February 2003 Influence of Interfacial Roughness on Fiber Sliding in Oxide Composites with La-Monacite 315 Asperity Fiber Monazite Deformed zone Fig. Al. Schematic showing asperity sliding and associated deformation zone on the end of the fiber using a fixed weight lowered slowly the contact geometry, thermal diffusivities(a) and the time velocity <10 m/s)by a viscous dashpot. When the interface which the heat is applied. A limitation of these models is debonded, the sliding fiber accelerated unstably until the indenter increases without limit as the sliding velocity increases (i.e. as contacted the matrix. The magnitude of the acceleration was diabatic conditions are approached), a consequence of the as- determined by the resultant force on the fiber(the difference sumption that the heat is dissipated at the interface rather than in etween the combined weight of the loading mass, indenter, and a deformation zone of finite volume. fiber and the opposing forces due to sliding friction and the For the analysis of sliding asperities, a convenient solution for dash-pot). An upper bound for this acceleration, corresponding to /, and l is that of a ian heat source applied for a time I over zero resistance from sliding and the dashpot, is the gravitational a circular contact area of radius r acceleration, g. This acceleration acting over the measured sliding displacement(-5 um)would result in a maximum velocity of 10 m/s. A less conservative overestimate obtained by assuming (A-5) that the sliding friction remains constant during the test gives a value smaller by a factor of 15 An upper bound for the sliding force on an asperity is given by With the upper-bound velocity of 10- m/s and the sliding taking the contact pressure equal to the hardness of the monazite istance8=5 um for the average analysis of Eq (A-1), the lower and a friction coefficient of unity, so that FJA=H. For asperity contact times between the limits of -r/v and 8/1, the temperature more than three orders of magnitude larger than the value of increase estimated from Eq (A-4)for an Al O/YAG asperity with estimated above. indicating that adiabatic conditions are not ro =0.2 um, a s 0.05 cm/s, k s 20 W(m- k),and other approached. For the ty sliding analysis(Eq.(A-2),the parameters as defined above is -0.5.C. An alternative analysis asperity,-05 um)giving a smaller equal to the dimensions of the based on the measured sliding force and uniform contact gave relevant sliding distance is smaller er heat input time, although still far from adiabatic conditions (INT $10-) It is worth noting the role of asperity size in the above analysis References Because both d in Eq.(A-3)and the sliding distance 8 that determines the sliding time(h) scale with the asperity size, the 'P. E. D. Morgan and D B. Marshall, "Ceramic Composites of Monazite and ratio /p/r increases with decreasing asperity size. Therefore, if the Am. Ceran.Soc,78,1553-63(1995 damage observed in Fig. 6 was caused by sequential sliding of es of various sizes, the conditions for the smaller asperities “xm上 perature Stability of the Al2O -LaPO4 System, "J.Am. Ceram. Soc. nature of these estimates it appears unlikely that large temperature D. B. Marshall, J. B. Davis, P. E. D. Morgan, and J. R, Por increases could have occurred in these experiments if slidingfor -Tolerant Oxide Composites, Key Eng Mater, 127-131, 27-36(199 occurred uniformly and i aPOavis. Eu. Ceram. so an d9. 242 -260(199 Oxide Composites of Alyo, 6J. B. Davis, D. B. Marshall, and P. E. D. Morgan ( Frictional Siding Analyses Oxide-Oxide Composites, J. Eur. Ceram Soc., 20 [5583- In the literature on frictional sliding, the assumption is made K. A. Keller, T.L. Mah, E. E Boakye, and T. A. Parthasara that work done by frictional forces is dissipated as heat at the mposites with Ceram. Eng. Sci. Proc., 21 [41525-34(2000) terface between the sliding surfaces. -4 Solutions for the RT. A. Parthasarathy, E. Boakeye, M. K. Cinibulk, and M. D. Perry, "Fabrication terface temperature as a function of the sliding velocity are and Testing of Oxide/Oxide Microcomposites with Monazite and Hibonite obtained from analysis of heat flow into the materials either side of Interlayers, J. Am. Ceram Soc., 82 [12]3575-83(1999 the interface. Solutions are available at a macroscopic level and D, Wilson, "Processing and Properties of an Oxide/Oxide (average) and at an asperity contact level for transient and -38(199 eady-state conditions. These solutions can be written in the general form an Oxide Faber-Oxide Matrix Composite,"Key. Eng Mater, 164-165, 85-90(1999) ""Evaluation of All-Oxide Composites Based on Coated Nextel 610 and 650 Fibers, AT A八e12 (A-4) Y. Hikichi and T, Nomura, "Melting Temperatures of Monazite and Xenotim where AT is the difference between the interface temperature and the remote temperature, Fs is the sliding force, v the velocity, A the C.H. Kite and womM. Riven "character catiom f ytrium Phosphate an contact area, k, and k, are the thermal conductivities of materials Yttrium Phosphate/Y ttrium Aluminate Laminate, "J. Am. Ceram. Soc., 78 [11 I and 2 either side of the interface, and l, and l, are functions of 3121-24(1995).on the end of the fiber using a fixed weight lowered slowly (velocity 104 m/s) by a viscous dashpot. When the interface debonded, the sliding fiber accelerated unstably until the indenter contacted the matrix. The magnitude of the acceleration was determined by the resultant force on the fiber (the difference between the combined weight of the loading mass, indenter, and fiber and the opposing forces due to sliding friction and the dash-pot). An upper bound for this acceleration, corresponding to zero resistance from sliding and the dashpot, is the gravitational acceleration, g. This acceleration acting over the measured sliding displacement (5 m) would result in a maximum velocity of 102 m/s. A less conservative overestimate obtained by assuming that the sliding friction remains constant during the test gives a value smaller by a factor of 15. With the upper-bound velocity of 102 m/s and the sliding distance   5 m for the average analysis of Eq. (A-1), the lower bound estimate for the heat input time is th 5 104 s. This is more than three orders of magnitude larger than the value of  estimated above, indicating that adiabatic conditions are not approached. For the asperity sliding analysis (Eq. (A-2)), the relevant sliding distance is smaller (equal to the dimensions of the asperity, 0.5 m) giving a smaller heat input time, although still far from adiabatic conditions (th/ 102 ). It is worth noting the role of asperity size in the above analysis. Because both d in Eq. (A-3) and the sliding distance  that determines the sliding time (th) scale with the asperity size, the ratio th/ increases with decreasing asperity size. Therefore, if the damage observed in Fig. 6 was caused by sequential sliding of asperities of various sizes, the conditions for the smaller asperities would have been further from adiabatic. Given the conservative nature of these estimates it appears unlikely that large temperature increases could have occurred in these experiments if sliding occurred uniformly. (3) Frictional Sliding Analyses In the literature on frictional sliding, the assumption is made that work done by frictional forces is dissipated as heat at the interface between the sliding surfaces.52–54 Solutions for the interface temperature as a function of the sliding velocity are obtained from analysis of heat flow into the materials either side of the interface. Solutions are available at a macroscopic level (average) and at an asperity contact level for transient and steady-state conditions. These solutions can be written in the general form54 T
Fsv A
k1
1 k2
2 1 (A-4) where T is the difference between the interface temperature and the remote temperature, Fs is the sliding force, v the velocity, A the contact area, k1 and k2 are the thermal conductivities of materials 1 and 2 either side of the interface, and l1 and l2 are functions of the contact geometry, thermal diffusivities (
) and the time over which the heat is applied. A limitation of these models is that T increases without limit as the sliding velocity increases (i.e., as adiabatic conditions are approached), a consequence of the as￾sumption that the heat is dissipated at the interface rather than in a deformation zone of finite volume. For the analysis of sliding asperities, a convenient solution for l1 and l2 is that of a gaussian heat source applied for a time t over a circular contact area of radius ro: 54
ro1/ 2 tan1
4t
ro 2 1/ 2 (A-5) An upper bound for the sliding force on an asperity is given by taking the contact pressure equal to the hardness of the monazite and a friction coefficient of unity, so that Fs/A  H. For asperity contact times between the limits of ro/v and /v, the temperature increase estimated from Eq. (A-4) for an Al2O3/YAG asperity with r0  0.2 m,
0.05 cm2 /s, k 20 W
(m
K)1 , 63 and other parameters as defined above is 0.5°C. An alternative analysis based on the measured sliding force and uniform contact gave T 5°C. References 1 P. E. D. Morgan and D. B. Marshall, “Ceramic Composites of Monazite and Alumina,” J. Am. Ceram. Soc., 78, 1553–63 (1995). 2 P. E. D. Morgan, D. B. Marshall, and R. M. Housley, “High Temperature Stability of Monazite–Alumina Composites,” Mater. Sci. Eng., A, A195, 215–22 (1995). 3 D. B. Marshall, P. E. D. Morgan, R. M. Housley, and J. T. Cheung, “High Temperature Stability of the Al2O3–LaPO4 System,” J. Am. Ceram. Soc., 81 [4] 951–56 (1998). 4 D. B. Marshall, J. B. Davis, P. E. D. Morgan, and J. R. Porter, “Interface Materials for Damage-Tolerant Oxide Composites,” Key Eng. Mater., 127–131, 27–36 (1997). 5 J. B. Davis, D. B. Marshall, and P. E. D. Morgan, “Oxide Composites of Al2O3 and LaPO4,” J. Eur. Ceram. Soc., 19, 2421–26 (1999). 6 J. B. Davis, D. B. Marshall, and P. E. D. Morgan, “Monazite Containing Oxide–Oxide Composites,” J. Eur. Ceram. Soc., 20 [5] 583–87 (2000). 7 K. A. Keller, T.-I. Mah, E. E. Boakye, and T. A. Parthasarathy, “Gel-Casting and Reaction Bonding of Oxide–Oxide Minicomposites with Monazite Interphase,” Ceram. Eng. Sci. Proc., 21 [4] 525–34 (2000). 8 T. A. Parthasarathy, E. Boakeye, M. K. Cinibulk, and M. D. Perry, “Fabrication and Testing of Oxide/Oxide Microcomposites with Monazite and Hibonite as Interlayers,” J. Am. Ceram. Soc., 82 [12] 3575–83 (1999). 9 S. M. Johnson, Y. Blum, C. Kanazawa, H.-J. Wu, J. R. Porter, P. E. D. Morgan, D. B. Marshall, and D. Wilson, “Processing and Properties of an Oxide/Oxide Composite,” Key Eng. Mater., 127–131, 231–38 (1997). 10S. M. Johnson, Y. Blum, and C. H. Kanazawa, “Development and Properties of an Oxide Fiber–Oxide Matrix Composite,” Key. Eng. Mater., 164–165, 85–90 (1999). 11K. A. Keller, T. Mah, T. A. Parthasarathy, E. E. Boakye, and M. Cinibulk, “Evaluation of All-Oxide Composites Based on Coated Nextel 610 and 650 Fibers,” Ceram. Eng. Sci. Proc., in press (2001). 12Y. Hikichi and T. Nomura, “Melting Temperatures of Monazite and Xenotime,” J. Am. Ceram. Soc., 70 [10] C-252–C-253 (1987). 13D. B. Marshall, P. E. D. Morgan, and R. M. Housley, “Debonding in Multilay￾ered Composites of Zirconia and LaPO4,” J. Am. Ceram. Soc., 80 [7] 1677–83 (1997). 14D.-H. Kuo and W. M. Kriven, “Characterization of Yttrium Phosphate and a Yttrium Phosphate/Yttrium Aluminate Laminate,” J. Am. Ceram. Soc., 78 [11] 3121–24 (1995). Fig. A1. Schematic showing asperity sliding and associated deformation zone. February 2003 Influence of Interfacial Roughness on Fiber Sliding in Oxide Composites with La-Monazite 315