COMPOSITES SCIENCE AND TECHNOLOGY ELSEVIER Composites Science and Technology 60(2000)1067-1076 The embrittlement of Nicalon/alumina composites at intermediate and elevated temperatures J.A. Celemin . J. LLorca Department of Materials Science, Polytechnic University of Madrid, E. T.S. de Ingenieros de Caminos, 28040 Madrid, Spain Received 13 April 1999: received in revised form 2 November 1999; accepted 22 December 1999 The strength and toughness of a 2-D woven Nicalon/Al,O3-matrix composite were measured at ambient, intermediate(800C) and elevated (1000-1200C)temperatures. The co tes exhibited non-linear behavior over the whole temperature range but their mechanical properties were significantly degraded at 800C and above. The in situ fiber strength and the interfacial sliding resistance were determined through quantitative microscopy techniques and they were used to predict the composite properties by means of using the appropriate micromechanical models. Comparison of the model and the experiments, together with the fracto- graphic observations, led to the conclusion that the strength reduction was caused by localized interface oxidation at 800 C and by the degradation of the fiber strength at 1000C and above. The decrease in the composite fracture energy was mainly induced by a transition in the fracture mode, which changed from the development of a diffuse damage zone with multiple matrix cracks at 25C to the propagation of a single dominant crack at 800C and above. C 2000 Elsevier Science Ltd. All rights reserved Keywords: Ceramic-matrix composites: Embrittlement; Mechanical properties; Fracture; Strength 1. Introduction (see, for instance, [7-9), aimed at elucidating the domi nant mechanisms of high-temperature degradation in It is now well established that tough, damage-tolerant these novel composites fiber-reinforced ceramics(FRCs) can be obtained by These investigations have pointed to interface oxida- appropriate design of the fiber/matrix interface. If the tion and fiber degradation as the main causes of the matrix is weakly bonded to the fibers, the matrix cracks reduction in strength and toughness at elevated tem- bifurcate at the interface and propagate along it. The perature [10]. In addition, several FRCs were identified cracks propagate through the matrix upon further whose mechanical properties exhibited a minimum loading, leaving the intact fibers in the crack wake. when tested (or exposed prior to testing)at intermediate These processes activate several mechanisms of energy (500-1000C)rather than at elevated temperatures [11 dissipation, such as multiple matrix cracking, crack 13]. This is important from the application standpoint deflection, and fiber failure and pull-out, which lead to because the structural integrity of the components non-linear behavior and to a remarkable improvement should be guaranteed over the whole temperature range in the fracture toughness [1-3. These FRCs were tar- of operation. However, the differences and similarities in geted for structural applications at elevated tempera- the embrittlement mechanisms between intermediate tures(>1000C), where the nickel-based superalloys (600-900 C)and elevated temperature(>1000 C)are become inadequate as they approach their melting not yet well established, and this is partially a result of point. It was soon found, however, that FRC often the lack of systematic studies on the mechanical prop experienced severe embrittlement when they were tested erties of FRCs as a function of temperature. In order to at elevated temperatures(>1000oC)in oxidizing envir- contribute to this research effort, the mechanical prop onments [4-6]. This prompted a huge amount of work erties of an alumina matrix reinforced with Nicalon Sic on the high-temperature mechanical behavior of FRCs fibers were measured at 25, 800, 1000 and 1200 C. The critical microstructural parameters which control the composite properties (interfacial sliding resistance and responding author fiber strength) were estimated as a function of tempera Current address: Universidad Pontificia Comillas de madrid ture through quantitative microscopy techniques. They 0266-3538/00/S. see front matter C 2000 Elsevier Science Ltd. All rights reserved PII:S0266-3538(00)00007-5
The embrittlement of Nicalon/alumina composites at intermediate and elevated temperatures J.A. CelemõÂn 1 , J. LLorca * Department of Materials Science, Polytechnic University of Madrid, E. T. S. de Ingenieros de Caminos, 28040 Madrid, Spain Received 13 April 1999; received in revised form 2 November 1999; accepted 22 December 1999 Abstract The strength and toughness of a 2-D woven Nicalon/Al2O3-matrix composite were measured at ambient, intermediate (800C), and elevated (1000±1200C) temperatures. The composites exhibited non-linear behavior over the whole temperature range but their mechanical properties were signi®cantly degraded at 800C and above. The in situ ®ber strength and the interfacial sliding resistance were determined through quantitative microscopy techniques and they were used to predict the composite properties by means of using the appropriate micromechanical models. Comparison of the model and the experiments, together with the fractographic observations, led to the conclusion that the strength reduction was caused by localized interface oxidation at 800C and by the degradation of the ®ber strength at 1000C and above. The decrease in the composite fracture energy was mainly induced by a transition in the fracture mode, which changed from the development of a diuse damage zone with multiple matrix cracks at 25C to the propagation of a single dominant crack at 800C and above. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Ceramic-matrix composites; Embrittlement; Mechanical properties; Fracture; Strength 1. Introduction It is now well established that tough, damage-tolerant ®ber-reinforced ceramics (FRCs) can be obtained by appropriate design of the ®ber/matrix interface. If the matrix is weakly bonded to the ®bers, the matrix cracks bifurcate at the interface and propagate along it. The cracks propagate through the matrix upon further loading, leaving the intact ®bers in the crack wake. These processes activate several mechanisms of energy dissipation, such as multiple matrix cracking, crack de¯ection, and ®ber failure and pull-out, which lead to non-linear behavior and to a remarkable improvement in the fracture toughness [1±3]. These FRCs were targeted for structural applications at elevated temperatures (>1000C), where the nickel-based superalloys become inadequate as they approach their melting point. It was soon found, however, that FRC often experienced severe embrittlement when they were tested at elevated temperatures (>1000C) in oxidizing environments [4±6]. This prompted a huge amount of work on the high-temperature mechanical behavior of FRCs (see, for instance, [7±9]), aimed at elucidating the dominant mechanisms of high-temperature degradation in these novel composites. These investigations have pointed to interface oxidation and ®ber degradation as the main causes of the reduction in strength and toughness at elevated temperature [10]. In addition, several FRCs were identi®ed, whose mechanical properties exhibited a minimum when tested (or exposed prior to testing) at intermediate (500±1000C) rather than at elevated temperatures [11± 13]. This is important from the application standpoint because the structural integrity of the components should be guaranteed over the whole temperature range of operation. However, the dierences and similarities in the embrittlement mechanisms between intermediate (600±900C) and elevated temperature (>1000C) are not yet well established, and this is partially a result of the lack of systematic studies on the mechanical properties of FRCs as a function of temperature. In order to contribute to this research eort, the mechanical properties of an alumina matrix reinforced with Nicalon SiC ®bers were measured at 25, 800, 1000 and 1200C. The critical microstructural parameters which control the composite properties (interfacial sliding resistance and ®ber strength) were estimated as a function of temperature through quantitative microscopy techniques. They 0266-3538/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(00)00007-5 Composites Science and Technology 60 (2000) 1067±1076 * Corresponding author. 1 Current address: Universidad Ponti®cia Comillas de Madrid
J.A. Celemin, J. LLorca/ Composites Science and Technology 60(2000)1067-1076 were used to predict the composite strength and toug men for an accurate control of the temperature. The ness using the available micromechanical data for FRCs heating rate was 12 C per min and each specimen was with a weak interface. The comparison between model held at the test temperature for I h prior to testing predictions and experimental results, together with the ensure uniform distribution of the temperature. Both microstructural analysis of the deformation and failure tensile and fracture tests were performed under stroke processes, shed more light on embrittlement mechan- control at a crosshead speed of 50 um /min The load (P) isms which control the mechancial behavior of this and the crosshead displacement of the testing machine material as a function of temperature with respect to the frame(v) were monitored during the tests, the latter through a lvdt transducer outside the furnace. In addition. the distance between two small 2. Materials and experimental techniques pins glued in the central region of the tensile specimens was measured through a laser extensometer. This The composite material was supplied by Dupont- extensometer was also used during the fracture tests to Lanxide Corporation(Newark, DE)in the form of rec- measure the crack mouth opening displacement angular plates of 3 mm nominal thickness. The fiber (CMOD)obtained from the distance between two alu- preform was manufactured by stacking several layers of mina pins glued symmetrically to the notch mouth. bi-directional (0 /90)Nicalon &-harness satin-weave Once broken, the fracture surfaces were sputtered fabric(Nippon Carbon, Tokyo, Japan). The average with Au-Pd for 3 min before being observed in the fiber radius, as determined by quantitative microscopy, scanning electron microscope. In addition, the speci was 7. 2 um. The fibers were coated by chemical var mens were sliced far away from the fracture surface with deposition with a thin layer of BN (approximately 100 a low speed diamond saw, and the longitudinal sections nm)and then with a thicker layer of Sic(3 um) onto were polished successively on diamond cloths of 40, 9, 3 the BN. The alumina matrix was infiltrated by using and 1 um grain size and finally on alumina of 0.3 um a direct metal oxidation process. The preform was grain size. They were cleaned for 30 min by ultrasound brought into contact with molten aluminum in air at in acetone to remove the alumina from polishing, and studied in the optical form a matrix of porous Al,O3 which grew into the preform. The residual aluminum was finally removed from the composite material using a proprietary techni- 3. Experimental results que. The volume fraction of fibers in the composite was 37%, while the Sic fiber coating occupied another 37%. 3.1. Mechanical properties The Al2O3 matrix comprised 18% of the composite volume and the rest(8%)was porosity. More details of The initial composite response during the tensile tests the manufacturing process and the microstructure can was linear. It was followed by a pronounced knee in the be found elsewhere [14-16 Tensile and notched-beam specimens were machined rom the plates. The tensile specimens had a dog-bone shape and were designed according to the specifications given by French and Wiederhorn [17]. The central part Thermocouples of the specimen had uniform width of 4 mm and a length of 15 mm. Load was applied through two cera- mic pins which were introduced into circular holes Hinge machined in the specimen heads. The pins were attached to two alumina rods connected, respectively to the actuator and to the load cell of the mechanical testing machine. Two bi-directional hinges were inserted in the Heating elements oad train to avoid bending stresses during the tests. The Lase experimental set-up is shown in Fig. 1. The fracture tests were carried out by three-point bending of notched prismatic bars. The loading span was 50 mm and the bar depth 10 mm. A notch of around 2 mm in length and 150 um in radius was introduced with a thin dia- Alumina rod mond wire LVDT The specimen and the loading fixture were placed in a urnace for the elevated temperature tests. (see Fig. 1) Two B-type thermocouples were attached to the speci- Fig. 1. Experimental set-up for the tensile tests at elevated temperature
were used to predict the composite strength and toughness using the available micromechanical data for FRCs with a weak interface. The comparison between model predictions and experimental results, together with the microstructural analysis of the deformation and failure processes, shed more light on embrittlement mechanisms which control the mechancial behavior of this material as a function of temperature. 2. Materials and experimental techniques The composite material was supplied by DupontLanxide Corporation (Newark, DE) in the form of rectangular plates of 3 mm nominal thickness. The ®ber preform was manufactured by stacking several layers of bi-directional (0/90) Nicalon 8-harness satin-weave fabric (Nippon Carbon, Tokyo, Japan). The average ®ber radius, as determined by quantitative microscopy, was 7.2 mm. The ®bers were coated by chemical vapor deposition with a thin layer of BN (approximately 100 nm) and then with a thicker layer of SiC (3 mm) onto the BN. The alumina matrix was in®ltrated by using a direct metal oxidation process. The preform was brought into contact with molten aluminum in air at 1000C. The aluminum reacted with the oxygen to form a matrix of porous Al2O3 which grew into the preform. The residual aluminum was ®nally removed from the composite material using a proprietary technique. The volume fraction of ®bers in the composite was 37%, while the SiC ®ber coating occupied another 37%. The Al2O3 matrix comprised 18% of the composite volume and the rest (8%) was porosity. More details of the manufacturing process and the microstructure can be found elsewhere [14±16]. Tensile and notched-beam specimens were machined from the plates. The tensile specimens had a dog-bone shape and were designed according to the speci®cations given by French and Wiederhorn [17]. The central part of the specimen had uniform width of 4 mm and a length of 15 mm. Load was applied through two ceramic pins which were introduced into circular holes machined in the specimen heads. The pins were attached to two alumina rods connected, respectively to the actuator and to the load cell of the mechanical testing machine. Two bi-directional hinges were inserted in the load train to avoid bending stresses during the tests. The experimental set-up is shown in Fig. 1. The fracture tests were carried out by three-point bending of notched prismatic bars. The loading span was 50 mm and the bar depth 10 mm. A notch of around 2 mm in length and 150 mm in radius was introduced with a thin diamond wire. The specimen and the loading ®xture were placed in a furnace for the elevated temperature tests. (see Fig. 1). Two B-type thermocouples were attached to the specimen for an accurate control of the temperature. The heating rate was 12C per min and each specimen was held at the test temperature for 1 h prior to testing to ensure uniform distribution of the temperature. Both tensile and fracture tests were performed under stroke control at a crosshead speed of 50 mm/min. The load (P) and the crosshead displacement of the testing machine with respect to the frame (n) were monitored during the tests, the latter through a LVDT transducer outside the furnace. In addition, the distance between two small pins glued in the central region of the tensile specimens was measured through a laser extensometer. This extensometer was also used during the fracture tests to measure the crack mouth opening displacement (CMOD) obtained from the distance between two alumina pins glued symmetrically to the notch mouth. Once broken, the fracture surfaces were sputtered with Au±Pd for 3 min before being observed in the scanning electron microscope. In addition, the specimens were sliced far away from the fracture surface with a low speed diamond saw, and the longitudinal sections were polished successively on diamond cloths of 40, 9, 3 and 1 mm grain size and ®nally on alumina of 0.3 mm grain size. They were cleaned for 30 min by ultrasound in acetone to remove the alumina from polishing, and studied in the optical microscope. 3. Experimental results 3.1. Mechanical properties The initial composite response during the tensile tests was linear. It was followed by a pronounced knee in the Fig. 1. Experimental set-up for the tensile tests at elevated temperature. 1068 J.A. CelemõÂn, J. LLorca / Composites Science and Technology 60 (2000) 1067±1076
J.A. Celemin, J. LLorca/ Composites Science and Technology 60(2000)1067-1076 1069 Table l problems with the specimen alignment precluded the Composite, matrix and fiber elastic moduli accurate determination of the modulus at 800 and Temperature(C 1000C and these were estimated using reasonable assumptions as indicated in [18]. The average values of the measured and estimated elastic moduli are shown in ErGPa) 135 Four P-CMOD curves corresponding to fracture tests at 25, 800, 1000, and 1200oC are depicted in Fig. 2(b) stress/ strain curve, which marked the transition to the They also presented an initial linear zone, which was non-linear regime induced by the onset of multiple followed by a non-linear region prior to the maximum matrix cracking. The results for the matrix cracking load in the tests at 25C. The observation of the notch non-linmear (defined as the stress at the beginning of the tip region through a telescope at this stage showed the are plotted in Fig. 2(a)as a function of the test tem- matrix cracks. The non -linear region was less noticeable perature. In addition, the elastic modulus was deter- at 800C and has practically disappeared at 1000 and mined from the initial slope of the stress/strain curve in 1200 C. Fracture took place by the propagation of a the specimens tested at 25 and 1200C. Experimental single dominant crack at these temperatures. 250 Matrix cracking stress Temperature 200 1000c 150 1200c 600H 200 200400600800100012001400 MOd (ut · Fracture energy 25 25 200400600800100012001400 200400600800100012001400 Temperature(.) strength,Ou;(b)load/crack mouth opening displacement curves; (c)nominal fracture toughness, Ko: (d)fracture energy,c, Nie"and hanical properties of the Al2O/Nicalon composite as a function of the test temperature: (a) tensile matrix crad
stress/strain curve, which marked the transition to the non-linear regime induced by the onset of multiple matrix cracking. The results for the matrix cracking stress, smc, (de®ned as the stress at the beginning of the non-linear regime) as well as for the tensile strength, su, are plotted in Fig. 2(a) as a function of the test temperature. In addition, the elastic modulus was determined from the initial slope of the stress/strain curve in the specimens tested at 25 and 1200C. Experimental problems with the specimen alignment precluded the accurate determination of the modulus at 800 and 1000C and these were estimated using reasonable assumptions as indicated in [18]. The average values of the measured and estimated elastic moduli are shown in Table 1. Four P-CMOD curves corresponding to fracture tests at 25, 800, 1000, and 1200C are depicted in Fig. 2(b). They also presented an initial linear zone, which was followed by a non-linear region prior to the maximum load in the tests at 25C. The observation of the notch tip region through a telescope at this stage showed the formation of a diuse damage zone, containing multiple matrix cracks. The non-linear region was less noticeable at 800C and has practically disappeared at 1000 and 1200C. Fracture took place by the propagation of a single dominant crack at these temperatures. Table 1 Composite, matrix and ®ber elastic moduli Temperature (C) 25 800 1000 1200 E (GPa) 73 69 52 45 Em(GPa) 145 137 98 80 Ef(GPa) 180 170 135 125 Fig. 2. Mechanical properties of the Al2O3/Nicalon composite as a function of the test temperature: (a) tensile matrix cracking stress, mc, and strength, u; (b) load/crack mouth opening displacement curves; (c) nominal fracture toughness, KQ; (d) fracture energy, GF. J.A. CelemõÂn, J. LLorca / Composites Science and Technology 60 (2000) 1067±1076 1069
J.A. Celemin, J. LLorca/ Composites Science and Technology 60(2000)1067-1076 The nominal fracture toughness, Ko, was obtained 25C [Fig 3(a)]. This indicates that the matrix cracks from the maximum load, Pu, and the initial notch did not propagate through the fibers, which remained gth, ao, according to [19 intact behind the crack tip bridging the crack surfaces They were broken in tension within the matrix as the KQ=5PuLa/BW/Y(a) (1 separation between the crack surfaces increased, and had to be pulled out prior to the complete specimen fracture. Fiber pull-out was also dominant in the speci where L is the span, B and w stand for the specimen mens tested at 800C [Fig 3(b)] and 1200oC [Fig 3(c)]. thickness and depth, respectively, a=ao/w, and Y(o)is although it should be noted that fibers broken in the a non-dimensional function given matrix crack plane were also observed in these cases Neither the fraction of pulled-out fibers nor the average 19179-12795a+3.3532a2-3.2260a3+1.2235a4 pull-out length were measured, but careful analyses of (1-a)3/(+2a) (2) This expression is valid for 0 <a<I when L/w=5. It should be noticed at this point that Ko depends on the specimen geometry and size because the length of the racture process zone around the crack tip was compar able to the specimen characteristic dimensions [20] Thus, Ko cannot be considered, strictly speaking,a material property but it is still a good parameter to estimate the influence of the temperature on the com posite toughness. This can also be analyzed through the fracture energy, GF, which stands for the energy spent 200pm to create a unit area of free surface. Assuming that the specimen fracture took place by the propagation of (b) crack from the notch to the back of the specimen, GE B(W-0Pdv where integral represents the area under the P-v The experimental results for the nominal fracture toughness and the fracture energy are plotted in Fig 2(c)and(d), respectively, as a function of the test tem- perature. Two main conclusions may be drawn from the results in Fig. 2. Firstly, the composite presented a duc tile behavior in the whole temperature range analyzed the matrix cracking stress was always significantly lower than the tensile strength, and the fracture toughness and the fracture energy were well above those measured in monolithic ceramics. Secondly, the strength and the toughness of the composite decreased significantly from ambient to 800oC and remained practically constant above this temperature 3. 2. Fractography. The analyses of the fracture surfaces in the scanning electron microscope corroborated the presence of a Fig 3. Fracture surface of the specimens tested at different tempera- weak fiber/matrix interface. Fibers protruding from the tures, showing fibers pulled out from the matrix: (a)25%C; (b)800oC fracture surface were observed in the specimens tested at (c)1200C
The nominal fracture toughness, KQ, was obtained from the maximum load, Pu, and the initial notch length, a0, according to [19] KQ 3 2 PuL 1=2 =BW3=2 Y 1 where L is the span, B and W stand for the specimen thickness and depth, respectively, a0=W, and Y( ) is a non-dimensional function given by Y 1:9179ÿ1:2795 3:3532 2ÿ3:2260 3 1:2235 4 1ÿ 3=2 12 2 This expression is valid for 0 < <1 when L=W 5. It should be noticed at this point that KQ depends on the specimen geometry and size because the length of the fracture process zone around the crack tip was comparable to the specimen characteristic dimensions [20]. Thus, KQ cannot be considered, strictly speaking, a material property but it is still a good parameter to estimate the in¯uence of the temperature on the composite toughness. This can also be analyzed through the fracture energy, GF, which stands for the energy spent to create a unit area of free surface. Assuming that the specimen fracture took place by the propagation of a crack from the notch to the back of the specimen, GF can be computed as GF 1 B W ÿ a0 Pdv 3 where the integral represents the area under the P±v curve. The experimental results for the nominal fracture toughness and the fracture energy are plotted in Fig. 2(c) and (d), respectively, as a function of the test temperature. Two main conclusions may be drawn from the results in Fig. 2. Firstly, the composite presented a ductile behavior in the whole temperature range analyzed: the matrix cracking stress was always signi®cantly lower than the tensile strength, and the fracture toughness and the fracture energy were well above those measured in monolithic ceramics. Secondly, the strength and the toughness of the composite decreased signi®cantly from ambient to 800C and remained practically constant above this temperature. 3.2. Fractography. The analyses of the fracture surfaces in the scanning electron microscope corroborated the presence of a weak ®ber/matrix interface. Fibers protruding from the fracture surface were observed in the specimens tested at 25C [Fig. 3(a)]. This indicates that the matrix cracks did not propagate through the ®bers, which remained intact behind the crack tip bridging the crack surfaces. They were broken in tension within the matrix as the separation between the crack surfaces increased, and had to be pulled out prior to the complete specimen fracture. Fiber pull-out was also dominant in the specimens tested at 800C [Fig. 3(b)] and 1200C [Fig. 3(c)], although it should be noted that ®bers broken in the matrix crack plane were also observed in these cases. Neither the fraction of pulled-out ®bers nor the average pull-out length were measured, but careful analyses of Fig. 3. Fracture surface of the specimens tested at dierent temperatures, showing ®bers pulled out from the matrix: (a) 25C; (b) 800C; (c) 1200C. 1070 J.A. CelemõÂn, J. LLorca / Composites Science and Technology 60 (2000) 1067±1076
J.A. Celemin, J. LLorca/Composites Science and Technology 60(2000)1067-1076 Table 2 Fraction of pulled-out fibers with different morphology on the fracture Temperature(°C)25 1000 ype I(%) Type Il(%) pe Ill (% These results can be used to compute the fiber failure probability, F, as a function of the fiber strength for Mirror each temperature. The strength data computed from the ist mirror radius were arranged in ascending order and 5 um corresponding failure probability, F=(i-0.5)/N, was assigned to each strength based on rank statistics, where Fig 4. Detail of the fracture surface of a pulled-out Nicalon SiC fiber, i is the rank and N is the total number of experimental showing the mirror-mist-hackle morphology data. The lowest strength was attributed to the fibers with a specular fracture surface(type Ill), following the analysis of Eckel and Bradt [22]. The highest strength the fracture surfaces led to two qualitative-but was assigned to the fibers with very short mirror radius unambiguous-conclusions. Firstly, the average fiber (type I). The results are shown in Fig. 5, and they are 1200C was shorter than in those tested at 25C pull-out length in the specimens tested at 1000 well approximated by a Weibull function of the form ondly, the fraction of fibers broken in the matrix crad plane was maximum at 800oC 3.3. In situ fiber strengi (5)where the parameter o* can be obtained from Fig. 5 If observed at higher magnification, the fracture sur- as the stress which gives a fracture probability equal to face of most of the pulled-out fibers showed the mor- 63%, and m* can be computed by the least squares fit phology depicted in Fig. 4, which includes a specular ting of (5) to the experimental results plotted in Fig. 5 circular region(mirror), an intermediate rough surface The values of os and m derived from the fracture mir (mist), and an abrupt external area(hackle). The mirror- ror data are not, in general, identical to the true in situ misf-hackle topography is typical on the fracture sur- fiber characteristic strength, ac, and Weibull modulus m, face of Nicalon Sic fibers broken in tension. An empirical relationship between the fracture mirror dius, am(expressed in m), and the fiber strength, s(in 100 MPa), has been shown by several authors to be of the 2.51 for Nicalon SiC fibers [21-23]. to determine the in situ fiber strength, the fracture surface of approximately 130 pulled-out fibers was analyzed for each temperature The majority of the fibers exhibited a distinct mirror- 25 misf-hackle structure(type II), where the mirror radius could be easily determined. However, this radius was too short to be accurately measured in a small fraction 1200c of fibers (type I) while no distinct fracture mirror boundary was seen in other fibers and the whole fiber 1000 2000 fracture surface was specular(type IIl). The proportion Fiber Strength, S(MPa) of fibers with type I, II and Ill fracture surfaces is Fig. 5. Cumulative fracture probability of the fibers, F, at different shown in Table 2 as a function of the test temperature temperatures as obtained from the fracture mirror data
the fracture surfaces led to two qualitative±±but unambiguous Ð conclusions. Firstly, the average ®ber pull-out length in the specimens tested at 1000 and 1200C was shorter than in those tested at 25C. Secondly, the fraction of ®bers broken in the matrix crack plane was maximum at 800C. 3.3. In situ ®ber strength If observed at higher magni®cation, the fracture surface of most of the pulled-out ®bers showed the morphology depicted in Fig. 4, which includes a specular circular region (mirror), an intermediate rough surface (mist), and an abrupt external area (hackle). The mirror± mist±hackle topography is typical on the fracture surface of Nicalon SiC ®bers broken in tension. An empirical relationship between the fracture mirror radius, am (expressed in m), and the ®ber strength, S (in MPa), has been shown by several authors to be of the form, S 2:51 am p 4 for Nicalon SiC ®bers [21±23]. To determine the in situ ®ber strength, the fracture surface of approximately 130 pulled-out ®bers was analyzed for each temperature. The majority of the ®bers exhibited a distinct mirror± mist±hackle structure (type II), where the mirror radius could be easily determined. However, this radius was too short to be accurately measured in a small fraction of ®bers (type I) while no distinct fracture mirror boundary was seen in other ®bers and the whole ®ber fracture surface was specular (type III). The proportion of ®bers with type I, II and III fracture surfaces is shown in Table 2 as a function of the test temperature. These results can be used to compute the ®ber failure probability, F, as a function of the ®ber strength for each temperature. The strength data computed from the mirror radius were arranged in ascending order and a corresponding failure probability, F=(iÿ0.5)/N, was assigned to each strength based on rank statistics, where i is the rank and N is the total number of experimental data. The lowest strength was attributed to the ®bers with a specular fracture surface (type III), following the analysis of Eckel and Bradt [22]. The highest strength was assigned to the ®bers with very short mirror radius (type I). The results are shown in Fig. 5, and they are well approximated by a Weibull function of the form F 1 ÿ exp ÿ S c " # m 5 (5) where the parameter c can be obtained from Fig. 5 as the stress which gives a fracture probability equal to 63%, and m can be computed by the least squares ®tting of (5) to the experimental results plotted in Fig. 5. The values of c and m derived from the fracture mirror data are not, in general, identical to the true in situ ®ber characteristic strength, c, and Weibull modulus m, Table 2 Fraction of pulled-out ®bers with dierent morphology on the fracture surface Temperature (C) 25 800 1000 1200 Type I (%) 22 20 24 31 Type II (%) 66 63 69 58 Type III (%) 12 17 7 11 Fig. 4. Detail of the fracture surface of a pulled-out Nicalon SiC ®ber, showing the mirror±mist±hackle morphology. Fig. 5. Cumulative fracture probability of the ®bers, F, at dierent temperatures as obtained from the fracture mirror data. J.A. CelemõÂn, J. LLorca / Composites Science and Technology 60 (2000) 1067±1076 1071