linearly with AK(in MPa m )in a log-log plot The plot yields a value of n=15 5 and A =3 4 X 10-(m/cycle(MPa m-m 4.3 SEM studies SEM fractographs of the fracture surface at Fig. 6. In the fast fracture region(KIC 5.9 MPa m), due to low AK cyclic and at monotonic loading(fast monotonic loading, whiskers failed predominantly by pull-out ture region) are presented in Figs 5 to ll. It is evi- dent that, at low AK(0-8 to 1-8 MPa m),a majority of the whiskers fail by producing a fat out wherein the whiskers stick out of the genera fracture surface which has a vertical level, same as fracture surface of the composite(see Fig. 6) the general fracture surface of the composite(see The matrix material failed predominantly by Fig. 5). On the other hand, in the fast fracture transgranular fracture (see Fig. 7)at low AK region, the whiskers fail predominantly by pull- fatigue(0 8 to 1- 8 MPa m). During monotonic

FCGR and fracture toughness of 25 wt’% SiC,,/AI,O, composite 507 Table 1. Fracture toughness determined by indentation and by using precracked specimen for 25 wt% Sic reinforced A&O3 composite Fracture toughness (MPa rnlf2) Precracked specimen (ASTM STP 410 method) Indentation technique Indentation￾strength method 8 6.1 537 535 f 0.17 5.8 5.45 6.0 5.5 5.6 Average: 5.96 + 0.15 5.48 f 0.08 p 5.6sr-------j G 0 5.60. Y f t 5x8- 5 a ; 5.50- 2 i / . u’ 5.l.5, 5.35 I I I I I I I I 19.5 20 20.5 21 21.5 22 22.5 23 23.5 24 2L.5 Square Root of Crack Length. dTi I qm’ Fig. 3. Dependence of indentation fracture toughness K, on the square root of crack length a”*. indentation fracture toughness of this composite when determined using the indentation technique increased as a function of the square root of the crack length. 4.2 FCGR studies Fatigue crack propagation behaviour of this ceramic material is reported in Fig. 4. The FCGR data of this material were fitted to the usual Paris equation da/dN = A (AlK)n,2C22 and the fatigue crack growth rate da/ldN (in m/cycle) increased linearly with AK (in MPa m1’2) in a log-log plot. The plot yields a value of 12 = 155 and A = 3.4 X lo-l5 [m/cycle (MPa ml”)-“]. 4.3 SEM studies SEM fractographs of the fracture surface at the low AK cyclic and a$ monotonic loading (fast frac￾ture region) are presented in Figs 5 to 11. It is evi￾dent that, at low AK (04 to 1.8 MPa m1’2), a majority of the whiskers fail by producing a flat fracture surface which has a vertical level, same as the general fracture surface of the composite (see Fig. 5). On the other hand, in the fast fracture region, the whiskers faril predominantly by pull- ~ R= 0.1 to 0.4, / f-50 Hz UI \ c IO7 - t a -8 6 10 - % MAlERIAL f i 169 - 0 25 Sic - Al201 &t x s :: 0 MgO PSZ nq & 10 -10 - I I I lo6 - R = 0.1, f z 1Hz 3 4 5 Stress Intensity Range, AK(MP am) Fig. 4. Fatigue crack propagation rate data. Fig. 5. At low AK (0.8 to 1.8 MPa ml’*) region, a majority of the whiskers failed with a square fracture without evidence of large-scale pull-out. Fig. 6. In the fast fracture region (K,, = 5.9 MPa ml”), due to monotonic loading, whiskers failed predominantly by pull-out mechanism. out wherein the whiskers stick out of the general fracture surface of the composite (see Fig. 6). The matrix material failed predominantly by transgranular fracture (see Fig. 7) at low AK fatigue (0.8 to 1.8 MPa m1’2). During monotonic

A. K. Ray, E.R. Fuller, S. Banerjee Fig. 7. At low AK(0-8 to 1 8 MPa m)region, the alumina Fig. 10. Crack deflection in the low AK(0-8 to 1-8 MPa m matrix failed predominantly through transgranular fracture Fig 8. In the fast fracture region(Kic =59 MPa m), due FIg. ll. River pattern marking with steps in the low AK(0-8 to monotonic loading, the alumina grains failed in a mixed to 1 8 MPa m)region(YZ- modulation SEM image mode, i.e. intergranular(5.5%)and transgranular(45%) racture regions, branching and deflection of the crack are virtually absent The distinction between the fractographic fea tures in the low AK fatigue region and the fast fracture region is very evident. This is discussed further below 5 Discussion 5.1 Indentation fracture toughness data In the indentation fracture toughness test, the direct crack measurement technique had been Fig9. Crack branching in the low AK (0-8 to 1-8 MPa m? adopted for obtaining a rapid assessment of the region. indentation fracture toughness, Ko. It can be seen from Fig. 3 that the kc values obtained by this loading, the alumina grains failed in a mixed mode technique increase with increase in the square root with about 55 by intergranular mode and the bal- of of the corresponding crack lengths. In this con- ance by transgranular mode, as shown in Fig 8 text, the presence of residual stresses plays an It is noteworthy that in the low AK region the important role. a residual compressive surface stress crack frequently branches and defects while it would decrease the apparent surface crack length propagates(Figs 9 and 10). Correspondingly, river while a residual tensile surface stress would do the pattern markings with steps are also present in the reverse. There are various ways in which surface cleavage facets(Fig. 11). However, in the fast stresses could be introduced into a material; of

508 A. K. Ray, E. R. Fuller, S. Banerjee Fig. 7. At low AK (0.8 to 1.8 MPa m”2) region, the alumina matrix failed predominantly through transgranular fracture. Fig. 10. Crack deflection in the low AK (0.8 to 1.8 MPa ml”) region. Fig. 8. In the fast fracture region (KIc = 5.9 MPa ml”), due to monotonic loading, the alumina grains failed in a mixed mode, i.e. intergranular (-55%) and transgranular (-45%). Fig. 11. River pattern marking with steps in the low AK (04 to 1.8 MPa ml”) region (YZ - modulation SEM image). Fig. 9. Crack branching in the low AK (0.8 to 1.8 MPa mu2) region. loading, the alumina grains failed in a mixed mode with about 55% by intergranular mode and the bal￾ance by transgranular mode, as shown in Fig. 8. It is noteworthy that in the low AK region the crack frequently branches and deflects while it propagates (Figs 9 and 10). Correspondingly, river pattern markings with steps are also present in the cleavage facets (Fig. 11). However, in the fast fracture regions, branching and deflection of the crack are virtually absent. The distinction between the fractographic fea￾tures in the low AK fatigue region and the fast fracture region is very evident. This is discussed further below. 5 Discussion 5.1 Indentation fracture toughness data In the indentation fracture toughness test, the direct crack measurement technique had been adopted’* for obtaining a rapid assessment of the indentation fracture toughness, Kc. It can be seen from Fig. 3 that the Kc values obtained by this technique increase with increase in the square root of the corresponding crack lengths. In this con￾text, the presence of residual stresses plays an important role. A residual compressive surface stress would decrease the apparent surface crack length, while a residual tensile surface stress would do the reverse. There are various ways in which surface stresses could be introduced into a material; of

FCGR and fracture toughness of 25 wt% SiC/Al2O, composit particular relevance to the production of samples The size of the radial cracks emanating from the for indentation testing is the process of surface Vickers indentation was controlled by varying the grinding brittle materials, e.g. using SiC or diamond indentation load. For the same composite, these abrasive wheels on glass, ceramics and ccrmcts. 3 authors used a parametric representation of the It is well documented that this surface-finishing fracture resistance as a fractional power function method induces residual stresses in materials such in crack extension of the form as alumina, 23 pyroceram C960 glass-ceramic24 and zirconia-toughened alumina. 5 KR=KoO△C/Co Several investigators have shown that if the where KR is a parameter describing the fracture slope of the kc (indentation fracture toughness) resistance for an R-curve type material,m mea vS.a/(square root of crack length) plot is posi- sures the relative steepness of the R-curve, tive, it indicates that the nature of residual surface the fracture resistance that corresponds to the stress present is compressive; if the slope is nega- smallest indentation crack radius. Co is the small- tive, then tensile residual surface stresses are pre- est indentation crack that causes failure in flexura sent. 26,27 Marshall and Lawn26 showed that such testing, AC is the crack extension(=C-Cp).The plots for tempered soda-lime glass plate produced total crack length is C and Cp is the traction-free tive slope indicating that the nature of resid- portion, such as exists in a pre-notched specimen ual stress is compressive. In line with the Marshall Ko and m are defined by and Lawn model. 26 Ikuma and Virkar27 thus cluded that a positive linear dependence of Ko=B(+B)*plYSoCo/2 afor transformation-toughenable ceramics indi cates the presence of residual surface compressive m=(-3B)(2+28) stresses induced by the tetragonal-to-monoclinic where the constant B=0 266, y is the configura transformation of Zro, or HfO2 particles in the tion coefficient and is equal to 1. 174. So is the nat near-surface layers upon surface grinding. Based ural strength of the composite corresponding to on the same theory, since the ceramic composite the minimum indentation load Po and is equal to under investigation here shows a positive linear 559 MPa. This is the maximum strength that dependence of Kc on a, it simply indicates that could be measured for specimens with indentation the residual surface stresses present in the compos- cracks before failures from natural Aaws dominate Ite are compressive in nature. he strength distribution Ponton and Rawlings concluded that in inden For their analysis. 8 indentation flaws were as- tation fracture toughness tests although the crack sumed to have traction from the outset, so Cp=0 length a increases with increasing indenter load P When m =0, KR is invariant with 4C and KR as expected, plots of Kc vs a do not necessarily Ko lues of m, Co and Ko for the produce a zero slope for the stress-free state same composite were 0-08, 18 1 um and 5.35 negative slope for the residual tensile stress state MPa m"2, respectively. Using the above expres- and a positive slope for the residual compressive sion, Fuller et al.observed that the fracture resis- Lawn mode(3 predicted by the Marshall and tance of the material Kg increases with crack According to them, the sign of extension, the so called rising R-curve phe- the slope depends both on the material and the nomenon. This behaviour was explained in terms Vickers indentation fracture toughness expression of the whiskers acting as elastic restraints to the d to calculate Kc. Rather, it was suggested point of rupture at small crack wall separation that a strong dependence of Kc on ais indica- In the present study, the average value of inden tive of a residual surface stress. However, the sign tation fracture toughness (table 1)was reasonably of the slope cannot be used to distinguish between in agreement with the fracture resistance value a residual compressive and a residual tensile sur- obtained by nist. Probably due to the non- face stress without Ko vs. a 2 data for both the uniform distribution of the Sic whiskers in the definite stress-free condition and the residual com- matrix of alumina [Fig. 1(b)], the value of Kc at a pressive or tensile stress condition in a given mate- load of 1. 2 kN was slightly high(Table I and Fig 3). The average fracture toughness Kic evaluated Krause et al. have reported a fracture resistance by using the precracked specimen was 5 96+0.15 value of 5.35+ 0.17 MPa m 2, measured by the MPa m 2. The large difference in toughness indentation-strength method, in an earlier investi- obtained by the two methods could primarily be strength method, strength tests were conducted in rater ted for the difference in crack tip loading gation on the same composite. In the indentation- acco four-point bend loading with the Vickers indenta For many brittle materials, the indentation frac- tion at the centre of the prospective tensile surface. ture toughness values were reported to be similar

FCGR and fracture toughness of 25 wt’% SiC,,/A1203 composite 509 particular relevance to the production of samples for indentation testing is the process of surface grinding brittle materials, e.g. using SIC or diamond abrasive wheels on glass, ceramics and cermets.23 It is well documented .that this surface-finishing method induces residual stresses in materials such as alumina,23 pyroceram C9606 glass-ceramic24 and zirconia-toughened alumina.25 Several investigators have shown that if the slope of the Kc (indentation fracture toughness) vs. u”~ (square root of crack length) plot is posi￾tive, it indicates that the nature of residual surface stress present is compre:ssive; if the slope is nega￾tive, then tensile residual1 surface stresses are pre￾sent.26,27 Marshall and :Lawn26 showed that such plots for tempered soda-lime glass plate produced a positive slope indicating that the nature of resid￾ual stress is compressive. In line with the Marshall and Lawn model, 26 Ikurna and Virkar2’ thus con￾cluded that a positive linear dependence of Kc on a”2 for transformation-toughenable ceramics indi￾cates the presence of residual surface compressive stresses induced by the tetragonal-to-monoclinic transformation of ZrO, or Hf02 particles in the near-surface layers upon surface grinding. Based on the same theory, since the ceramic composite under investigation here shows a positive linear dependence of Kc on a1’2, it simply indicates that the residual surface stresses present in the compos￾ite are compressive in na.ture. Ponton and Rawlings]’ concluded that in inden￾tation fracture toughness tests although the crack length a increases with increasing indenter load P as expected, plots of Kc vs. u1’2 do not necessarily produce a zero slope ffor the stress-free state, a negative slope for the residual tensile stress state and a positive slope for the residual compressive stress state, as predicted by the Marshall and Lawn model. 26 According to them, I9 the sign of the slope depends both on the material and the Vickers indentation fracture toughness expression used to calculate Kc. Fkather, it was suggested” that a strong dependence of Kc on u”~ is indica￾tive of a residual surface stress. However, the sign of the slope cannot be used to distinguish between a residual compressive and a residual tensile sur￾face stress without Kc vs. #2 data for both the definite stress-free condition and the residual com￾pressive or tensile stress condition in a given mate￾rial type. l9 Krause et al.* have reported a fracture resistance value of 5.35 f 0.17 MPa m1’2, measured by the indentation-strength method, in an earlier investi￾gation on the same com:posite. In the indentation￾strength method, strength tests were conducted in four-point bend loading with the Vickers indenta￾tion at the centre of the prospective tensile surface. The size of the radial cracks emanating from the Vickers indentation was controlled by varying the indentation load. For the same composite, these authors’ used a parametric representation of the fracture resistance as a fractional power function in crack extension of the form: & = Ko (AC / Co)“’ (3) where KR is a parameter describing the fracture resistance for an R-curve type material, m mea￾sures the relative steepness of the R-curve, K, is the fracture resistance that corresponds to the smallest indentation crack radius, Co is the small￾est indentation crack that causes failure in flexural testing, AC is the crack extension (= C - C,). The total crack length is C and C, is the traction-free portion, such as exists in a pre-notched specimen. K, and m are defined by:’ K, = p@( 1 + /3)” + p) YSoCo1’2 (4) m = (1 - 3/I) (2 + 2/3) (5) where the constant p = 0.266, Y is the configura￾tion coefficient and is equal to 1.174. So is the nat￾ural strength of the composite corresponding to the minimum indentation load PO and is equal to 559 MPa. This is the maximum strength that could be measured for specimens with indentation cracks before failures from natural flaws dominate the strength distribution. For their analysis, * indentation flaws were as￾sumed to have traction from the outset, so C, = 0. When m = 0, KR is invariant with AC and KR = K, = Kc. The values of m, Co and K, for the same composite’ were 0.08, 18.1 pm and 535 MPa m1’2, respectively. Using the above expres￾sion, Fuller et al.* observed that the fracture resis￾tance of the material KR increases with crack extension, the so called rising R-curve phe￾nomenon. This behaviour was explained in terms of the whiskers acting as elastic restraints to the point of rupture at small crack wall separations. In the present study, the average value of inden￾tation fracture toughness (Table 1) was reasonably in agreement with the fracture resistance value obtained by NIST.* Probably due to the non￾uniform distribution of the SIC whiskers in the matrix of alumina [Fig. l(b)], the value of Kc at a load of 1.2 kN was slightly high (Table 1 and Fig. 3). The average fracture toughness K,, evaluated by using the precracked specimen was 596 + 0.15 MPa m1’2. The large difference in toughness obtained by the two methods could primarily be accounted for the difference in crack tip loading rates. For many brittle materials, the indentation frac￾ture toughness values were reported to be similar

510 A.K. Ray, E.R. Fuller, S. Banerjee to those obtained by large crack methods such a Vickers hardness indentation introduced at a using a double cantilever beam or compact ten- load of 0.8 kn was used as a crack starter. As sion20,22specimen On the other hand, it was often a result, significant residual stresses could be contended that indentation toughness induced in the specimen. If these residual stresses approximation of the fracture from small, natu- just ahead of the advancing crack front (i. e within rall wever, one should the plastic zone) were compressive in nature, they make sure that the residual stress field, induced by could decrease the observed fatigue crack growth he plastic zone produced by the indentation, is rate and increase the observed Kic of the material small enough compared with the crack length that However, if they were tensile in nature, the effect the indentation plastic zone has a minimum effect would be opposite. Some more fracture toughness on the extension of cracks tests, including those where a slot or notch is used Previous investigators. 30,33 have also reported as a crack starter, should be carried out to con that the considerable local branching at the cor- firm and check the Kic data reported in table I ners of the indentation and small amount of defl- In a recent paper, the Kic value of 15 vol%(or ection give rise to the appearance of local 12 64% by weight) silicon carbide reinforced alu curvature in the crack path. The branching of mina ceramic composite using compact tension cracks produced at the corners of the indentation specimen reported to be 4 5 MPa m. Th was also observed in a previous study* and could toughness value is somewhat lower than the Kic partly account for the rising trend in the KR(frac- value determined by us. This difference could be ture resistance)values. This branching behaviour attributed to a difference in the porosity of the and the crack deflection observed(Figs 9 and 10) laterals. or in the amount or size of the silicon can also be explained in terms of a grain-bridging carbide whiskers used, or in the orientation of the phenomenon associated with microstructural crack plane or the specimen geometry. Also,as toughening. Possibly, on the scale of grain sizes, the whisker volume contents are different, the the grains of alumina were entangled with the sili- strength of the whiskers and the matrix-whisker con carbide whiskers in such a way that, because interfacial bonding would obviously vary between of the presence of a complex residual stress field, the two test cases high resistance to crack propagation was created and hence the crack tended to find a new starting 5.3 Fatigue crack growth rates point at the weakest area away from this region The results of the present study(Fig. 4) showed that 25 wt% silicon carbide whisker reinforced 5.2 Fracture toughness of precracked specimens alumina ceramic composites were susceptible to The Kc values determined using precracked four- the fatigue crack growth phenomenon, in a man point bend specimens could not rcadily be com- ncr similar to metallic matcrials. FCGR data on pared with those reported on this material by 25 wt% silicon carbide reinforced alumina com nisT, due to the difference in the techniques posite have not been reported earlier. However, used for determination of toughness. The scatter recently, FCGR data of 15 vol%(which is equiva- in the KIc values obtained from the precracked lent to 12 64 wt%)silicon carbide alumina ceramic specimens, shown in Table 1, could be due to the composite were given. The crack growth rate in non-uniform distribution of the silicon carbide the material studied by us was about 100 times whiskers, apart from the system error inherent in faster, at a given AK, than that in the other mate the Kic determination rial, mainly due to larger porosity content in the The plane of crack propagation in specimens former compared with the latter which is almost tested was parallel to the Lt plane. Since most of devoid of obvious processing faws like porosity the whiskers were perpendicular to the crack The difference could also be attributable to other plane, they would tend to bridge the crack plane factors, such as the strength of the whiskers and more effectively and enhance the toughness. the matrix-whisker interfacial bonding Therefore, the fracture toughness for the crack Our material was observed to have much less planes parallel to the hot-pressing direction(the resistance to fatigue than Ce-TZp-alumina com L and ST planes)should be substantially higher posite and MgO-PSZ composite20 As explained than that for crack planes which are perpendicular earlier, 2 the presence of the transformation zone to the hot-pressing direction. Hansson et al. ahead of the crack tip in these materials could clearly showed that for 33 vol SiC whisker rein- result in the absorption of significant energy, and forced alumina composite, the fracture toughness this could retard the observed fatigue crack for crack planes parallel to the hot-pressing direc- growth rate tion is substantially higher than that for perpen Plots of daldn vs. AK for the 12 64 wt% silicon dicular crack planes arbide alumina composite and for the mgo-psz

510 A. K. Ray, E. R. Fuller, S. Banerjee to those obtained by large crack methods such as using a double cantilever beam** or compact ten￾sion*‘,** specimen. On the other hand, it was often contended that indentation toughness is a close approximation of the fracture from small, natu￾rally occurring flaws. 8,28m32 However, one should make sure that the residual stress field, induced by the plastic zone28 produced by the indentation, is small enough compared with the crack length that the indentation plastic zone has a minimum effect on the extension of cracks. Previous investigators 8,30,33 have also reported that the considerable local branching at the cor￾ners of the indentation and small amount of defl￾ection give rise to the appearance of local curvature in the crack path. The branching of cracks produced at the corners of the indentation was also observed in a previous study34 and could partly account for the rising trend in the KR (frac￾ture resistance) values. This branching behaviour and the crack deflection observed (Figs 9 and 10) can also be explained in terms of a grain-bridging phenomenon associated with microstructural toughening. Possibly, on the scale of grain sizes, the grains of alumina were entangled with the sili￾con carbide whiskers in such a way that, because of the presence of a complex residual stress field, high resistance to crack propagation was created and hence the crack tended to find a new starting point at the weakest area away from this region.29 5.2 Fracture toughness of precracked specimens The K,, values determined using precracked four￾point bend specimens could not readily be com￾pared with those reported on this material by NIST,8 due to the difference in the techniques used for determination of toughness. The scatter in the K,, values obtained from the precracked specimens, shown in Table 1, could be due to the non-uniform distribution of the silicon carbide whiskers, apart from the system error inherent in the K,, determination. The plane of crack propagation in specimens tested was parallel to the LT plane. Since most of the whiskers were perpendicular to the crack plane, they would tend to bridge the crack plane more effectively and enhance the toughness. Therefore, the fracture toughness for the crack planes parallel to the hot-pressing direction (the L and ST planes) should be substantially higher than that for crack planes which are perpendicular to the hot-pressing direction. Hansson et a1.35 clearly showed that for 33 ~01% Sic whisker rein￾forced alumina composite, the fracture toughness for crack planes parallel to the hot-pressing direc￾tion is substantially higher than that for perpen￾dicular crack planes. A Vickers hardness indentation introduced at a load of 0.8 kN was used as a crack starter. As a result, significant residual stresses could be induced in the specimen. If these residual stresses just ahead of the advancing crack front (i.e. within the plastic zone) were compressive in nature, they could decrease the observed fatigue crack growth rate and increase the observed K,, of the material. However, if they were tensile in nature, the effect would be opposite. Some more fracture toughness tests, including those where a slot or notch is used as a crack starter, should be carried out to con￾firm and check the K,, data reported in Table 1. In a recent paper, ** the K,, value of 15 ~01% (or 12.64% by weight) silicon carbide reinforced alu￾mina ceramic composite using compact tension specimens was reported to be 4.5 MPa ml’*. This toughness value is somewhat lower than the K,, value determined by us. This difference could be attributed to a difference in the porosity of the materials, or in the amount or size of the silicon carbide whiskers used, or in the orientation of the crack plane or the specimen geometry. Also, as the whisker volume contents are different, the strength of the whiskers and the matrix-whisker interfacial bonding would obviously vary between the two test cases. 5.3 Fatigue crack growth rates The results of the present study (Fig. 4) showed that 25 wt% silicon carbide whisker reinforced alumina ceramic composites were susceptible to the fatigue crack growth phenomenon, in a man￾ner similar to metallic materials. FCGR data on 25 wt% silicon carbide reinforced alumina com￾posite have not been reported earlier. However, recently, FCGR data of 15 ~01% (which is equiva￾lent to 12.64 wt%) silicon carbide alumina ceramic composite were given. ** The crack growth rate in the material studied by us was about 100 times faster, at a given AK, than that in the other mate￾rial, mainly due to larger porosity content in the former compared with the latter which is almost devoid of obvious processing flaws like porosity.36 The difference could also be attributable to other factors, such as the strength of the whiskers and the matrix-whisker interfacial bonding. Our material was observed to have much less resistance to fatigue than Ce-TZP-alumina com￾posite*l and MgO-PSZ composite.*’ As explained earlier,20~21 the presence of the transformation zone ahead of the crack tip in these materials could result in the absorption of significant energy, and this could retard the observed fatigue crack growth rate. Plots of daldN vs. AK for the 1264 wt% silicon carbide alumina composite and for the MgO-PSZ

FCGR and fracture toughness of 25 wt% SiC AlO, composite 5l1 composite exhibited a single linear stage with the or tensile fracture is thus discounted, whiskers are exponent values of 15 and 28, respectively. Our most likely to fail by fatigue. At low AK, the material also exhibited a single linear stage(Fig 4) whiskers which had bridged the crack after the without the presence of a detectable threshold. The surrounding alumina grains had failed by cleav value of the exponent was 15.5 in our material age, would continue to experience fatigue loading As already discussed, the Vickers hardness then fail with a square fracture which is typical of indentation when used as a crack starter could fatigue generate residual stresses which in turn could infl During fast fracture under monotonic loading uence the FCGR. The FCGR test data on speci- such as during the fracture toughness testing, 55%0 mens where the crack starter is a slotted notch of the a-Al2O3 grains of the matrix failed by inter instead of an indentation, if generated, would granular fracture. The value of K during such confirm if the use of indentation as a crack starter monotonic loading is 5. 9 MPa m". At such val indeed influences the fCgr or not. Such studies ues of K,, the traction force ahead of the crack tip have been reported elsewhere. 5 is adequate to produce intergranular failure of those grains which are favourably oriented with 5.4 Mechanism of fracture respect to it. The matrix failure was predomi- Since the mechanism of fracture of the whiskers nantly intergranular. Nevertheless, the whiskers and the a-alumina grains are entirely different in were located mainly at the grain boundaries the low AK fatiguc and the fast fracture regions, Therefore the probability of the advancing crack the scheme of crack growth in each region is dis- front interacting with the whiskers is extremely cussed separately below to highlight these differ igh. The whiskers tending to bridge the advanc- ences g crack quite frequently would therefore becom During fatigue loading at low AK values, that is debonded and pull out. This hypothesis is con- phen Kmax 2 MPa m, the a-alumina grains of firmed by the fact that, during monotonic frac the matrix failed mainly by transgranular cleavage ture, failure of the whiskers by the pull-out with frequent crack branching and crack defied- mechanism was frequently observed in the frac tion. Also, the cleavage facets revealed river pat- tographs terns and steps. At the low values of AK, the K After some of the grains have failed by the alues are low. Consequently, the traction force intergranular mode, the other neighbouring grains- head of the crack tip is not large enough to pr which are less favourably oriented or are bridged mote intergranular fracture by the whiskers across the grain boundaries--fai At the same time, the whiskers could fail by by clcavagc. The schematic of crack propagation three different modes: (i) pull out, (i) tensile frac- during monotonic and cyclic loading is given else Lure and (iii) fatigue. Since only a few of the where whiskers failed due to pull- out at low AK (see Fig To prevent fracture of this ceramic composite 5), this naturally indicates that the maximum trac- under monotonic loading, its microstructural fea tion forces generated ahead of the crack tip during tures would have to be strengthened to avoid the low AK fatigue was not adequate to produce intergranular fracture of a-alumina and the pull- pull-out. Thus it is likely that the whiskers con- out of whiskers. This requires that the grain tinue to bridge the crack even after some of the boundary strength of a-alumina and the whisker- surrounding alumina grains have failed by trans- matrix interfacial strength should be increased. granular cleavage. Therefore, under these circum- Similarly, to retard crack extension during low AK stances. the whiskers could fail due to tensile fatigue, intergranular cleavage fracture of a-alu fracture or fatigue. Now, since the strength of the mina grains and fatigue failure resistance of the B-SiC whisker is about 6 5 to 7 times highcr than silicon carbide whiskers should be improved, possi- the crack tip were to be distributed in proportion whiskers in the matrix during hot-pressing 3 that of a-alumina, 31, the tensile fracture of the bly by using finer a-alumina powder 3, 4 and by hisker is unlikely if the traction forces ahead of improving the uniformity of distribution of the to the relative cross-sections of the B-Sic whiskers and a-alumina in the plane of the crack. Even if the whiskers were to carry the major part of the 6 Conclusions traction forces ahead of the crack tip, the high traction forces would produce failure by pull-out The results of the foregoing study lead to the fol- rather than by tensile fracture as was observed lowing conclusions in the fast fracture region(see Fig. 6) where KIc ()Indentation fracture toughness increased values and consequently the traction forces were with increase in the square root of crack high. Since the possibility of large-scale pull-out length. However, the Kic values obtained

FCGR and fracture toughness of 2.5 wt% SiC,,/Alz03 composite 511 composite exhibited a single linear stage with the exponent values of 15 and 28, respectively. Our material also exhibited a single linear stage (Fig. 4) without the presence of a detectable threshold. The value of the exponent wals 15.5 in our material. As already discussed, the Vickers hardness indentation when used as a crack starter could generate residual stresses which in turn could infl￾uence the FCGR. The FCGR test data on speci￾mens where the crack starter is a slotted notch instead of an indentation, if generated, would confirm if the use of indentation as a crack starter indeed influences the FCGR or not. Such studies have been reported elsewhere.‘5 5.4 Mechanism of fracture Since the mechanism of fracture of the whiskers and the a-alumina grains are entirely different in the low AK fatigue and the fast fracture regions, the scheme of crack growth in each region is dis￾cussed separately below to highlight these differ￾ences.34 During fatigue loading at low AK values, that is when K,,,,, < 2 MPa ml’*, the a-alumina grains of the matrix failed mainly by transgranular cleavage with frequent crack branching and crack deflec￾tion. Also, the cleavage facets revealed river pat￾terns and steps. At the low values of AK, the K,,, values are low. Consequently, the traction force ahead of the crack tip is not large enough to pro￾mote intergranular fracture. At the same time, the whiskers could fail by three different modes: (i) pull out, (ii) tensile frac￾ture and (iii) fatigue. Since only a few of the whiskers failed due to pul!l-out at low AK (see Fig. 5), this naturally indicates that the maximum trac￾tion forces generated ahead of the crack tip during the low AK fatigue was not adequate to produce pull-out. Thus it is likely that the whiskers con￾tinue to bridge the crack even after some of the surrounding alumina grains have failed by trans￾granular cleavage. Therefore, under these circum￾stances, the whiskers could fail due to tensile fracture or fatigue. Now, since the strength of the P-Sic whisker is about 6.5 to 7 times higher than that of cu-alumina,37,38 the tensile fracture of the whisker is unlikely if the traction forces ahead of the crack tip were to be Idistributed in proportion to the relative cross-sections of the P-Sic whiskers and a-alumina in the plane of the crack. Even if the whiskers were to carry the major part of the traction forces ahead of the crack tip, the high traction forces would produce failure by pull-out rather than by tensile fracture, as was observed in the fast fracture region (see Fig. 6) where K,, values and consequently the traction forces were high. Since the possibility of large-scale pull-out or tensile fracture is thus discounted, whiskers are most likely to fail by fatigue. At low AK, the whiskers which had bridged the crack after the surrounding alumina grains had failed by cleav￾age, would continue to experience fatigue loading, then fail with a square fracture which is typical of fatigue. During fast fracture under monotonic loading such as during the fracture toughness testing, 55% of the ~A1203 grains of the matrix failed by inter￾granular fracture. The value of KI during such monotonic loading is 5.9 MPa ml’*. At such val￾ues of K,, the traction force ahead of the crack tip is adequate to produce intergranular failure of those grains which are favourably oriented with respect to it. The matrix failure was predomi￾nantly intergranular. Nevertheless, the whiskers were located mainly at the grain boundaries. Therefore the probability of the advancing crack front interacting with the whiskers is extremely high. The whiskers tending to bridge the advanc￾ing crack quite frequently would therefore become debonded and pull out. This hypothesis is con￾firmed by the fact that, during monotonic frac￾ture, failure of the whiskers by the pull-out mechanism was frequently observed in the frac￾tographs. After some of the grains have failed by the intergranular mode, the other neighbouring grains￾which are less favourably oriented or are bridged by the whiskers across the grain boundaries-fail by cleavage. The schematic of crack propagation during monotonic and cyclic loading is given else￾where.34 To prevent fracture of this ceramic composite under monotonic loading, its microstructural fea￾tures would have to be strengthened to avoid intergranular fracture of a-alumina and the pull￾out of whiskers. This requires that the grain boundary strength of a-alumina and the whisker￾matrix interfacial strength should be increased. Similarly, to retard crack extension during low AK fatigue, intergranular cleavage fracture of a-alu￾mina grains and fatigue failure resistance of the silicon carbide whiskers should be improved, possi￾bly by using finer a-alumina powder’3,‘4 and by improving the uniformity of distribution of the whiskers in the matrix during hot-pressing.13,*4 6 Conclusions The results of the foregoing study lead to the fol￾lowing conclusions. (1) Indentation fracture toughness increased with increase in the square root of crack length. However, the K,, values obtained

512 A.K. Ray, E. R. Fuller, S. Banerjee from the precracked four-point bend speci 13. Becher, P. F.& Wei, G. C, Toughening behaviour in mens were higher and had a value given by C-whisker-reinforced alumina. Am. Ceram. Soc K1c=596±0l5MPam12 67(12)(1984)267-9 14. Wei, G. C& becher, P F, Development of Sic whi (2)The 25 wt% silicon carbide whisker rein reinforced ceramics. J. Am. Ceram. Soc. Bull hiskey forced alumina ceramic composite is suscep 1985)298-304 tible to a fatigue crack growth phenomenon 15. Ray, A.K.& banerjee hich is similar to that observed in the case of metallic materials. But the crack growth exponent is higher(n =15.5) 16. Brown Jr, w. F& Srawley, J. E, in ASTM STP (3) At low AK fatigue(0-8 to 1-8 MPa m ), the American Society for Testing and Materials, phila hia. PA. 1966 whiskers failed by fatigue, whereas during 17 Yamade, Y.& Kishi, T, Acoustic emission study for monotonic fracture, they failed by pull-out. fracture origin of sintered mullite in 4-point bending test (4)The matrix at low AK fatigue was predomi The Sumitomo Search, 45(3) (1991)17-24 18. Anstis, G. R, Chantikul, P, Lawn, B. R.& marshall nantly transgranular with frequent crack D. B, A critical evaluation of indentation techniques branching and deflection, in contrast to a measuring fracture toughness: I direct crack measurement J. Am. Ceram Soc 64(1981)533-8 mixed mode type (45% transgranular and 9. vickers indentation, fracture toughness on the surface 55%/ intergranular) failure during the mono- Ponton, C. B.& Rawlings, R. D, Dependence of the tonic fracture crack length. Br. Ceram. Trans. J, 88(1989)83-90 20. Dauskardt, R. H, Marshall, D. B. Ritchie, R.O. yclic fatigue-crack propagation in magnesia-partiall stabilized zirconia ceramics. Am. Ceram. Sc Reference 21. Tsai, J. F, Yu, C.S.& Shetty, D. K,, Fatigue crack I. Becher, P, F, Such, C. H, Angelini, P. Tiegs, T. N propagation in ceria-partially stabilized zirconia( Ce-TZPH Toughening behaviour in whisker-reinforced ceramic matrix alumina composites. J, Am. Ceram. Soc., 73(10)(1990) composites. J. Am. Ceram. Soc., 71(12)(1988)1050-61 2992-3001. 2. Becher, P. F, Microstructural design of toughened 22. Dauskardt, R. H, James, M.R., Porter, J. R& Ritchie ceramics. J. Am. Ceram Soc., 72(2)(1991)255-69 R.O., Cyclic fatigue crack growth in a SiC whisker-rein 3. Becher, P. F.& Tiegs, T. N, Toughening behaviour forced alumina ceramic composite: long and small crack involving multiple mechanisms: whisker reinforcement behaviour. J. Am. Ceram. Soc, 75(4)(1992)759-71 and zirconia toughening. J. 4m. Ceram. Soc., 70(9) 23. Lange, F. F, James, M.R.&Green,DJ,Determina (1987)6514 tion of residual stresses caused by grinding in polycrys- 4. Angelini, P, Mader, w.& becher, P F, Strain and frac- talline Al,O3. J. Am. Ceram. Soc., 66(1983)C-16 ture in whisker reinforced ceramics In MRS Proceedings 24. Cook, R F, Lawn, BR, Dabbs, T P& Chantikul Vol. 78, Advanced Structural Ceramics. ed. P. F. Becher Effect of machining damage on the strength of a glass M. v Swain and S. Somuja Materials Research Socicty, ceramic. J. Arm. Cerum. Soc., 64 (1981)C-121-2. Pittsburgh, PA, 1987, pp. 241-57 25. Green, D J, Lange, F. F.& James, M.R., Factors infl. 5. Ruhle. M. Dalgeish. Evans. A G. On the toughen uencing residual surface stresses due to a stress-induced ing of ceramics by whiskers. Scr. Metall, 21 ( 1987)681-6 phase transformation. J. Am. Ceram Soc, 66(1983)6239 6. Warren. R. Sarin. V. K. fracture of whisker rein- B. R. An indentation tech forced ceramics. In Application of fracture Mechanics to nique for measuring stresses in tempered glass-surfaces Composite Materials, ed. K. Friedrich. Elsevier, Amster Am. Ceram.Soc,60(1977)86-7 27. Ikuma. Y.& Virkar, A 7. Krause Jr,R. F.& Fuller Jr, E.R., Fracture toughness fracture toughness in transformation-toughened ceramics behaviour of a silicon carbide whisker reinforced alumina J. Mater.Sci,19(1984)223-8 with selected properties. In Proc. the Fossil Energy Mate- 28. Bhattacharya, A. K.& Petrovic, J, J, Hardness and frac rials Conference, Report No. ORNL/FMP/87/G, Martin ture toughness of SiC-particle-reinforced MoSi, composite Marietta Encrgy Systcms, Inc, Oak Ridge National Lab- J.Am. Ceram.Soc…,7410)(1991)2700-3 oratory, TN, USA, August 1987, pp 38-55 29. Swanson, P. L, Fairbanks, C. J, Lawn, B. R. Mai 8. Krause Jr, R. F, Fuller Jr, E. R. rhodes, J. F, frac Y.w.& Hockey, B J, Crack-interface grain bridging as ure resistance behaviour of silicon carbide whisker-rein- a fracture resistance mechanism in ceramics: 1, experiment forced alumina composites with different poros study in alumina. J. Am. Ceram Soc., 70(4)(1987)279 Am. Cerum.Soc,73(3)(1990)55966 30. Ramchandran, N. Shetty, D. K, Rising crack growth 9. Campbell, G. H, Ruhle, M, Dalgleish B. J. Evans, A.G resistance(R-curve)behaviour of toughened alumina and Whisker toughening: a comparision between AL, O, and licon nitride. J. Am. Ceram. Soc., 74(10)(1991)2634-41 Si3N4 toughened with silicon carbide. J. Am. Ceram. 31. Anderson, R. M.& Braun, L. M, Technique for the Soc,733)(1990)521-30. R-curve determination of Y-TZP using indentation-pro- 10. St anical properties, m. Ceram.Soc,73l0)(1990305962 hermal shock resistance and ther 32. Swain, M. v, R-curve behaviour and thermal shock resistance of ceramics. J. Am. Ceram. Soc., 73(3)(1990) ceramic matrix composite. J.Am 621_8 740-3. 33. Pezzotti. G. Tanaka, I.& Ok T, Si,N//SIC 11. Porter J. R.& Chokshi, A. H, Creep performance of whisker composites without sintering aids: 11, fracture haviour. Am. Ceram. s 10)(1990)303945 ture 86, ed, J, A. Pask and A. G. Evans. Pl 4. Ray, A. K, Das, S.K.& Banerjee, S, Fractography of New York, 1986, pp. 919-28 the fatigued and fractured regions in a silicon carbide 12. Tiegs, T.N.& Becher, P. T, Thermal shock behaviour whisker reinforced alumina composite, J. Eur. Ceram of an alumina SiC whisker composite. J. Am. Ceram Soc,705)(1987)C-109l1 35. Hansson, T, Warren, R& Wasen, J, fracture tough

512 (2) (3) (4) A. K. Ray, E. R. Fuller, S. Banerjee from the precracked four-point bend speci￾mens were higher and had a value given by K,, = 596 f 0.15 MPa m1’2. The 25 wt% silicon carbide whisker rein￾forced alumina ceramic composite is suscep￾tible to a fatigue crack growth phenomenon which is similar to that observed in the case of metallic materials. But the crack growth exponent is higher (n = 15.5). At low AK fatigue (0.8 to 1 G3 MPa ml”), the whiskers failed by fatigue, whereas during monotonic fracture, they failed by pull-out. The matrix at low AK fatigue was predomi￾nantly transgranular with frequent crack branching and deflection, in contrast to a mixed mode type (45% transgranular and 55% intergranular) failure during the mono￾tonic fracture. References 1. 2. 3. 4. 5. 6. I. 8. 9. 10. 11. 12. Becher, P. F., Hsueh, C. H., Angelini, P. & Tiegs, T. N., Toughening behaviour in whisker-reinforced ceramic matrix composites. J. Am. &ram. Sot., 71(12) (1988) 1050-61. Becher, P. F., Microstructural design of toughened ceramics. J. Am. Ceram. Sot., 72(2) (1991) 2.5-69. Becher, P. F. & Tiegs, T. N., Toughening behaviour involving multiple mechanisms: whisker reinforcement and zirconia toughening. J. Am. Ceram. Sot., 70(9) (1987) 6514. Angelini, P., Mader, W. & Becher, P. F., Strain and frac￾ture in whisker reinforced ceramics. In MRS Proceedings Vol. 78, Advanced Structural Ceramics, ed. P. F. Becher, M. V. Swain and S. Somuja. Materials Research Society, Pittsburgh, PA, 1987, pp. 241-57. Ruhle, M., Dalgeish, B. J. & Evans, A. G., On the toughen￾ing of ceramics by whiskers. Ser. Metalf., 21 (1987) 681-6. Warren, R. & Sarin, V. K., Fracture of whisker rein￾forced ceramics. In Application of Fracture Mechanics to Composite Materials, ed. K. Friedrich. Elsevier, Amster￾dam, in press. Krause Jr, R. F. & Fuller Jr, E. R., Fracture toughness behaviour of a silicon carbide whisker reinforced alumina with selected properties. In Proc. the Fossil Energy Mate￾rials Conference, Report No. ORNL/FMP/87/G, Martin Marietta Energy Systems, Inc., Oak Ridge National Lab￾oratory, TN, USA, August 1987, pp. 38-55. Krause Jr, R. F., Fuller Jr, E. R. & Rhodes, J. F., Frac￾ture resistance behaviour of silicon carbide whisker-rein￾forced alumina composites with different porosities. J. Am. Ceram. Sot., 73(3) (1990) 559-66. Campbell, G. H., Ruhle, M., Dalgleish B. J. & Evans, A. G., Whisker toughening: a comparision between Al,O, and S&N, toughened with silicon carbide. J. Am. Ceram. Sot., 73(3) (1990) 521-30. Solomah, A. C. & Reichert, W., Mechanical properties, thermal shock resistance and thermal stability of zirconia￾toughened alumina-l0 ~01% silicon carbide whisker ceramic matrix composite. J. Am. Ceram. Sot., 73(3) (1990) 740-3. Porter J. R. & Chokshi, A. H., Creep performance of Sic-whisker reinforced alumina. In Ceramic Microstruc￾ture ‘86, ed. J. A. Pask and A. G. Evans. Plenum Press, New York, 1986, pp. 919-28. Tiegs, T. N. & Becher, P. T., Thermal shock behaviour of an alumina Sic whisker composite. J. Am. Ceram. Sot., 70(5) (1987) C-109-1 1. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. Becher, P. F. & Wei, G. C., Toughening behaviour in Sic-whisker-reinforced alumina. J. Am. Ceram. Sot., 67( 12) (1984) 267-9. Wei, G. C. & Becher, P. F., Development of Sic whisker￾reinforced ceramics. J. Am. Ceram. Sot. Bull., 64(2) (1985) 298-304. Ray, A. K. & Banerjee, S., An articulated bridge fixture for precracking ceramic specimens in fatigue crack growth rate studies of 25 wt% Sic reinforced A&O, com￾posite. J. Am. Ceram. Sot., accepted. Brown Jr, W. F. & Srawley, J. E., in ASTM STP 410. American Society for Testing and Materials, Philadel￾phia, PA, 1966. Yamade, Y. & Kishi, T., Acoustic emission study for Fracture origin of sintered mullite in 4-point bending test. The Sumitomo Search, 45(3) (1991) 17-24. Anstis, G. R., Chantikul, P., Lawn, B. R. & Marshall, D. B., A critical evaluation of indentation techniques for measuring fracture toughness: I, direct crack measurement. J. Am. Ceram. Sot., 64 (1981) 533-8. Ponton, C. B. & Rawlings, R. D., Dependence of the Vickers indentation, fracture toughness on the surface crack length. Br. Ceram. Trans. J., 88 (1989) 83-90. Dauskardt, R. H., Marshall, D. B. & Ritchie, R. O., Cyclic fatigue-crack propagation in magnesia-partially stabilized zirconia ceramics. J. Am. Ceram. Sot., 73(4) (1990) 893-903. Tsai, J. F., Yu, C. S. & Shetty, D. K., Fatigue crack propagation in ceria-partially stabilized zirconia (Ce-TZPk alumina composites. J. Am. Ceram. Sot., 73(10) (1990) 2992-3001. Dauskardt, R. H., James, M. R., Porter, J. R. & Ritchie, R. O., Cyclic fatigue crack growth in a SIC whisker-rein￾forced alumina ceramic composite: long and small crack behaviour. J. Am. Ceram. Sot., 75(4) (1992) 759-71. Lange, F. F., James, M. R. & Green, D. J., Determina￾tion of residual stresses caused by grinding in polycrys￾talline Al,O,. J. Am. Ceram. Sot., 66 (1983) C-167. Cook, R. F., Lawn, B. R., Dabbs, T. P. & Chantikul, P., Effect of machining damage on the strength of a glass ceramic. J. Am. Ceram. Sot., 64 (1981) C-121-2. Green, D. J., Lange, F. F. & James, M. R., Factors infl￾uencing residual surface stresses due to a stress-induced phase transformation. J. Am. Ceram. Sot., 66 (1983) 623-9. Marshall, D. B. & Lawn, B. R., An indentation tech￾nique for measuring stresses in tempered glass - surfaces. J. Am. Ceram. Sot., 60 (1977) 86-7. Ikuma, Y. & Virkar, A. V., Crack-size dependence of fracture toughness in transformation - toughened ceramics. J. Mater. Sci., 19 (1984) 2223-8. Bhattacharya, A. K. & Petrovic, J. J., Hardness and frac￾ture toughness of Sic-particle-reinforced MoSi, composite. J. Am. Ceram. Sot., 74(10) (1991)) 2700-3. Swanson, P. L., Fairbanks, C. J., Lawn, B. R. Mai, Y. W. & Hockey, B. J., Crack-interface grain bridging as a fracture resistance mechanism in ceramics: I, experimental study in alumina. J. Am. Ceram. Sot., 70(4) (1987) 279. Ramchandran, N. & Shetty, D. K., Rising crack growth resistance (R-curve) behaviour of toughened alumina and silicon nitride. J. Am. Ceram. Sot., 74(10) (1991) 2634-41. Anderson, R. M. & Braun, L. M., Technique for the R-curve determination of Y-TZP using indentation-pro￾duced flaws. J. Am. Ceram. Sot., 73(10) (1990) 3059-62. Swain, M. V., R-curve behaviour and thermal shock resistance of ceramics. J. Am. Ceram. Sot., 73(3) (1990) 521-8. Pezzotti, G., Tanaka, I. & Okamoto, T., Si,N&iC￾lvhisker composites without sintering aids: 11, fracture behaviour. J. Am. Ceram. Sot., 73(10) (1990) 3039-45. Ray, A. K., Das, S. K. & Banerjee, S., Fractography of ihe fatigued and fractured regions in a silicon carbide whisker reinforced alumina composite. J. Eur. Ceram. sot., 15 (1995) 191-9. 35. Hansson, T., Warren, R. & Wasen, J., Fracture tough-