314 Journal of the American Ceramic SocieryDavis et al. Vol 86. No. 2 Table I. Misfit Strains and Stresses Fiber radius(Rμum) Microstructural roughness Amplitude, Sr(um) 0.05 0.2 0. Period, A(ur 0.001 0.002 0.004 0.004 g (MPa) 0.5 0.5 (△RR)(m=mAg) 0.0006 0.0003 0.0015 Ide for comparisons: stresse ated as in Table I but with radial he latter being the maximum misfit str V. Summary and Conclusions (1) Adiabatic Sliding If we assume that the work done by sliding friction is dissipated La-monazite is compatible with mullite, YAG, Zro2, and entirely by uniform adiabatic heating in a zone of deformed AlO. The interfaces between La-monazite and these materials are sufficiently weak to allow debonding when a crack ap monazite adjacent to the plane of sliding, the temperature rise is proaches the interface from within the monazite. This occurs even in the presence of substantial residual compressive △T= stresses normal to the interface. as in the case of the mullite fiber in an alumina matrix where T, is the sliding friction stress, 8 is the sliding displacement, All the monazite-coated fibers in this study(single crystal h is the thickness of the deformation zone, and p and co are the mullite and alumina, eutectic Al,O3/YAG, and Al,O3 ZrO2) density and specific heat of the monazite. For the sliding experi- underwent sliding in single fiber pushout experiments. Sliding ment corresponding to Fig. 6, the measured parametes o and Cp are T. o occurred along a single interfacial debond when the displace- 200 MPa, 8=5 Hm and h.2 lents were small and/or the fiber surfaces were relatively 500 J(kg K),Eq(A-D)gives AT= 2000oC smooth. At larger displacements, the eutectic fibers, which had An alternative estimate based on incremental sliding of individ rougher interfaces than the single crystal fibers, caused exten- ual asperities, as depicted in Fig Al, gives the temperature rise as sive damage in the ApoA coating adjacent to the fiber. The HAa mullite fibers, which had smooth surfaces but large oscillations △T= diameter, caused deformation through the entire thickness of the coating in regions of large misfit strain. Damage mecha- where H is the hardness of the monazite, A is the cross-sectional nisms included fracture, dislocation plasticity, and occasional area of the asperity and A, is the cross-sectional area of the plastic twinning. The fibers were undamaged, as might be expecte deformation zone created by the asperity as it slides(the sliding given their higher hardnesses. The relative softness of La- force acting on the asperity being set equal to HA ) If we take H monazite, resulting from its ability to deform plastically at low as the room temperature hardness of monazite (-5 GPa)and temperatures, may be critical for use as a composite AAa≈2( from fig.6),Eq(A-2) gIves△T=1000° terface Both of these estimates are subject to considerable uncertainty 3. TEM observations showed densely packed fine crystallites of (a factor of-2) associated with the parameters h and A /A, as well nazite in the most heavily deformed regions, resembling as the assumption of uniform heating within the zone. Neverthe recrystallized microstructures. Several analyses indicated that the sliding velocity is sufficiently large to cause adiabatic condi- stick-slip motion or cataclastic flow caused large increases in tion local sliding velocities and deformation rates. The detailed mechanisms responsible for this microstructure, which is un- (2) Estimated Sliding Velocity and Transient Heating Effects usual for such a refractory material at low temperature, have not The time in transient heat conduction problems always appears been identified. However, a parallel exists in the recrystallize- normalized by the characteristic time,T tion from radiation damage at much lower temperatures in a-monazite than in other minerals paF (A-3) conductivity and d is a characteristic Appendix a diffusion distar fiber sliding problem, d is the depth of the deformation zone and the conditions are close to adiabatic only if the time. taken to heat the deformation zone is small compared with T. If we assume that heat is conducted only into the Estimates of heating from Fiber sliding monazite (k≈2WmK) t is -10-7 s for a zone of 0.2 um. The time th is given by In= 8/v, where 8 is the sliding Several approaches, based on different tions about distance and y is the sliding velocity dissipation mechanisms, may be taken to estim Although the sliding velocity was not measured in the exp temperature rises during fiber sliding. Some from these ments described in Section Il, a very conservative upper bound alyses are summarized as follows: may be estimated. The experiments involved loading the indenterV. Summary and Conclusions La-monazite is compatible with mullite, YAG, ZrO2, and Al2O3. The interfaces between La-monazite and these materials are sufficiently weak to allow debonding when a crack ap￾proaches the interface from within the monazite. This occurs even in the presence of substantial residual compressive stresses normal to the interface, as in the case of the mullite fiber in an alumina matrix. All the monazite-coated fibers in this study (single crystal mullite and alumina, eutectic Al2O3/YAG, and Al2O3/ZrO2) underwent sliding in single fiber pushout experiments. Sliding occurred along a single interfacial debond when the displace￾ments were small and/or the fiber surfaces were relatively smooth. At larger displacements, the eutectic fibers, which had rougher interfaces than the single crystal fibers, caused exten￾sive damage in the LaPO4 coating adjacent to the fiber. The mullite fibers, which had smooth surfaces but large oscillations in diameter, caused deformation through the entire thickness of the coating in regions of large misfit strain. Damage mecha￾nisms included fracture, dislocation plasticity, and occasional twinning. The fibers were undamaged, as might be expected given their higher hardnesses. The relative softness of La￾monazite, resulting from its ability to deform plastically at low temperatures, may be critical for its use as a composite interface. TEM observations showed densely packed fine crystallites of monazite in the most heavily deformed regions, resembling recrystallized microstructures. Several analyses indicated that significant frictional heating during sliding was unlikely unless stick-slip motion or cataclastic flow caused large increases in local sliding velocities and deformation rates. The detailed mechanisms responsible for this microstructure, which is un￾usual for such a refractory material at low temperature, have not been identified. However, a parallel exists in the recrystalliza￾tion from radiation damage at much lower temperatures in La-monazite than in other minerals. Appendix A Estimates of Heating from Fiber Sliding Several approaches, based on different assumptions about dissipation mechanisms, may be taken to estimate limits on local temperature rises during fiber sliding. Some results from these analyses are summarized as follows: (1) Adiabatic Sliding If we assume that the work done by sliding friction is dissipated entirely by uniform adiabatic heating in a zone of deformed monazite adjacent to the plane of sliding, the temperature rise is T s cph (A-1) where s is the sliding friction stress,  is the sliding displacement, h is the thickness of the deformation zone, and  and cp are the density and specific heat of the monazite. For the sliding experi￾ment corresponding to Fig. 6, the measured parameters are s 200 MPa,   5 m and h 0.2 m. With   5 g/cm3 and cp  500 J
(kg
K) 1 , 61 Eq. (A-1) gives T  2000°C. An alternative estimate based on incremental sliding of individ￾ual asperities, as depicted in Fig A1, gives the temperature rise as T HAa cpAb (A-2) where H is the hardness of the monazite, Aa is the cross-sectional area of the asperity and Ab is the cross-sectional area of the plastic deformation zone created by the asperity as it slides (the sliding force acting on the asperity being set equal to Aa). If we take H as the room temperature hardness of monazite (5 GPa)1 and Ab/Aa 2 (from Fig. 6), Eq. (A-2) gives T  1000°C. Both of these estimates are subject to considerable uncertainty (a factor of 2) associated with the parameters h and Aa/Ab as well as the assumption of uniform heating within the zone. Neverthe￾less, they indicate that large local temperature rises could occur if the sliding velocity is sufficiently large to cause adiabatic condi￾tions. (2) Estimated Sliding Velocity and Transient Heating Effects The time in transient heat conduction problems always appears normalized by the characteristic time, : 62  cpd2 k (A-3) where k is the thermal conductivity and d is a characteristic diffusion distance. In the fiber sliding problem, d is the depth of the deformation zone and the conditions are close to adiabatic only if the time, th, taken to heat the deformation zone is small compared with . If we assume that heat is conducted only into the monazite (k 2 W
(m
K)1 ),61  is 107 s for a zone of depth 0.2 m. The time th is given by th  /v, where  is the sliding distance and v is the sliding velocity. Although the sliding velocity was not measured in the experi￾ments described in Section II, a very conservative upper bound may be estimated. The experiments involved loading the indenter Table II. Misfit Strains and Stresses Value Sapphire Mullite YAG/Al2O3 Al2O3/ZrO2 Fiber radius (R/m) 50 25 50 50 Microstructural roughness Amplitude, r (m) 0.05 0.05 0.2 0.2 Period, r (m) 22 1 1 r/R 0.001 0.002 0.004 0.004 r (MPa)‡ 200 300 770 730 Fiber diameter fluctuation Amplitude, R (m) 0.5 2.5 0.5 1 Period, R (m) 500 100 1000 400 (R/R) (zmax/R) † 0.0006 0.03 0.0003 0.0015 R (MPa)‡ 120 4500 60 270 † zmax is the maximum sliding displacement (10 m) ‡ Nominal radial misfit stresses intended only as rough guide for comparisons: stresses calculated as in Table 1 but with radial misfit strains r/R and (R/R) (zmax/R), the latter being the maximum misfit strain for sinusoidal diameter fluctuation (zmax  R). 314 Journal of the American Ceramic Society—Davis et al. Vol. 86, No. 2