310 Journal of the American Ceramic SocieryDavis et al. Vol 86. No. 2 For cracks oriented normal to the fiber axis(the most important sliding of these fibers is expected to deform the monazite without case for a composite), U is the axial stress in the fiber and od is damaging the fibers the radial stress at the fiber surface. The ratio of the axial to the Wear and abrasion of ceramics are known to cause intense radial stress is -2 for all the fibers (Table D), both stresses being plastic deformation, similar to that in heavily cold-worked metals, compressive for the mullite fibers and tensile for the others. with fine, heavily deformed wear debris as in Fig. 6-8 Therefore, the residual stresses should favor debonding for mullite The depth of the deformed zone is expected to be similar to the fibers and fiber penetration for both eutectic fibers. However, this dimensions of the sliding asperities, consistent with the observa- result is sensitive to the volume fraction of fibers. For a fiber tions of Figs. 6-8(500 nm depth of monazite deformation from volume fraction of 0.5, a typical value for structural composites sliding of Al,O/YAG fiber with roughness amplitude 200 nn the magnitudes of the axial stresses decrease by a factor of -2 to and wavelength -l um). Mullite fibers, with larger roughness a level similar to the radial stresses. Then the residual stresses do amplitude (2.5 um)and wavelength (100 um), deform the not affect the condition for debonding and observations from entire coating, rather than just a thin layer. Abrasive wear of cracks oriented as in the model indentation experiments ar interfaces in a composite can affect the fiber sliding resistance representative of transverse cracking in the composite. The add and thus the mechanical properties of the composite, particu- tional influence of the residual stress field of the indentation, larly during fatigue. which favors penetration of the crack into the fiber, makes the The mechanism responsible for forming the dense nano- indentation crack a conservative indicator for debonding crystalline regions that resemble recrystallized grains, as in Fig. 6, is not known. Recrystallization normally occurs only at suffi- ciently high temperatures and long times to allow dislocation (2) Efects of Misfit Stresses climb. This would not be expected during room-temperature Misfit stresses were generated during fiber sliding by roughness deformation of a refractory material, such as LaPO4, and was not at two length scales, one microstructural (grooves that form at observed in indented monazite. 3 In alumina, which has a similar intersections of grain boundaries in the monazite coating or melting point, recovery and recrystallization of cold-worked m lamellae boundaries of the eutectic fibers with the fiber/coating crostructure typically requires temperatures of at least 800oC interface), and the other caused by long- range fluctuations in fiber and perhaps as high as 1200 C. this raises a question of whether diameter(Fig. I and Table In). Sliding displacements in the friction caused local heating in these experiments, or whether ushout experiments exceeded the microstructural dimensions by a another mechan tht be responsible for this microstruct factor of -5-10, but were smaller than the period of the diamete Two possible mechanisms are low-temperature amorphization and fluctuations by factors of 10-100. The microstructural roug recovery, which has been observed in wear and abrasion of ness dominated the misfit strains for the eutectic fibers and two-phase metals, or very fine-scale comminution accompanied sapphire fibers (Table m) by densification by local deformation. For the mullite fibers, the superposition of misfit strains caused A) Local Heating Effects: Several estimates of temperature by thermal expansion mismatch(Table D)and diameter fluctua- rises during sliding, based on different assumptions about heat tions(at the maximum sliding displacement) would cause com- dissipation mechanisms, are given in Appendix A. An upper pressive radial stresses as high as 5.2 GPa in some regions and adiabatic)limit for quasi-static continuous deformation gives ension in others. Because this maximum compressive stress is temperature rises between~800°-2000°C,de on whethe similar to the hardness of LaPO4(5 GPa), plastic deformation analysis is performed for individual asperities or for an average should occur throughout the coating, as observed in Fig. I contact area. However, according to a very conservative estimate For the other fibers. the maximum radial mismatch caused by an upper-bound for the sliding velocity is several orders of fluctuations in fiber diameter is of similar magnitude and opposite magnitude smaller than that required for adiabatic heating. A ign to the thermal expansion mismatch. Therefore, deformation of similar conclusion is drawn from application of frictional sliding the coating should depend on the microstructural roughness(both analyses, 2-54 which give small temperature increments for ti the roughness shape and the mismatch strain, dr/R). The single upper-bound sliding ve -05C for an asperity calculation rystal fibers had smaller microstructural mismatch strains(Sr/R< and -5C for an average calculation) 0. 002)than the eutectic fibers(SrR s 0.004) These calculations indicate that significant increases in tem The only oxide fibers currently available commercially in quantities sufficient to fabricate composites are polycrystalline ure could not have occurred in these experiments if the assa tions of quasi-static, continuous deformation are valid. Several with grain size -50-100 nm and diameter 12 HI mechanisms could potentially violate these conditions by produc- urface roughness due to grain-boundary grooving in as-fabricated ing local discontinuous deformation. One is stick slip motion fibers is typically very small(<5 nm for Nextel 720, 3M Corp, which causes local sliding velocities significantly larger than during processing of the matrix to depths up to approximately half upper-bound average velocity by a factor of -100 to approach of the grain size(-20-50 nm). Although this roughness amplitude adiabatic conditions(Appendix A). Although this is possible(local is smaller than that of the eutectic fibers the mismatch strain is elastic unloading could cause local velocities approaching sonic similar or larger(Sr/R s 0.003-0.005). Therefore, deformation of values), experiments and geological observations have found less the coating might be expected if these fibers were to be embedded heating during stick-slip than during stable sliding>(reduction of in a matrix with stiffness similar to that used in this study ormal stress by interface separation waves were suggested as a However, in a composite with a porous matrix, the response would cause be mitigated by the reduced constraint, owing to the lower elastic Another mechanism is cataclastic flow o accompanied by ffness of the matrix plastic deformation of the debris. Fine-grained (50-100 nr angular, and porous monazite debris characteristic of cataclastic flow was observed in some regions(Fig. 7). The prevalence of ( Plastic Deformation of LaPO, other deformation microstructures (dislocations, nano- The sliding of rough interfaces over distances large compared rystalline regions)also varied from place to place, suggesti e rou ivelength caused plastic deformation of that there was spatial and perhaps temporal variation in the monazite coatings (F 8). Plastic deformation of monazite by intensity of deformation during the pushout experiments. Local twinning and dislocations has also been observed after quasi-static adiabatic heating could occur during cataclastic flow as a result contact with spherical indenters at room temperature. ,/ Such of imperfect contact between the debris and the surround deformation can occur in any brittle material in the presence of leading to reduced heat conduction to the surroundings, or by ufficient hydrostatic pressure to suppress fracture . 38-43Because local stick-slip motion of the angular debris causing rapid onazite, with a hardness of 5 GPa, is much softer than alumina, mpact of sharp particles. In geological studies, fine-grained irconia, and mullite(hardnesses ranging between 10-40 GPa), debris(fault gouge)is itself suspected to influence whetherFor cracks oriented normal to the fiber axis (the most important case for a composite), p is the axial stress in the fiber and d is the radial stress at the fiber surface. The ratio of the axial to the radial stress is 2 for all the fibers (Table I), both stresses being compressive for the mullite fibers and tensile for the others. Therefore, the residual stresses should favor debonding for mullite fibers and fiber penetration for both eutectic fibers. However, this result is sensitive to the volume fraction of fibers. For a fiber volume fraction of 0.5, a typical value for structural composites, the magnitudes of the axial stresses decrease by a factor of 2 to a level similar to the radial stresses. Then the residual stresses do not affect the condition for debonding and observations from cracks oriented as in the model indentation experiments are representative of transverse cracking in the composite. The addi￾tional influence of the residual stress field of the indentation, which favors penetration of the crack into the fiber, makes the indentation crack a conservative indicator for debonding. (2) Effects of Misfit Stresses Misfit stresses were generated during fiber sliding by roughness at two length scales, one microstructural (grooves that form at intersections of grain boundaries in the monazite coating or lamellae boundaries of the eutectic fibers with the fiber/coating interface), and the other caused by long-range fluctuations in fiber diameter (Fig. 1 and Table II). Sliding displacements in the pushout experiments exceeded the microstructural dimensions by a factor of 5–10, but were smaller than the period of the diameter fluctuations by factors of 10–100. The microstructural rough￾ness dominated the misfit strains for the eutectic fibers and sapphire fibers (Table II). For the mullite fibers, the superposition of misfit strains caused by thermal expansion mismatch (Table I) and diameter fluctua￾tions (at the maximum sliding displacement) would cause com￾pressive radial stresses as high as 5.2 GPa in some regions and tension in others. Because this maximum compressive stress is similar to the hardness of LaPO4 (5 GPa1 ), plastic deformation should occur throughout the coating, as observed in Fig. 11. For the other fibers, the maximum radial mismatch caused by fluctuations in fiber diameter is of similar magnitude and opposite sign to the thermal expansion mismatch. Therefore, deformation of the coating should depend on the microstructural roughness (both the roughness shape and the mismatch strain, r/R). The single crystal fibers had smaller microstructural mismatch strains (r/R  0.002) than the eutectic fibers (r/R 0.004). The only oxide fibers currently available commercially in quantities sufficient to fabricate composites are polycrystalline, with grain size 50–100 nm and diameter 12 m.33,34 The surface roughness due to grain-boundary grooving in as-fabricated fibers is typically very small (5 nm for Nextel 720TM, 3M Corp., St. Paul, MN).35 However, the grooves would be expected to grow during processing of the matrix to depths up to approximately half of the grain size (20–50 nm). Although this roughness amplitude is smaller than that of the eutectic fibers, the mismatch strain is similar or larger (r/R 0.003–0.005). Therefore, deformation of the coating might be expected if these fibers were to be embedded in a matrix with stiffness similar to that used in this study. However, in a composite with a porous matrix, the response would be mitigated by the reduced constraint, owing to the lower elastic stiffness of the matrix. (3) Plastic Deformation of LaPO4 The sliding of rough interfaces over distances large compared with the roughness wavelength caused plastic deformation of monazite coatings (Figs. 5–8). Plastic deformation of monazite by twinning and dislocations has also been observed after quasi-static contact with spherical indenters at room temperature.31,37 Such deformation can occur in any brittle material in the presence of sufficient hydrostatic pressure to suppress fracture.38–43 Because monazite, with a hardness of 5 GPa,1 is much softer than alumina, zirconia, and mullite (hardnesses ranging between 10–40 GPa),44 sliding of these fibers is expected to deform the monazite without damaging the fibers. Wear and abrasion of ceramics are known to cause intense plastic deformation, similar to that in heavily cold-worked metals, with fine, heavily deformed wear debris as in Fig. 6–8.43,45–48 The depth of the deformed zone is expected to be similar to the dimensions of the sliding asperities, consistent with the observa￾tions of Figs. 6–8 (500 nm depth of monazite deformation from sliding of Al2O3/YAG fiber with roughness amplitude 200 nm and wavelength 1 m). Mullite fibers, with larger roughness amplitude (2.5 m) and wavelength (100 m), deform the entire coating, rather than just a thin layer. Abrasive wear of interfaces in a composite can affect the fiber sliding resistance and thus the mechanical properties of the composite, particu￾larly during fatigue.49 The mechanism responsible for forming the dense nano￾crystalline regions that resemble recrystallized grains, as in Fig. 6, is not known. Recrystallization normally occurs only at suffi￾ciently high temperatures and long times to allow dislocation climb.50 This would not be expected during room-temperature deformation of a refractory material, such as LaPO4, and was not observed in indented monazite.31 In alumina, which has a similar melting point, recovery and recrystallization of cold-worked mi￾crostructures typically requires temperatures of at least 800°C,45 and perhaps as high as 1200°C.51 This raises a question of whether friction caused local heating in these experiments, or whether another mechanism might be responsible for this microstructure. Two possible mechanisms are low-temperature amorphization and recovery, which has been observed in wear and abrasion of two-phase metals,48 or very fine-scale comminution accompanied by densification by local deformation. (A) Local Heating Effects: Several estimates of temperature rises during sliding, based on different assumptions about heat dissipation mechanisms, are given in Appendix A. An upper (adiabatic) limit for quasi-static continuous deformation gives temperature rises between 800°–2000°C, depending on whether analysis is performed for individual asperities or for an average contact area. However, according to a very conservative estimate, an upper-bound for the sliding velocity is several orders of magnitude smaller than that required for adiabatic heating. A similar conclusion is drawn from application of frictional sliding analyses,52–54 which give small temperature increments for this upper-bound sliding velocity (0.5°C for an asperity calculation and 5°C for an average calculation). These calculations indicate that significant increases in temper￾ature could not have occurred in these experiments if the assump￾tions of quasi-static, continuous deformation are valid. Several mechanisms could potentially violate these conditions by produc￾ing local discontinuous deformation. One is stick slip motion, which causes local sliding velocities significantly larger than average.55 The local velocity would need to exceed the maximum upper-bound average velocity by a factor of 100 to approach adiabatic conditions (Appendix A). Although this is possible (local elastic unloading could cause local velocities approaching sonic values), experiments and geological observations have found less heating during stick-slip than during stable sliding55 (reduction of normal stress by interface separation waves were suggested as a cause). Another mechanism is cataclastic flow30 accompanied by plastic deformation of the debris. Fine-grained (50 –100 nm), angular, and porous monazite debris characteristic of cataclastic flow was observed in some regions (Fig. 7). The prevalence of other deformation microstructures (dislocations, nano￾crystalline regions) also varied from place to place, suggesting that there was spatial and perhaps temporal variation in the intensity of deformation during the pushout experiments. Local adiabatic heating could occur during cataclastic flow as a result of imperfect contact between the debris and the surroundings, leading to reduced heat conduction to the surroundings, or by local stick-slip motion of the angular debris causing rapid impact of sharp particles. In geological studies, fine-grained debris (fault gouge) is itself suspected to influence whether 310 Journal of the American Ceramic Society—Davis et al. Vol. 86, No. 2