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The wear behaviour of Al2O3-SiC ceramic nanocomposites
Scripta mater. 42 (2000) 555–560 www.elsevier.com/locate/scriptamat
THE WEAR BEHAVIOUR OF Al2O3-SiC CERAMIC NANOCOMPOSITES H. J. Chen, W. M. Rainforth and W. E. Lee Department of Engineering Materials, The University of Sheffield, Mappin St., Sheffield, S1 3JD UK (Received July 14, 1999) (Accepted in revised form November 18, 1999) Keywords: Ceramic nanocomposites; Wear
Introduction Since the initial work of Niihara [1], the superior properties of ceramic nanocomposites have been extensively investigated (the term nanocomposite is also now used to describe ceramics with grain sizes of a few m). For alumina based nanocomposites, mechanical strengths in excess of 1GPa have been achieved, in combination with high fracture toughness (4.8MPam0.5) and hardness (17.5–20GPa). Recent work has also indicated that the erosive wear resistance of nanocomposites is superior to the corresponding monolith [2,3]. It is well recognised that alumina ceramics suffer a time dependant transition from mild to severe wear, with the time to the transition principally dependent on the grain size of the material [4 – 6]. The abrupt transition to severe wear is associated with the onset of grain boundary fracture. Modelling this transition [4,5] has demonstrated that the grain size effect can be predicted by considering the combined effects of the contact stresses and the pre-existing thermal mismatch stresses. Barceinas & Rainforth [6] have demonstrated that, during the pre-transition period, dislocation pile-ups at the grain boundary result in intergranular crack initiation, which ultimately leads to general intergranular fracture and a catastrophic increase in wear rate. Increasing the grain size increases slip length and therefore the dislocation density in the pile-ups responsible for initiating intergranular fracture. Existing wear studies of ceramic nanocomposites [2,3] have not examined the wear behaviour in relation to this transition, rather they have compared the wear of the composite with the post-transition behaviour of the monolith. Ceramic nanocomposites should provide two significant differences in behaviour compared with the monolith for the same grain size. Firstly, the modification of inherent grain boundary strength could remove the catastrophic nature of surface damage associated with intergranular fracture that is responsible for the transition. Secondly, the change in dislocation density and residual stress-state in the composite compared with the monolith could alter the time dependant nature of the damage accumulation process. This paper compares the sliding wear behaviour of alumina-SiC nanocomposites with additions up to 15vol%SiC, with the alumina monolith. Two alumina monoliths are compared, one with a coarser grain size than the composites, and one with a similar grain size to the composites, both of which are known to give transitions in wear rate under the sliding conditions used here. 1359-6462/00/$–see front matter. © 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(99)00403-0
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Figure 1. Grain size as a function of SiC addition. Hot pressed ⽧1600°C 2h, f hot pressed 1600°C, 1h.
Experimental Nanocomposites containing 2.5, 5, 10, 15 volume % SiC were manufactured from Alcan Chemicals Ltd (UK) 99.5% Al2O3 and Ibiden Co. (Japan) -SiC. The powders were dispersed in distilled water containing 0.2wt% Dispex A40 dispersant (Allied Colloids) and ball milled using high purity alumina balls for 24h. The slip was cast into a mould, dried and sintered at 1200°C for 2h in argon. Discs were hot pressed in a graphite die at 1600°C for 2h at a pressure of 25MPa followed by annealing at 1300°C for 2h in argon. This yielded monolithic ceramics with a density ⬎99.5% theoretical and composites with ⬎97% theoretical. An additional monolithic alumina sample was fabricated under identical conditions but only hot pressed for 1h (i.e. hot pressed 1h at 1600°C, 25MPa, followed by annealing at 1300°C for 2h in argon), to yield a ceramic with a similar grain size to that of the composites. The density of this monolith was, within experimental error, the same as the monolith hot pressed for 2h at 1600°C. Fracture toughness testing was undertaken by indentation using the method of Anstis et al. [7]. Three point bending was used to determine the flexural strength (modulus of rupture, MOR) using carefully polished rectangular samples 40mm long by 3mm square cross-section. Grain size measurements were taken from thermally etched surfaces examined in the SEM (Jeol 6400). A SchwartzSaltykoff analysis was used to determine grain size distributions from in excess of 100 grains in each case. The SiC distribution was determined from both SEM images and TEM (Jeol 200CX). Wear testing of selected compositions was undertaken on a tri-pin-on-disc machine (see ref. [6]) at a speed of 0.24m/s and a load of 20N/pin against a zirconia toughened alumina disc counterface for a total distance of 100km. The Lancaster wear coefficient (wear volume (mm3) normalised by the distance slid (m) and the load (N)) was determined by weight loss (accuracy ⫾2 ⫻ 10⫺5 g). Results & Discussion Fig. 1 gives the grain size as a function of SiC addition, for the same hot pressing conditions of 2h at 1600°C, with the additional data point for the monolith hot pressed for 1h at 1600°C. As with previous studies [e.g. 8], small additions of SiC gave a substantial reduction in grain size compared with the monolith for identical processing conditions. While the grain size measurements in Fig. 1 indicate the average grain size, they do not indicate the grain size distribution. The monolith hot pressed for 2h at 1600°C exhibited a bimodal grain size distribution with a small fraction (⬃13%) 20 –30m in size. The
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Figure 2. a) Fracture toughness and b) Modulus of rupture as a function of SiC addition for samples hot pressed at 1600°C for 2h.
addition of SiC greatly reduced the size and proportion of grains of the coarser distribution. For example, the 2.5vol% SiC composite addition contained 3% of grains in the size range 8 –13m, while the 5 and 10vol%SiC composites contained only ⬃1% of grains with a grain size ⬎⬃8m. SEM suggested that the coarser grains contained a lower fraction of SiC than the finer grains. TEM indicated that the composites could be placed in the inter/intra-granular type on the basis of the SiC distribution (as defined by Niihara [1]). The fracture toughness and strength values for the ceramics hot pressed for 2h at 1600°C are given in Fig. 2, and the hardness in Fig. 3. The strength and toughness broadly followed the same trend as the grain size, with a substantial increase in both properties for a 2.5vol% SiC addition, but smaller changes for further SiC additions. Fracture of the monolith was almost entirely intergranular, while that of the composites was predominantly transgranular. Fig. 4 gives the wear coefficient as a function of SiC addition for selected compositions, including both monoliths (average grain size of 4.5m and 9.3m, both quoted as average wear rate from entire test, therefore including post transition behaviour, see later). The addition of SiC resulted in a substantial reduction in wear coefficient compared with the monolith, irrespective of grain size of the monolith. The extent of the effect is made more obvious by considering the distance slid to the same wear volume. Taking the 15vol%SiC composite as an example, the same wear volume was achieved after 20km sliding for the monolith and 283km for the composite, over an order of magnitude improvement in wear resistance. After a short initial smooth running period that lasted only a few km, the monolith with ⬃9.3m average grain size exhibited an abrupt transition in behaviour, associated with high vibration and noise levels produced from the sliding couple. The transition was associated with surface intergranular fracture, Fig. 5, although much of the surface was obscured by a thick layer of compacted wear debris.
Figure 3. Vickers hardness as a function of SiC addition for samples hot pressed at 1600°C for 2h.
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Figure 4. Wear coefficient as a function of SiC addition. ⽧and f correspond to the grain sizes given in Fig. 1.
The finer grain sized monolith exhibited smooth sliding (‘mild wear’) for a greater distance (⬃60km) prior to the transition to intergranular fracture. The wear coefficient in the mild wear regime was 1 ⫻ 10⫺7mm3/Nm. In contrast, the 5 and 15vol% alumina composites exhibited smooth running throughout the test, resulting in optically reflective worn surfaces. SEM examination indicated that the worn surface of the 5vol% SiC composite contained a significant proportion of transgranular fracture, Fig. 6. The remaining surface regions were microscopically smooth. The worn surface of the 15vol%SiC composite was dominated by smooth, generally featureless regions, but with local fine scale pitting, Fig. 7. For approximately equal grain size of 4.0 – 4.5m, the monolith exhibited a marked transition to catastrophic wear associated with intergranular fracture, while there was no transition for the composite. Both monolithic aluminas exhibited this transition in wear rate, the grain size difference resulting in different times to the transition. Prior to the transition, the worn surface of the monolith was largely featureless, i.e. there was virtually no evidence of fracture. The wear rate in this regime was 1 ⫻ 10⫺7mm3/Nm, i.e. lower than that of either composite. The transition to catastrophic wear was abrupt and resulted in an increase in wear rate of just under 2 orders of magnitude. The behaviour of the composites was quite different. No transition in wear rate was observed. Rather, surface fracture (5vol% addition) and pitting (15vol% addition) occurred early on in the test, but did not increase in intensity during the test (rather, the wear rate steadily decreased during the test suggesting that the extent decreased with time). The comparison of wear behaviour between monolith and composite is therefore difficult. The pre-transition wear of the monolith contained no fracture (and gave the lowest wear rates), while the
Figure 5. Secondary electron image of the worn monolith (hot pressed 1600°C, 2h), showing compacted wear debris covering a surface of intergranular fracture.
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Figure 6. Backscattered electron image of the worn surface of the 5%vol SiC composite, showing smooth regions (left) and transgranular surface (centre).
composite exhibited some degree of surface fracture/pitting throughout the test. Nevertheless, fracture in the composite was stable while that in the monolith was catastrophic. This probably reflects the improved grain boundary strength of the composite, a factor noted by several workers examining the macroscopic fracture behaviour [e.g. 9]. The thermal mismatch between SiC (4.1– 4.5 ⫻ 10⫺6 K⫺1) and Al2O3 (⬃8.1 ⫻ 10⫺6 K⫺1) results in significant tensile residual stresses in the matrix, ranging from 80MPa for a 4% SiC addition to 680MPa for a 35% SiC addition [9]. These stresses are fundamental to the enhancement of properties of the composite compared with the monolith [9]. However, residual stresses are particularly important in wear because of the lack of constraint at a free surface, and the residual stress will be additive with the tensile stresses imposed by the contacting asperity. The pitting in the 15vol%SiC composite occurred on a scale similar to that of the SiC clusters observed in the TEM (although there was no evidence that individual SiC particles were being removed). This suggests that the pitting was a result of the tensile stresses in the matrix close to SiC particles, which would be particularly significant where the SiC was clustered. As with mechanical strength, improved wear resistance would therefore be expected from improved SiC distribution. The lower wear rate for the pre-transition monolithic aluminas than the 15vol%SiC composite implies that, in the absence of fracture, the SiC addition does not provide an improvement in wear rate,
Figure 7. Backscattered electron image of the worn surface of the 15%vol SiC composite, showing a predominantly smooth surface with localized pitting.
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rather, the greater local residual tensile stresses in the composite may increase wear rate compared with the monolith. All published studies that compare the monolith with the composite have made the comparison with fracture dominated wear in monolithic alumina [e.g. 2,3]. While the removal of a catastrophic transition in wear rate is a major benefit provided by the composite, the greater wear rate in the ‘mild regime’, where the majority of aluminas operate in industrial applications, must be considered a significant disadvantage. Conclusions 1. For a similar grain size, the addition of SiC to alumina to form an inter/intra-granular composite resulted in a substantial reduction in sliding wear rate. 2. The monolithic alumina suffered a transition from ‘mild wear’ to catastrophic intergranular wear after a sliding distance determined by the grain size. 3. The composites did not exhibit any transition behaviour, but exhibited surface transgranular fracture (5vol%SiC) and pitting (15vol%SiC) throughout the test. The pitting was believed to result from local tensile stresses in the matrix arising from thermal mismatch between SiC and Al2O3. 4. The wear rate of the monolithic alumina in the ‘mild wear’ regime was lower than that of the composite materials. References 1. 2. 3. 4. 5. 6. 7. 8. 9.
K. Niihara, J. Ceram. Soc. Jpn. 99, 974 (1991). R. W. Davidge, R. J. Brook, F. Cambier, M. Poorteman, A. Leriche, D. O’Sullivan, S. Hampshire, and T. Kennedy, Br. Ceram. Trans. 96, 121 (1997). R. W. Davidge, P. C. Twigg, and F. L. Riley, J. Eur. Ceram. Soc. 16, 799 (1996). S. J .Cho, B. J. Hockey, B. R. Lawn, and S. J. Bennison, J. Am. Cream. Soc. 72, 1249 (1989). H. Liu and M. E. Fine, J. Am. Ceram. Soc. 76, 2393 (1993). O. Barceinas-Sa´nchez and W. M. Rainforth, Acta Mater. 46, 6475 (1998). G. R. Anstis, P. Chantikul, B. Lawn, and D. B. Marshall, J. Am. Ceram. Soc. 64, 533 (1981). J. Zhao, L. C. Stearns, M. P. Harmer, H. M. Chan, G. A. Miller, and R. E. Cook, J. Am. Ceram. Soc. 76, 503 (1993). R. I. Todd, M. A. M. Bourke, C. E. Borsa, and R. J. Brook, Acta Mater. 45, 1791 (1997).
THE WEAR BEHAVIOUR OF Al2O3-SiC CERAMIC NANOCOMPOSITES H. J. Chen, W. M. Rainforth and W. E. Lee Department of Engineering Materials, The University of Sheffield, Mappin St., Sheffield, S1 3JD UK (Received July 14, 1999) (Accepted in revised form November 18, 1999) Keywords: Ceramic nanocomposites; Wear
Introduction Since the initial work of Niihara [1], the superior properties of ceramic nanocomposites have been extensively investigated (the term nanocomposite is also now used to describe ceramics with grain sizes of a few m). For alumina based nanocomposites, mechanical strengths in excess of 1GPa have been achieved, in combination with high fracture toughness (4.8MPam0.5) and hardness (17.5–20GPa). Recent work has also indicated that the erosive wear resistance of nanocomposites is superior to the corresponding monolith [2,3]. It is well recognised that alumina ceramics suffer a time dependant transition from mild to severe wear, with the time to the transition principally dependent on the grain size of the material [4 – 6]. The abrupt transition to severe wear is associated with the onset of grain boundary fracture. Modelling this transition [4,5] has demonstrated that the grain size effect can be predicted by considering the combined effects of the contact stresses and the pre-existing thermal mismatch stresses. Barceinas & Rainforth [6] have demonstrated that, during the pre-transition period, dislocation pile-ups at the grain boundary result in intergranular crack initiation, which ultimately leads to general intergranular fracture and a catastrophic increase in wear rate. Increasing the grain size increases slip length and therefore the dislocation density in the pile-ups responsible for initiating intergranular fracture. Existing wear studies of ceramic nanocomposites [2,3] have not examined the wear behaviour in relation to this transition, rather they have compared the wear of the composite with the post-transition behaviour of the monolith. Ceramic nanocomposites should provide two significant differences in behaviour compared with the monolith for the same grain size. Firstly, the modification of inherent grain boundary strength could remove the catastrophic nature of surface damage associated with intergranular fracture that is responsible for the transition. Secondly, the change in dislocation density and residual stress-state in the composite compared with the monolith could alter the time dependant nature of the damage accumulation process. This paper compares the sliding wear behaviour of alumina-SiC nanocomposites with additions up to 15vol%SiC, with the alumina monolith. Two alumina monoliths are compared, one with a coarser grain size than the composites, and one with a similar grain size to the composites, both of which are known to give transitions in wear rate under the sliding conditions used here. 1359-6462/00/$–see front matter. © 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(99)00403-0
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Figure 1. Grain size as a function of SiC addition. Hot pressed ⽧1600°C 2h, f hot pressed 1600°C, 1h.
Experimental Nanocomposites containing 2.5, 5, 10, 15 volume % SiC were manufactured from Alcan Chemicals Ltd (UK) 99.5% Al2O3 and Ibiden Co. (Japan) -SiC. The powders were dispersed in distilled water containing 0.2wt% Dispex A40 dispersant (Allied Colloids) and ball milled using high purity alumina balls for 24h. The slip was cast into a mould, dried and sintered at 1200°C for 2h in argon. Discs were hot pressed in a graphite die at 1600°C for 2h at a pressure of 25MPa followed by annealing at 1300°C for 2h in argon. This yielded monolithic ceramics with a density ⬎99.5% theoretical and composites with ⬎97% theoretical. An additional monolithic alumina sample was fabricated under identical conditions but only hot pressed for 1h (i.e. hot pressed 1h at 1600°C, 25MPa, followed by annealing at 1300°C for 2h in argon), to yield a ceramic with a similar grain size to that of the composites. The density of this monolith was, within experimental error, the same as the monolith hot pressed for 2h at 1600°C. Fracture toughness testing was undertaken by indentation using the method of Anstis et al. [7]. Three point bending was used to determine the flexural strength (modulus of rupture, MOR) using carefully polished rectangular samples 40mm long by 3mm square cross-section. Grain size measurements were taken from thermally etched surfaces examined in the SEM (Jeol 6400). A SchwartzSaltykoff analysis was used to determine grain size distributions from in excess of 100 grains in each case. The SiC distribution was determined from both SEM images and TEM (Jeol 200CX). Wear testing of selected compositions was undertaken on a tri-pin-on-disc machine (see ref. [6]) at a speed of 0.24m/s and a load of 20N/pin against a zirconia toughened alumina disc counterface for a total distance of 100km. The Lancaster wear coefficient (wear volume (mm3) normalised by the distance slid (m) and the load (N)) was determined by weight loss (accuracy ⫾2 ⫻ 10⫺5 g). Results & Discussion Fig. 1 gives the grain size as a function of SiC addition, for the same hot pressing conditions of 2h at 1600°C, with the additional data point for the monolith hot pressed for 1h at 1600°C. As with previous studies [e.g. 8], small additions of SiC gave a substantial reduction in grain size compared with the monolith for identical processing conditions. While the grain size measurements in Fig. 1 indicate the average grain size, they do not indicate the grain size distribution. The monolith hot pressed for 2h at 1600°C exhibited a bimodal grain size distribution with a small fraction (⬃13%) 20 –30m in size. The
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Figure 2. a) Fracture toughness and b) Modulus of rupture as a function of SiC addition for samples hot pressed at 1600°C for 2h.
addition of SiC greatly reduced the size and proportion of grains of the coarser distribution. For example, the 2.5vol% SiC composite addition contained 3% of grains in the size range 8 –13m, while the 5 and 10vol%SiC composites contained only ⬃1% of grains with a grain size ⬎⬃8m. SEM suggested that the coarser grains contained a lower fraction of SiC than the finer grains. TEM indicated that the composites could be placed in the inter/intra-granular type on the basis of the SiC distribution (as defined by Niihara [1]). The fracture toughness and strength values for the ceramics hot pressed for 2h at 1600°C are given in Fig. 2, and the hardness in Fig. 3. The strength and toughness broadly followed the same trend as the grain size, with a substantial increase in both properties for a 2.5vol% SiC addition, but smaller changes for further SiC additions. Fracture of the monolith was almost entirely intergranular, while that of the composites was predominantly transgranular. Fig. 4 gives the wear coefficient as a function of SiC addition for selected compositions, including both monoliths (average grain size of 4.5m and 9.3m, both quoted as average wear rate from entire test, therefore including post transition behaviour, see later). The addition of SiC resulted in a substantial reduction in wear coefficient compared with the monolith, irrespective of grain size of the monolith. The extent of the effect is made more obvious by considering the distance slid to the same wear volume. Taking the 15vol%SiC composite as an example, the same wear volume was achieved after 20km sliding for the monolith and 283km for the composite, over an order of magnitude improvement in wear resistance. After a short initial smooth running period that lasted only a few km, the monolith with ⬃9.3m average grain size exhibited an abrupt transition in behaviour, associated with high vibration and noise levels produced from the sliding couple. The transition was associated with surface intergranular fracture, Fig. 5, although much of the surface was obscured by a thick layer of compacted wear debris.
Figure 3. Vickers hardness as a function of SiC addition for samples hot pressed at 1600°C for 2h.
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Figure 4. Wear coefficient as a function of SiC addition. ⽧and f correspond to the grain sizes given in Fig. 1.
The finer grain sized monolith exhibited smooth sliding (‘mild wear’) for a greater distance (⬃60km) prior to the transition to intergranular fracture. The wear coefficient in the mild wear regime was 1 ⫻ 10⫺7mm3/Nm. In contrast, the 5 and 15vol% alumina composites exhibited smooth running throughout the test, resulting in optically reflective worn surfaces. SEM examination indicated that the worn surface of the 5vol% SiC composite contained a significant proportion of transgranular fracture, Fig. 6. The remaining surface regions were microscopically smooth. The worn surface of the 15vol%SiC composite was dominated by smooth, generally featureless regions, but with local fine scale pitting, Fig. 7. For approximately equal grain size of 4.0 – 4.5m, the monolith exhibited a marked transition to catastrophic wear associated with intergranular fracture, while there was no transition for the composite. Both monolithic aluminas exhibited this transition in wear rate, the grain size difference resulting in different times to the transition. Prior to the transition, the worn surface of the monolith was largely featureless, i.e. there was virtually no evidence of fracture. The wear rate in this regime was 1 ⫻ 10⫺7mm3/Nm, i.e. lower than that of either composite. The transition to catastrophic wear was abrupt and resulted in an increase in wear rate of just under 2 orders of magnitude. The behaviour of the composites was quite different. No transition in wear rate was observed. Rather, surface fracture (5vol% addition) and pitting (15vol% addition) occurred early on in the test, but did not increase in intensity during the test (rather, the wear rate steadily decreased during the test suggesting that the extent decreased with time). The comparison of wear behaviour between monolith and composite is therefore difficult. The pre-transition wear of the monolith contained no fracture (and gave the lowest wear rates), while the
Figure 5. Secondary electron image of the worn monolith (hot pressed 1600°C, 2h), showing compacted wear debris covering a surface of intergranular fracture.
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Figure 6. Backscattered electron image of the worn surface of the 5%vol SiC composite, showing smooth regions (left) and transgranular surface (centre).
composite exhibited some degree of surface fracture/pitting throughout the test. Nevertheless, fracture in the composite was stable while that in the monolith was catastrophic. This probably reflects the improved grain boundary strength of the composite, a factor noted by several workers examining the macroscopic fracture behaviour [e.g. 9]. The thermal mismatch between SiC (4.1– 4.5 ⫻ 10⫺6 K⫺1) and Al2O3 (⬃8.1 ⫻ 10⫺6 K⫺1) results in significant tensile residual stresses in the matrix, ranging from 80MPa for a 4% SiC addition to 680MPa for a 35% SiC addition [9]. These stresses are fundamental to the enhancement of properties of the composite compared with the monolith [9]. However, residual stresses are particularly important in wear because of the lack of constraint at a free surface, and the residual stress will be additive with the tensile stresses imposed by the contacting asperity. The pitting in the 15vol%SiC composite occurred on a scale similar to that of the SiC clusters observed in the TEM (although there was no evidence that individual SiC particles were being removed). This suggests that the pitting was a result of the tensile stresses in the matrix close to SiC particles, which would be particularly significant where the SiC was clustered. As with mechanical strength, improved wear resistance would therefore be expected from improved SiC distribution. The lower wear rate for the pre-transition monolithic aluminas than the 15vol%SiC composite implies that, in the absence of fracture, the SiC addition does not provide an improvement in wear rate,
Figure 7. Backscattered electron image of the worn surface of the 15%vol SiC composite, showing a predominantly smooth surface with localized pitting.
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rather, the greater local residual tensile stresses in the composite may increase wear rate compared with the monolith. All published studies that compare the monolith with the composite have made the comparison with fracture dominated wear in monolithic alumina [e.g. 2,3]. While the removal of a catastrophic transition in wear rate is a major benefit provided by the composite, the greater wear rate in the ‘mild regime’, where the majority of aluminas operate in industrial applications, must be considered a significant disadvantage. Conclusions 1. For a similar grain size, the addition of SiC to alumina to form an inter/intra-granular composite resulted in a substantial reduction in sliding wear rate. 2. The monolithic alumina suffered a transition from ‘mild wear’ to catastrophic intergranular wear after a sliding distance determined by the grain size. 3. The composites did not exhibit any transition behaviour, but exhibited surface transgranular fracture (5vol%SiC) and pitting (15vol%SiC) throughout the test. The pitting was believed to result from local tensile stresses in the matrix arising from thermal mismatch between SiC and Al2O3. 4. The wear rate of the monolithic alumina in the ‘mild wear’ regime was lower than that of the composite materials. References 1. 2. 3. 4. 5. 6. 7. 8. 9.
K. Niihara, J. Ceram. Soc. Jpn. 99, 974 (1991). R. W. Davidge, R. J. Brook, F. Cambier, M. Poorteman, A. Leriche, D. O’Sullivan, S. Hampshire, and T. Kennedy, Br. Ceram. Trans. 96, 121 (1997). R. W. Davidge, P. C. Twigg, and F. L. Riley, J. Eur. Ceram. Soc. 16, 799 (1996). S. J .Cho, B. J. Hockey, B. R. Lawn, and S. J. Bennison, J. Am. Cream. Soc. 72, 1249 (1989). H. Liu and M. E. Fine, J. Am. Ceram. Soc. 76, 2393 (1993). O. Barceinas-Sa´nchez and W. M. Rainforth, Acta Mater. 46, 6475 (1998). G. R. Anstis, P. Chantikul, B. Lawn, and D. B. Marshall, J. Am. Ceram. Soc. 64, 533 (1981). J. Zhao, L. C. Stearns, M. P. Harmer, H. M. Chan, G. A. Miller, and R. E. Cook, J. Am. Ceram. Soc. 76, 503 (1993). R. I. Todd, M. A. M. Bourke, C. E. Borsa, and R. J. Brook, Acta Mater. 45, 1791 (1997).