Availableonlineatwww.sciencedirect.com SCIENCE DIRECT● E噩≈S ELSEVIER Journal of the European Ceramic Society 25(2005)3649-3655 www.elsevier.com/locate/jeurceramsoc Critical crack-healing condition for Sic whisker reinforced alumina under stress Wataru Nakao*, Masato Ono, Sang-Kee Lee, Koji Takahashi, Kotoji Ando Department of Energy and Safery Engineering, Yokohama National University 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan Received 11 April 2004; received in revised form I September 2004, accepted 12 September 2004 Available online 8 December 2004 Abstract Alumina reinforced by Sic whisker, called here"alumina( w)"was developed with the objective of improving fracture toughness and crack- healing ability. The composites were crack-healed at 1200C for h in air under elevated static and cyclic stresses. The bending strength at 1200C of the crack-healed composites were investigated. The threshold static stress during crack-healing of alumina(w)has been determined to be 250 MPa, and the threshold cyclic stress was found to be 300 MPa. Considering that the crack growth is time-dependent, the threshold stress of every condition during crack-healing of alumina( w) was found to be 250 MPa. The results showed that the threshold stress intensity factor during crack-healing was 3. 8 MPam". The same experiment conditions were applied to specimens cracked and annealed at 1300C for I h in Ar, to remove the tensile residual stress at a tip of the crack. Thus, the threshold stress intensity factor during crack-healing was found to be 3.2 MPa 2 for the specimens crack-healed with annealing. The threshold stress intensity factor during crack-healing of alumina( w)was chosen to be 3.2 MPam"to facilitate comparison with the values of the threshold stress intensity factor during crack-healing. The residual stress was slightly larger than the intrinsic value C 2004 Elsevier Ltd. All rights reserved. Keywords: Crack-healing Composites; AlO3; SiC whiskers 1. Introduction nanocomposite ceramics". Some Al2O3 /SiC nanocompos- Alumina(Al2 O3) has three weak points: (1)low bendir for alumina whose value is 1300C, was achieved by ur strength(oB 400 MPa), (2)low heat-resistance limit tem- formly distributing nanosize SiC particles in alumina grains perature for strength(THR N950C, and(3)low fracture Related to above weakness(3), two possibilities to overcome toughness(KIC 4.0MPam). These weaknesses restrict low fracture toughness are(a)increase in fracture tough- the application of Al2O3 for important components. If these ness by reinforcing whiskers and fibers, and(b)endowing weaknesses were satisfactorily overcome, Al2O3 would be a strong self-crack-healing ability to heal the cracks. As to a leading candidate material for advanced gas turbine and the above(b), monolithic Al2O3 and AlO3/SiC compos- engine, because alumina exhibits much greater resistance to ites have very interesting crack-healing ability. 1, 7-15 That the oxidation than silicon nitride crack-healing behavior of monolithic Al,O3 was induced not For the weakness(1)above, the grain growth of Al2O3 by intrinsic crack-healing but by the secondary sintering, is luring sintering was retarded and strength was increased reported by the previous study , By contrast, Al2O3/SIC by the Hall-Petch effect similar to mullite/SiC by adding composite has been crack-healed by reaction of Sic and the 15-20 mass% nanosize SiC particles. Considering item(2), Oz in the atmosphere. The crack-healing behavior of the pre- Niihara and coworkers-6 have proposed the concept of vious Al203/SiC composite is assumed to be insufficient to overcome weakness(3)above. However, the good self-crack Corresponding author healing ability was introduced as for mullite/SiC2, 16-20 and E-imail address: nakao @ynu ac jp(w. Nakao) Si3 N4/SiC21-29 by adding 15-20 mass% nanosize SiC parti 0955-2219/S-see front matter c 2004 Elsevier Ltd. All rights reserved doi: 10.1016/j- jeurceramsoc 2004.09.021
Journal of the European Ceramic Society 25 (2005) 3649–3655 Critical crack-healing condition for SiC whisker reinforced alumina under stress Wataru Nakao∗, Masato Ono, Sang-Kee Lee, Koji Takahashi, Kotoji Ando Department of Energy and Safety Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan Received 11 April 2004; received in revised form 1 September 2004; accepted 12 September 2004 Available online 8 December 2004 Abstract Alumina reinforced by SiC whisker, called here “alumina(w)” was developed with the objective of improving fracture toughness and crackhealing ability. The composites were crack-healed at 1200 ◦C for 8 h in air under elevated static and cyclic stresses. The bending strength at 1200 ◦C of the crack-healed composites were investigated. The threshold static stress during crack-healing of alumina(w) has been determined to be 250 MPa, and the threshold cyclic stress was found to be 300 MPa. Considering that the crack growth is time-dependent, the threshold stress of every condition during crack-healing of alumina(w) was found to be 250 MPa. The results showed that the threshold stress intensity factor during crack-healing was 3.8 MPa m1/2. The same experiment conditions were applied to specimens cracked and annealed at 1300 ◦C for 1 h in Ar, to remove the tensile residual stress at a tip of the crack. Thus, the threshold stress intensity factor during crack-healing was found to be 3.2 MPa m1/2 for the specimens crack-healed with annealing. The threshold stress intensity factor during crack-healing of alumina(w) was chosen to be 3.2 MPa m1/2 to facilitate comparison with the values of the threshold stress intensity factor during crack-healing. The residual stress was slightly larger than the intrinsic value. © 2004 Elsevier Ltd. All rights reserved. Keywords: Crack-healing; Composites; Al2O3; SiC whiskers 1. Introduction Alumina (Al2O3) has three weak points:1 (1) low bending strength (σB ≈ 400 MPa), (2) low heat-resistance limit temperature for strength (THR ≈ 950 ◦C), and (3) low fracture toughness (KIC ≈ 4.0 MPa m1/2). These weaknesses restrict the application of Al2O3 for important components. If these weaknesses were satisfactorily overcome, Al2O3 would be a leading candidate material for advanced gas turbine and engine, because alumina exhibits much greater resistance to oxidation than silicon nitride. For the weakness (1) above, the grain growth of Al2O3 during sintering was retarded and strength was increased by the Hall–Petch effect similar to mullite/SiC2 by adding 15–20 mass% nanosize SiC particles. Considering item (2), Niihara and coworkers3–6 have proposed the concept of ∗ Corresponding author. E-mail address: wnakao@ynu.ac.jp (W. Nakao). “nanocomposite ceramics”. Some Al2O3/SiC nanocomposites exhibit excellent strength and THR. The increased of THR, for alumina whose value is 1300 ◦C, was achieved by uniformly distributing nanosize SiC particles in alumina grains. Related to above weakness (3), two possibilities to overcome low fracture toughness are (a) increase in fracture toughness by reinforcing whiskers and fibers, and (b) endowing a strong self-crack-healing ability to heal the cracks. As to the above (b), monolithic Al2O3 and Al2O3/SiC composites have very interesting crack-healing ability.1,7–15 That the crack-healing behavior of monolithic Al2O3 was induced not by intrinsic crack-healing but by the secondary sintering, is reported by the previous study.1,13 By contrast, Al2O3/SiC composite has been crack-healed by reaction of SiC and the O2 in the atmosphere. The crack-healing behavior of the previous Al2O3/SiC composite is assumed to be insufficient to overcome weakness (3) above. However, the good self-crackhealing ability was introduced as for mullite/SiC2,16–20 and Si3N4/SiC21–29 by adding 15–20 mass% nanosize SiC parti- 0955-2219/$ – see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jeurceramsoc.2004.09.021
3650 w Nakao et al. /Journal of the European Ceramic Sociery 25(2005)3649-3655 of a-Al2O3 was 5-6 um. The Sic whiskers were located at grain boundaries between a-Al2O3 grains and were preferer tially oriented within the plane perpendicular to the pressing axis. The density of the sintered plate was 3.83g/cm3.The ic whi sintered plate was cut into the 3mm x 4 mm x 23 mm rect angular specimens bar that were polished to a mirror finish on one face and the edges of specimens were beveled 45to reduce the likelihood of edge initiated failures A semi-elliptical surface crack of 100 um in surface length, as shown in Fig. 2, was made at the center of the tensile surface of specimens with a Vickers indenter, using a load of 196N. The aspect ratio(alc)of the pre-crack which is depth(a) to half the surface length(c)was 0.9. In this invest 5 gation, the pre-crack was healed in air while applying tensile static or cyclic stresses by the three-point loading system shown in Fig 3. The pre-crack was subjected to tensile stress Fig. 1. Microstructure of the SiC reinforced alumina composite, alumina( w). before the crack-healing was started by heating the furnace to avoid the crack-healing under no-stress. Then, the specimen was kept at the above condition for 8 h to finish completely cles. However, oxygen is necessary for the crack-healing, so the crack-healing process. The applied cyclic stress was sinu- em bedded flaws cannot be healed soidal with a stress ratio. maximum stress/minimum stress In conclusion, for higher structural integrity, both high of 0.2 and a frequency of 5 Hz. Moreover, the crack-healing fracture toughness and crack-healing ability should be satis- behavior under stress was also investigated for specimens factorily achieved. From this perspective, alumina reinforced annealed at 1300C for I h in Ar after pre-cracking so as to by 20 mass%SiC whisker, abbreviated alumina( w),was sin- remove the residual stress introduced during pre-cracking by tered and the mechanical properties of alumina( w)were in- using the indentation method vestigated in the previous studies. 4, 5 Alumina(w)exhibited large fracture toughness(6.5 MPam )and excellent crack healing ability. However, the basic crack-healing behavior as a function of crack-healing temperature and time was not well Tension direction investigated. Moreover, crack-healing behavior under stress and the critical stress condition were not investigated at all Therefore, alumina( w) has been subjected to crack-healing under elevated static and cyclic stresses at 1200C, corre sponding to the limiting temperature for the bending strength of alumina( w). The bending strength of alumina( w) crack- Vickers healed under stress has been measured at the crack-healing indentation emperature. From the results, an upper limiting stress that can be applied during crack-healing has been determined for alumina( w) 2. Experimental The a-Al2O3 powder(AKP-20, Sumitomo Chemicals Co td., Japan) used in this study has a purity of 99.999% and a 照 Pre-crack mean particle size of 0. 4-0.6 um. The SiC whiskers (SCw Tateho Chemical Industry Co Ltd, Japan)used have diame ters between 0. 8 and 1.0 um and lengths from 30 to 100 um The mixture of a-Al2O3 powder and 20 mass% SiC whisker was blended well in isopropyl alcohol for 12 h using alumina balls and an alumina mill pot. Then, the slurry was dried Rectangular plates of 50 mm x 50 mm x 9 mm were sintered via uniaxial hot press in Ar at 1850C for I h at 40 MPa. Fig. I shows the microstructure of the sintered SiC whisker Fig. 2. SEM images of (a)surface shapes and(b)cross-sectional shapes of reinforced alumina composite, alumina( w). The grain size the crack and indentation
3650 W. Nakao et al. / Journal of the European Ceramic Society 25 (2005) 3649–3655 Fig. 1. Microstructure of the SiC reinforced alumina composite, alumina(w). cles. However, oxygen is necessary for the crack-healing, so embedded flaws cannot be healed. In conclusion, for higher structural integrity, both high fracture toughness and crack-healing ability should be satisfactorily achieved. From this perspective, alumina reinforced by 20 mass% SiC whisker, abbreviated alumina(w), was sintered and the mechanical properties of alumina(w) were investigated in the previous studies.14,15 Alumina(w) exhibited large fracture toughness (6.5 MPa m1/2) and excellent crackhealing ability. However, the basic crack-healing behavior as a function of crack-healing temperature and time was not well investigated. Moreover, crack-healing behavior under stress and the critical stress condition were not investigated at all. Therefore, alumina(w) has been subjected to crack-healing under elevated static and cyclic stresses at 1200 ◦C, corresponding to the limiting temperature for the bending strength of alumina(w). The bending strength of alumina(w) crackhealed under stress has been measured at the crack-healing temperature. From the results, an upper limiting stress that can be applied during crack-healing has been determined for alumina(w). 2. Experimental The -Al2O3 powder (AKP-20, Sumitomo Chemicals Co. Ltd., Japan) used in this study has a purity of 99.999% and a mean particle size of 0.4–0.6m. The SiC whiskers (SCW, Tateho Chemical Industry Co. Ltd., Japan) used have diameters between 0.8 and 1.0m and lengths from 30 to 100m. The mixture of -Al2O3 powder and 20 mass% SiC whiskers was blended well in isopropyl alcohol for 12 h using alumina balls and an alumina mill pot. Then, the slurry was dried. Rectangular plates of 50 mm × 50 mm × 9 mm were sintered via uniaxial hot press in Ar at 1850 ◦C for 1 h at 40 MPa. Fig. 1 shows the microstructure of the sintered SiC whisker reinforced alumina composite, alumina(w). The grain size of -Al2O3 was 5–6m. The SiC whiskers were located at grain boundaries between -Al2O3 grains and were preferentially oriented within the plane perpendicular to the pressing axis. The density of the sintered plate was 3.83 g/cm3. The sintered plate was cut into the 3 mm × 4 mm × 23 mm rectangular specimens bar that were polished to a mirror finish on one face and the edges of specimens were beveled 45◦ to reduce the likelihood of edge initiated failures. A semi-elliptical surface crack of 100m in surface length, as shown in Fig. 2, was made at the center of the tensile surface of specimens with a Vickers indenter, using a load of 19.6 N. The aspect ratio (a/c) of the pre-crack which is depth (a) to half the surface length (c) was 0.9. In this investigation, the pre-crack was healed in air while applying tensile static or cyclic stresses by the three-point loading system shown in Fig. 3. The pre-crack was subjected to tensile stress before the crack-healing was started by heating the furnace to avoid the crack-healing under no-stress. Then, the specimen was kept at the above condition for 8 h to finish completely the crack-healing process. The applied cyclic stress was sinusoidal with a stress ratio, maximum stress/minimum stress, of 0.2 and a frequency of 5 Hz. Moreover, the crack-healing behavior under stress was also investigated for specimens annealed at 1300 ◦C for 1 h in Ar after pre-cracking so as to remove the residual stress introduced during pre-cracking by using the indentation method. Fig. 2. SEM images of (a) surface shapes and (b) cross-sectional shapes of the crack and indentation.
w. Nakao et al / Journal of the European Ceramic Sociery 25 (2005)3649-3655 3651 1500 中Pn Fig 3. Dimensions of the specimen and the three-point loading system used Fig. 5. Temperature dependence of the bending strength of the All fracture tests of the specimens crack-healed were per- crack-healed at 1300 C for 2h in air, with the room temperature formed on a three-point loading system with a span of 16 m rengths of the specimens as-received and as-cracked and the at 1200C, corresponding to the crack-healing temperature. without the pre-crack heat-treated at 1300C for 2 h in air so The cross-head speed in the monotonic test was 0.5 mm/min. cracks introduced during machining.(A )Crack-healed; ( )he (A)as-cracked; (O)as-received. 3. Result fractured with plastic deformation at 1300C. Thus, the lim iting temperature for the bending strength of alumina( w)was determined to be 1200oc In terms of basic knowledge, the crack-healing behavior of alumina(w)under no-stress 4, 5 is now reviewed below Fig 6 shows the relation between the applied stress during Fig. 4 shows the specimen surface crack-healed at 1300C the crack-healing treatment for the specimens as-cracked and for 2h. The pre-crack after crack-healing cannot be observed the bending strength at the crack-healing temperature of the in this figure. Fig. 5 shows the temperature dependence of the specimens crack-healed under static and cyclic stress.The bending strength of the specimens crack-healed at 1300oC ray colored and open triangle indicate the bending streng of the specimen crack-healed under static stress, Oap, S, and for 2 h in air, with the room temperature bending strengths of cyclic stress, ap, C, respectively, where the values of Oap, C the specimens as-received and as-cracked and the specimen without the pre-crack heat-treated at 1300 C for 2 h in air so are the maximum of each applied cyclic stress. The bend- as to heal cracks introduced during machining. The bendir ing strength of O MPa indicates the specimen fractured dur- ength of alumina(w) was reduced from 1000 to 500 MPa Ing crack-healing Alumina(w) with the pre-crack of 100 um vere never fractured during crack-healing treatment under by cracking, and then that was recovered to the same strength static stresses below 250 MPa, and the crack-healed specimen as the as-received specimen by crack-healing at 1300C for I h. It is, therefore, confirmed that crack-healing is complete had the same bending strength as the specimens crack-healed after holding the specimen at 1300C for I h. Moreover, the bending strength of the crack-healed specimen was slightly decreased by temperature increase from 400 to 1000C but decreased with increasing temperature above 1000C The specimens were fractured elastically below 1200C, and indentation 100200300400500 50um Fig. 6. Relation between the applied stress during the crack-healing treat- ment for the specimens as-cracked and the bending strength healing temperature of the specimens crack-healed under stat Fig 4. Surface shapes of the crack and indentation crack-healed at 1300C stress.(A)Crack-healed under static stress; (V) crack-heale for 2 h in air stress;(O)crack-healed under no stress
W. Nakao et al. / Journal of the European Ceramic Society 25 (2005) 3649–3655 3651 Fig. 3. Dimensions of the specimen and the three-point loading system used for this investigation. All fracture tests of the specimens crack-healed were performed on a three-point loading system with a span of 16 mm at 1200 ◦C, corresponding to the crack-healing temperature. The cross-head speed in the monotonic test was 0.5 mm/min. 3. Result In terms of basic knowledge, the crack-healing behavior of alumina(w) under no-stress14,15 is now reviewed below. Fig. 4 shows the specimen surface crack-healed at 1300 ◦C for 2 h. The pre-crack after crack-healing cannot be observed in this figure. Fig. 5 shows the temperature dependence of the bending strength of the specimens crack-healed at 1300 ◦C for 2 h in air, with the room temperature bending strengths of the specimens as-received and as-cracked and the specimen without the pre-crack heat-treated at 1300 ◦C for 2 h in air so as to heal cracks introduced during machining. The bending strength of alumina(w) was reduced from 1000 to 500 MPa by cracking, and then that was recovered to the same strength as the as-received specimen by crack-healing at 1300 ◦C for 1 h. It is, therefore, confirmed that crack-healing is complete after holding the specimen at 1300 ◦C for 1 h. Moreover, the bending strength of the crack-healed specimen was slightly decreased by temperature increase from 400 to 1000 ◦C, but decreased with increasing temperature above 1000 ◦C. The specimens were fractured elastically below 1200 ◦C, and Fig. 4. Surface shapes of the crack and indentation crack-healed at 1300 ◦C for 2 h in air. Fig. 5. Temperature dependence of the bending strength of the specimens crack-healed at 1300 ◦C for 2 h in air, with the room temperature bending strengths of the specimens as-received and as-cracked and the specimen without the pre-crack heat-treated at 1300 ◦C for 2 h in air so as to heal cracks introduced during machining. ( ) Crack-healed; ( ) heat-treated; () as-cracked; () as-received. fractured with plastic deformation at 1300 ◦C. Thus, the limiting temperature for the bending strength of alumina(w) was determined to be 1200 ◦C. Fig. 6 shows the relation between the applied stress during the crack-healing treatment for the specimens as-cracked and the bending strength at the crack-healing temperature of the specimens crack-healed under static and cyclic stress. The gray colored and open triangle indicate the bending strength of the specimen crack-healed under static stress, σap,S, and cyclic stress, σap,C, respectively, where the values of σap,C are the maximum of each applied cyclic stress. The bending strength of 0 MPa indicates the specimen fractured during crack-healing. Alumina(w) with the pre-crack of 100m were never fractured during crack-healing treatment under static stresses below 250 MPa, and the crack-healed specimen had the same bending strength as the specimens crack-healed Fig. 6. Relation between the applied stress during the crack-healing treatment for the specimens as-cracked and the bending strength at the crackhealing temperature of the specimens crack-healed under static and cyclic stress. ( ) Crack-healed under static stress; () crack-healed under cyclic stress; ( ) crack-healed under no stress.
3652 w Nakao et al. /Journal of the European Ceramic Sociery 25(2005)3649-3655 Critical Equivalent Crack Length gc<o 4005 Applied Stres Fig. 7. Relatio ment for the specimen annealed after pre-cracking and the bending strength Fig 8. Schematic diagram of the crack growth and healing behavior during at the crack-healing temperature of the specimens crack-healed under static the crack-healing under stress. ( Crack-healed under static stres stress(o) Crack-healed under static stress; (O)crack-healed under no stress. crack-healing under cyclic stress under no-stress at 1200C. Crack-heal ing under static stress the temperature that the crack-healing rate becomes non- of 300 MPa, a few cracked specimens were fractured dur- negligible compared with the crack growth rate. Moreover, ing the crack-healing treatment. All cracked specimens were the crack starts healing when the crack-healing rate becomes fractured during crack-healing under static stress of 350 MPa Pa. larger than the crack growth rate. The threshold stress im- Therefore, the threshold static stress during crack-healing poses an upper limit to the crack growth rate thereby limiting of alumina(w)having the pre-crack, o s, was found to be the crack length to less than the critical crack length before 250 MPa, where the threshold stress during crack-healing crack-healing starts. From a comparison with the values of defined as the upper stress limit not to fracture the specimen ap s and ap.C, it may be confirmed that the crack growth be- during crack-healing. Also, the threshold cyclic stress, o havior of alumina(w)is time dependent rather than cyclic de was found to be 300 MPa. The details of the reason for Oap, 5 p ndent. It is. therefore, concluded that applying static stress is the most fracturable condition for crack-healing behavior being smaller than oap.c are discussed in Section 4 under stress and that the threshold stresses of every cond Fig 7 shows the relation between the applied stress during tion during crack-healing of alumina(w), ofs, has been de- the crack-healing treatment for the specimen annealed after pre-cracking and the bending strength at the crack-healing termined to be 250 MPa. temperature of the specimens crack-healed under static stress From this figure, the threshold stress during crack-healing 4.2. Stress intensity factor of the stress limiting during was found to be 350 MPa crack-healing treatmen The stress intensity factor for the tip of the pre-crack dur 4. Discussion ing the crack-healing treatment, KHs, was estimated. Since a ensional residual stress was introduced during pre-cracking 4.1. Mechanism of crack growth and crack-healing by using the indentation method, it is necessary for the esti mation to consider the stress intensity factor of the residual Fig. 8 shows the schematic diagram of the crack stress, KR, as expressed by the following equation and healing behavior during the crack-healing under The solid lines indicate the equivalent crack length KHS Kap+ Kr (1) during the crack-healing under static stress. Also the dash lines indicate it under cyclic stress. The driving force for where Kap is evaluated by Newman-Raju equation 2 using crack growth, which is called the"crack driving force" by the stress applying during the crack-healing treatment,a Irwin, increases with increasing applied stress and crack Moreover, ceramics having small flow show non-linear frac length. Thus, the crack growth rate increased with increas- ture mechanics. Therefore, the residual stress was evaluated ng the time applied stress to the crack. On the other hand, by the following procedure the driving force for crack-healing, called for short"crack The stress intensity factor of the residual stress, KR, was healing force"7, 3I is not affected by the applied stress. The evaluated by subtracting the critical stress intensity factor of crack-healing rate increased simply with the temperature in- the specimen as cracked, KM, from the value of the specimen creasing Crack-healing starts preventing crack growth above cracked and annealed at 1300C for I h in Ar to remove the
3652 W. Nakao et al. / Journal of the European Ceramic Society 25 (2005) 3649–3655 Fig. 7. Relation between the applied stress during the crack-healing treatment for the specimen annealed after pre-cracking and the bending strength at the crack-healing temperature of the specimens crack-healed under static stress. ( ) Crack-healed under static stress; (♦) crack-healed under no stress. under no-stress at 1200 ◦C. Crack-healing under static stress of 300 MPa, a few cracked specimens were fractured during the crack-healing treatment. All cracked specimens were fractured during crack-healing under static stress of 350 MPa. Therefore, the threshold static stress during crack-healing of alumina(w) having the pre-crack, σC ap,S, was found to be 250 MPa, where the threshold stress during crack-healing is defined as the upper stress limit not to fracture the specimen during crack-healing. Also, the threshold cyclic stress, σC ap,S, was found to be 300 MPa. The details of the reason for σC ap,S being smaller than σC ap,C are discussed in Section 4. Fig. 7 shows the relation between the applied stress during the crack-healing treatment for the specimen annealed after pre-cracking and the bending strength at the crack-healing temperature of the specimens crack-healed under static stress. From this figure, the threshold stress during crack-healing was found to be 350 MPa. 4. Discussion 4.1. Mechanism of crack growth and crack-healing Fig. 8 shows the schematic diagram of the crack growth and healing behavior during the crack-healing under stress. The solid lines indicate the equivalent crack length change during the crack-healing under static stress. Also the dash lines indicate it under cyclic stress. The driving force for crack growth, which is called the “crack driving force” by Irwin,30 increases with increasing applied stress and crack length. Thus, the crack growth rate increased with increasing the time applied stress to the crack. On the other hand, the driving force for crack-healing, called for short “crackhealing force”17,31 is not affected by the applied stress. The crack-healing rate increased simply with the temperature increasing. Crack-healing starts preventing crack growth above Fig. 8. Schematic diagram of the crack growth and healing behavior during the crack-healing under stress. (—) Crack-healed under static stress; (- - -) crack-healing under cyclic stress. the temperature that the crack-healing rate becomes nonnegligible compared with the crack growth rate. Moreover, the crack starts healing when the crack-healing rate becomes larger than the crack growth rate. The threshold stress imposes an upper limit to the crack growth rate thereby limiting the crack length to less than the critical crack length before crack-healing starts. From a comparison with the values of σC ap,S and σC ap,C, it may be confirmed that the crack growth behavior of alumina(w) is time dependent rather than cyclic dependent. It is, therefore, concluded that applying static stress is the most fracturable condition for crack-healing behavior under stress and that the threshold stresses of every condition during crack-healing of alumina(w), σC HS, has been determined to be 250 MPa. 4.2. Stress intensity factor of the stress limiting during crack-healing treatment The stress intensity factor for the tip of the pre-crack during the crack-healing treatment, KHS, was estimated. Since a tensional residual stress was introduced during pre-cracking by using the indentation method, it is necessary for the estimation to consider the stress intensity factor of the residual stress, KR, as expressed by the following equation: KHS = Kap + KR (1) where Kap is evaluated by Newman–Raju equation32 using the stress applying during the crack-healing treatment, σap. Moreover, ceramics having small flow show non-linear fracture mechanics. Therefore, the residual stress was evaluated by the following procedure. The stress intensity factor of the residual stress, KR, was evaluated by subtracting the critical stress intensity factor of the specimen as cracked, KM, from the value of the specimen cracked and annealed at 1300 ◦C for 1 h in Ar to remove the
w. Nakao et al / Journal of the European Ceramic Sociery 25 (2005)3649-3655 3653 Do =0.236×2csec 2ao(0.236×2c KI =0.236×2cseM 2o0(0.236×2c Crack Length, 2c(um) Each data set of Kc and KM was subjected to the least square fitting by using Eq (6). Both curves are approximately Fig 9. Critical stress intensity factors, Kc and KM, as a function of surface constant at crack lengths above 103 um, and the values ofKic length of pre-crack, 2c, for the specimen as-cracked cracked and annealed after pre- and KIM, corresponding to the constant values in Fig9,were cracking. (A)As-cracked; (O)annealed after pre-cracking. determined to be 6.5 and 4.0 MPam", respectively. From the obtained values, the stress intensity factor of the tensional residual stress, kc: residual stress resulting from the introduction of a pre-crack KR=Kc-KM (2) of 2c=100 um was determined to be 1.6 MPat ned val KR, it is possible to In the previous study 5, the bending strength of the speci- calculate the value of KHs for the specimen as mens as-cracked and annealed after pre-cracking, OM and oc, Eq (1). On the other hand, KHS for the specimen annealed had been measured From the results, the critical stress inten- after pre-cracking was equal to Kap. Fig. 10 shows the sity factors, Kc and KM, were evaluated by the Newman-Raju relation between the KHs for the specimens as-cracked and equation. Fig 9 shows the kc and KM as a function of 2 annealed after pre-cracking and the bending strength at the where the gray colored diamond and open triangles indicate crack-healing temperature of the specimens crack-healed the values of Kc and KM, respectively. The difference be- under static stress. The gray colored triangle and the open tween Kc and KM indicates KR. The crack size dependence diamond indicate the results for the specimens as-cracked of KR can be obtained by determining the formula between and annealed after pre-cracking, respectively. The threshold rack size and KM or Kc. One of the present authors33-35 stress intensity factors during crack-healing, KHS, have has proposed non-linear fracture mechanics for engineering been determined to be 3.8 and 3.2 MPam for the speci ceramics by using process zone size, as shown in Eq (3) mens crack-healed without annealing and with annealing espectively. From a comparison with the values of the threshold stress intensity factor during crack-healing, the (3) residual stress is evaluated slightly larger than the intrinsic Dc KIM\= 会 where Dc is size limit of the process zone and oo is the stress forming the process zone, corresponding to the fracture ength of the plain specimen. The equivalent crack length, ◇ evaluated from the stress intensity factor by using the Newman-Raju equation. Assuming alc=0.9, a/H<I and c/B<l, the relation between surface length of the pre-crack and ae was expressed by ae=0.236(2c) Moreover, the critical stress intensity factors, Kc and K were obtained from Eq (5)using oC, OM and a 1/2 /2 acking and the bending strength at the crack-healing tem- Introducing Eqs. (4)and(5)to Eq (3), the stress intensity oecimens crack-healed under static stress. (A)As-cracked factors of the fracture conditions, kc or KM, related with the ()annealed after pre-cracking
W. Nakao et al. / Journal of the European Ceramic Society 25 (2005) 3649–3655 3653 Fig. 9. Critical stress intensity factors, KC and KM, as a function of surface length of pre-crack, 2c, for the specimen as-cracked and annealed after precracking. () As-cracked; ( ) annealed after pre-cracking. residual stress, KC: KR = KC − KM (2) In the previous study15, the bending strength of the specimens as-cracked and annealed after pre-cracking, σM and σC, had been measured. From the results, the critical stress intensity factors,KC andKM, were evaluated by the Newman–Raju equation. Fig. 9 shows the KC and KM as a function of 2c, where the gray colored diamond and open triangles indicate the values of KC and KM, respectively. The difference between KC and KM indicates KR. The crack size dependence of KR can be obtained by determining the formula between crack size and KM or KC. One of the present authors33–35 has proposed non-linear fracture mechanics for engineering ceramics by using process zone size, as shown in Eq. (3): DC = π 8 KIC σo 2 = ae sec πσC 2σo − 1 DC = π 8 KIM σo 2 = ae sec πσM 2σo − 1 (3) where DC is size limit of the process zone and σo is the stress forming the process zone, corresponding to the fracture strength of the plain specimen. The equivalent crack length, ae, was evaluated from the stress intensity factor by using the Newman–Raju equation. Assuming a/c = 0.9, a/H 1 and c/B 1, the relation between surface length of the pre-crack and ae was expressed by: ae = 0.236 (2c) (4) Moreover, the critical stress intensity factors, KC and KM, were obtained from Eq. (5) using σC, σM and ae: KC = σC(πae) 1/2, KM = σM(πae) 1/2 (5) Introducing Eqs. (4) and (5) to Eq. (3), the stress intensity factors of the fracture conditions, KC or KM, related with the equivalent crack length, 2c, according Eq. (6): DC = π 8 KIC σo 2 = 0.236 × 2c sec KC 2σo π 0.236 × 2c 1/2 − 1 DC = π 8 KIM σo 2 = 0.236 × 2c sec KM 2σo π 0.236 × 2c 1/2 − 1 (6) Each data set of KC and KM was subjected to the least square fitting by using Eq. (6). Both curves are approximately constant at crack lengths above 103 m, and the values of KIC and KIM, corresponding to the constant values in Fig. 9, were determined to be 6.5 and 4.0 MPa m1/2, respectively. From the obtained values, the stress intensity factor of the tensional residual stress resulting from the introduction of a pre-crack of 2c = 100m was determined to be 1.6 MPa m1/2. By adding the obtained value of KR, it is possible to calculate the value of KHS for the specimen as-cracked from Eq. (1). On the other hand, KHS for the specimen annealed after pre-cracking was equal to Kap. Fig. 10 shows the relation between the KHS for the specimens as-cracked and annealed after pre-cracking and the bending strength at the crack-healing temperature of the specimens crack-healed under static stress. The gray colored triangle and the open diamond indicate the results for the specimens as-cracked and annealed after pre-cracking, respectively. The threshold stress intensity factors during crack-healing, KC HS, have been determined to be 3.8 and 3.2 MPa m1/2 for the specimens crack-healed without annealing and with annealing, respectively. From a comparison with the values of the threshold stress intensity factor during crack-healing, the residual stress is evaluated slightly larger than the intrinsic Fig. 10. Relation between the KHS for the specimens as-cracked and annealed after pre-cracking and the bending strength at the crack-healing temperature of the specimens crack-healed under static stress. ( ) As-cracked; (♦) annealed after pre-cracking.
3654 w. Nakao et al. / Journal of the European Ceramic Society 25(2005)3649-3655 value. Therefore, the threshold stress intensity factor during and alumina-SiC composite. Br. Ceram. Trans., 1996, 95, 23- crack-healing of alumina(w) is selected as 3.2 MPam.It is, however, confirmed that both values did not differ greatly 8. Gupta, T. K, Crack healing and strengthening of thermally shocked although the applied stress changes by 50 MPa alumina. Am. Ceram. Soc.1976. 59. 259-262 9. Mitomo, M, Nishihara, T. and Tsutsumi, M., Crack healing in sil- nitride and alumina ceramics. Mater 1976-1978. 5. Conclusion A. J. Oxidation behaviour and effects of SiC- whisk Alumina reinforced by SiC whisker, alumina( w) was de Mater Sci.. 1994 veloped with the objective of improving fracture toughness 11. Chou,L.A,Chan, H Harmer, M. P, Effect of annealing and crack-healing ability. The composites were crack-healed environment on the cr ing and mechanical behavior of sill- nanocomposites. J.Am. Cera. Soc. at 1200C for & h in air under elevated static and cyclic 1998.81.1203-1208 tresses and the bending strength at 1200C of the crack 12. Deng, Z.Y., Shi, J. L, Zhang, Y. F, Lai, T.R. and Guo, J. K, Creep healed composites were then investigated. Alumina( w)with de- particle-reinforced alu- he pre-crack of 100 um were never fractured during crack- mina.J.Am.Cerm.Soc,1999,82,944-952. healing treatment under static stresses below 250 MPa, and 13. Ando, K, Kim, B. S, Kodama, S, Ryu, S. H, Takahash Saito, S, Fatigue strength of an Al2 O3/SiC composite al the crack-healed specimen had the same bending strength lithic Al2O3 subjected to crack-healing treatment. Soc as the specimens crack-healed under no-stress at 1200oC. Jpm,2003.52,1464-1470. Therefore. the threshold static stress during crack-healing of 14. Takahashi, K Yokouchi, M, Lee, S K and Ando, K, Crack-healing alumina(w) was found to be 250 MPa. Also, the threshold behavior of Al2O toughened by SiC whiskers. J. Am. Ceram. Soc. cyclic stress was found to be 300 MPa. Considering that the 2003,86,2143-2147 15. Ando. K. Yokouchi. M.. Lee. S. K. Takahashi. K. Nakao. W. and crack growth is time-dependent, the threshold stress of ev- Suenaga, H, Crack-healing behavior, high temperature strength and ery condition during crack-healing of alumina( w) has been fracture toughness of alumina reinforced by SiC whiskers. J. Soc. concluded to be 250 MPa. Moreover, the same experiment at.sc.lpn,2004,53,599606. is conducted on specimens annealed at 1300C for I h in 16. Ando, K, Tuji, K, Furusawa, K,Hanagata, T, Chu, M.Cand Ar after pre-cracking. Thus, the threshold static stress dur- Sato, S, Effect of pre-crack size and testing temperature on fracture trength properties of crack healed mullite. J. Soc. Mat. Sci. Jpn. ing crack-healing of alumina( w)annealed after pre-cracking 2001,50,920-925 has been determined to be 350 MPa. From the results the 17. Ando, K, Furusawa, K, Chu, M. C, Hanagata, T, Tuji, K. and 38232MmAm小吧 ato, S, Crack healing behavior under stress of mullite/silicon carbide 84.2073-2078 healed without annealing and with annealing, respectively. A 18. Ando, K, Chu, M. C, Tuji, K, Hirasawa, T, Kobayashi, Y. and comparison with the values of the threshold stress intensity ato,S, Crack healing behaviour and high-temperature strength factor during crack-healing shows that the residual stress is of mullite/SiC composite ceramics. J. Eur. Ceram. Soc., 2002, 22, slightly larger than the intrinsic value. Therefore, the thresh 1313-1319 old stress intensity factor during crack-healing of alumina( w) 19. Ando, K, TsuL, K, Nakatani, M, Chu, M. C, Sato, S and is selected as 3. 2 MPam/2 of structural mullite. J. Soc. Mat. Sci. Jpn., 2002, 51, 458-464 20. Ono, M., Ishida, W, Nakao, W, Ando, K, Mori, S. and Yokouchi References toughness of mullite/SiC whisker composite ceramic. J. Soc. Mat. Sci. Jpn., in press. 1. Kim, B. S, Ando, K, Chu, M. C. and Saito, S, Crack-healing be- 21. Ando, K, Ikeda, T, Sato, S, Yao, F and Kobayashi, Y, A preliminary havior of monolithic alumina and strength of crack-healed member study on crack healing behavior of Si3Na/SiC composite ceramics. JSoe.Mat.Sc.Jpn,2003,52,667-673 atigue Fract. Eng. Mater: Struct, 1998, 21, 119-122 2. Chu, M. C, Sato, S, Kobayashi, Y. and Ando, K, Damage heal- 22. Chu, M. C, Ando, K, Sato, S, Hirasawa, T. and Kobayashi, Y. ing and strengthealing behavior in intelligent mullite/SiC cerar Crack-healing behavior of silicon nitride ceramics(effect of chemical atigue Fract. Eng. Mater: Struct, 1995, 18, 1019-1029 composition on crack healing ability ) High Pressure Inst. Jpn., 1998. 3. Niihara, K. and Nakahira, A, Strengthening of oxide ceramics by 36,82-89 SiC and Si3N4 dispersions. In Proceedings of the Third International 23. Ando, K, Chu, M. C, Kobayashi, Y, Yao, F and Sato, S, The study Symposium on Ceramic Materials and Components for Engines, 1988 on crack healing behavior of silicon nitrid cs.Jpn. Soc. Mech. pp.919926 Eng,1998,64A,1936-194 4. Nihara, K, New design concept of structural ceramics-ceramics 24. Ando, K, Chu, M. C, Kobayashi, Y, Yao, F. and Sato, S, Crack nanocomposite. J. Ceram. Soc. pn, 1991, 99,974 aling behavior and high temperature strength of silicon nitride ce- 5. Ohji, T, Nakahara, A, Hirano, T. and Niihara, K, Tensile creep amics.Jpn. Soc. Mech. Eng, 1999, 65 A, 1132-1139 behavior of alumina/silicon carbide nanocomposite. J. Am. Ceram. 25. Yao, F, Ando, K, Chu, M. C. and Sato, S, Static cyclic fatigue Soc.1994.77,32593562 behaviour of crack-healed Si3N4/SiC composite ceramics. J. Eur: Ce- 6. Jeong, Y. K, Nakahira, A. and Niihara, K, Effects of additives on rm.SoC.,2001,21,991-997 microstructure and properties of alumina-silicon carbide 6. Ando, K, Houjou, K, Chu, M. C S. Takahashi sites.J.Am. Ceran.Soc.,1999,82,3609-3612. Sakamoto. S. et al. Crack-healing bel Si3 Ng/SiC ceram- 7. Moffatt, J. E, Plumbridge, w. J. and Hermann, R, High tem- ics under stress and fatigue strength perature crack annealing effect on fracture toughness of alumina (1000°C).J. Eur Ceram.Soc.,2002,22,139-1346
3654 W. Nakao et al. / Journal of the European Ceramic Society 25 (2005) 3649–3655 value. Therefore, the threshold stress intensity factor during crack-healing of alumina(w) is selected as 3.2 MPa m1/2. It is, however, confirmed that both values did not differ greatly although the applied stress changes by 50 MPa. 5. Conclusion Alumina reinforced by SiC whisker, alumina(w) was developed with the objective of improving fracture toughness and crack-healing ability. The composites were crack-healed at 1200 ◦C for 8 h in air under elevated static and cyclic stresses and the bending strength at 1200 ◦C of the crackhealed composites were then investigated. Alumina(w) with the pre-crack of 100 m were never fractured during crackhealing treatment under static stresses below 250 MPa, and the crack-healed specimen had the same bending strength as the specimens crack-healed under no-stress at 1200 ◦C. Therefore, the threshold static stress during crack-healing of alumina(w) was found to be 250 MPa. Also, the threshold cyclic stress was found to be 300 MPa. Considering that the crack growth is time-dependent, the threshold stress of every condition during crack-healing of alumina(w) has been concluded to be 250 MPa. Moreover, the same experiment is conducted on specimens annealed at 1300 ◦C for 1 h in Ar after pre-cracking. Thus, the threshold static stress during crack-healing of alumina(w) annealed after pre-cracking has been determined to be 350 MPa. From the results, the threshold stress intensity factor during crack-healing has been evaluated as 3.8 and 3.2 MPa m1/2 for the specimens crackhealed without annealing and with annealing, respectively. A comparison with the values of the threshold stress intensity factor during crack-healing shows that the residual stress is slightly larger than the intrinsic value. 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