December 1997 Control of Interfacial Properties through Fiber Coatings: Monazite Coatings 2993 experiments(Figs. 6 and 7)showed that, as the specimen thick- ing. The compressive radial stress, NR, is positive in Eq. (1)an ness increased, Pp and P, both increased. This trend is predicted increases the load that is required for debonding. As the coating by the modified LH equations(Eqs. (6)and(7). These modi- thickness increases in the Al2O3 fiber system, the tensile axial ed LH equations were used to fit the maximum stress, PP, and stress increases while the compressive radial stress decreases the sliding stress after complete debonding Ph, versus the spe Fig. 1). Using the LH model, both effects would predict a men thickness, t, as shown in Figs. 6 and 7 ecrease in the peak debond stress Pp with increasing coating Using the material properties that are shown in Table I, the thickness; this is in agreement with the trend that has beer elastic parameters B, and B2 were computed for the Al2O3 and observed experimentally(Fig. 5), where an increasing coating the YAG fiber systems(Eqs. (2)and (3). In these calculations, thickness has decreased the required pushout stress(plotted as the interphase was assumed to have no effect on these parar pushout load in Fig. 5 eters. Values of B, and B2 were estimated to be 0.107 and In addition to affecting the stress that is needed to propagate 0.947, respectively, for the Al2O, fiber system, and 0. 149 and a debond, the residual stresses also affect the frictional sliding 0.926, respectively, for the YAG fiber system. Using this ap- of the fiber following debonding. To facilitate discussion, ar h. values for l and H were estimated for each average value of the sliding stress is calculated using the rela system and each coating thickness (Table Il). If desired, tion T= P, /2mrL). The average sliding stress is plotted against can be separated into its components using the defi the coating thickness in Fig 8 and exhibits a constant value as nition of g and the elastic calculation of the residual the coating thickness changes. To understand the factors that radial clam affect frictional sliding, we again use the LH model. The tensile Using the lh equations, we obtained a detailed ch axial stress is predicted to have little effect on frictional sliding ization of the interface. As such. the effect of coating thicknes Eq (7). However, a decrease in the compressive radial stress on the pushout response could be mechanistically explained by with increasing coating thickness would be predicted to reduce applying the LH mode the frictional pushout stress(Eq.(7). Thus, the experiment observation of a constant sliding stress is not consistent with IV. Discussion his prediction and can occur only in one of two ways: (i)there is an increase in asperity pressure, To, with an increase in coat Interfacial properties of two oxide fiber/oxide matri kX mode ing thickness or(ii) To dominates the interfacial sliding me- ystems have been analyzed using fiber pushout testing. These chanics(this latter case is indeed the case with the YAG fiber properties are discussed below system, where the residual thermal clamping stress is tensile Debond nd Sliding in th yet the fiber still resists frictional pushout Al,O/LaPO,Al2O, Fiber System Interfacial fracture energies, Ti, were determined using the The AlO3 fiber system has been calculated to have a tensile procedure that has been outlined in the previous section. The residual axial stress in the fiber and a compressive residual fracture energy in the Al2O3 fiber system varied, from a valu radial stress across the sliding interface(Fig. 1). A tensile axial of 47 J/m2 at a coating thickness of 6.5 um to a value of 1l J/m2 for a large coating thickness of 23.5 um(Table Il). This stress appears as a negative PR value in Eq (I)and decreases result is contrary to the principal supposition that the Ti value would remain constant. However, a B-Al2O3 reaction product CTTTTTTTTTTTT l-16,2J/m 到 占2000 chanin=121 MPa 000 4000 55J/m2 l000 Embedded Fiber Length, L (mm) ig. 7. Variations of peak debond stress(e) just before complete debonding (Pp) and (O)sliding stress immediately following comple debonding(P) for YAG fiber system, as a function of embedded fiber length(L)(coating thicknesses of (a)2 um and( b)9 um)experiments (Figs. 6 and 7) showed that, as the specimen thick￾ness increased, PP and Pl both increased. This trend is predicted by the modified LH equations (Eqs. (6) and (7)). These modi￾fied LH equations were used to fit the maximum stress, PP, and the sliding stress after complete debonding Pl , versus the speci￾men thickness, t, as shown in Figs. 6 and 7. Using the material properties that are shown in Table I, the elastic parameters B1 and B2 were computed for the Al2O3 and the YAG fiber systems (Eqs. (2) and (3)). In these calculations, the interphase was assumed to have no effect on these param￾eters. Values of B1 and B2 were estimated to be 0.107 and 0.947, respectively, for the Al2O3 fiber system, and 0.149 and 0.926, respectively, for the YAG fiber system. Using this ap￾proach, values for Gi , sclamping, and m were estimated for each fiber system and each coating thickness (Table II). If desired, sclamping can be separated into its components using the defi￾nition of sclamping and the elastic calculation of the residual radial clamping stress. Using the LH equations, we obtained a detailed character￾ization of the interface. As such, the effect of coating thickness on the pushout response could be mechanistically explained by applying the LH model. IV. Discussion Interfacial properties of two oxide fiber/oxide matrix model systems have been analyzed using fiber pushout testing. These properties are discussed below. (1) Debonding and Sliding in the Al2O3 /LaPO4 /Al2O3 Fiber System The Al2O3 fiber system has been calculated to have a tensile residual axial stress in the fiber and a compressive residual radial stress across the sliding interface (Fig. 1). A tensile axial stress appears as a negative PR value in Eq. (1) and decreases the magnitude of the applied stress that is required for debond￾ing. The compressive radial stress, NR, is positive in Eq. (1) and increases the load that is required for debonding. As the coating thickness increases in the Al2O3 fiber system, the tensile axial stress increases while the compressive radial stress decreases (Fig. 1). Using the LH model, both effects would predict a decrease in the peak debond stress PP with increasing coating thickness; this is in agreement with the trend that has been observed experimentally (Fig. 5), where an increasing coating thickness has decreased the required pushout stress (plotted as pushout load in Fig. 5). In addition to affecting the stress that is needed to propagate a debond, the residual stresses also affect the frictional sliding of the fiber following debonding. To facilitate discussion, an average value of the sliding stress is calculated using the rela￾tion t 4 p1/(2prL). The average sliding stress is plotted against the coating thickness in Fig. 8 and exhibits a constant value as the coating thickness changes. To understand the factors that affect frictional sliding, we again use the LH model. The tensile axial stress is predicted to have little effect on frictional sliding (Eq. (7)). However, a decrease in the compressive radial stress with increasing coating thickness would be predicted to reduce the frictional pushout stress (Eq. (7)). Thus, the experimental observation of a constant sliding stress is not consistent with this prediction and can occur only in one of two ways: (i) there is an increase in asperity pressure, t0, with an increase in coat￾ing thickness or (ii) t0 dominates the interfacial sliding me￾chanics (this latter case is indeed the case with the YAG fiber system, where the residual thermal clamping stress is tensile yet the fiber still resists frictional pushout). Interfacial fracture energies, Gi , were determined using the procedure that has been outlined in the previous section. The fracture energy in the Al2O3 fiber system varied, from a value of 47 J/m2 at a coating thickness of 6.5 mm to a value of 11 J/m2 for a large coating thickness of 23.5 mm (Table II). This result is contrary to the principal supposition that the Gi value would remain constant. However, a b-Al2O3 reaction product Fig. 7. Variations of peak debond stress (d) just before complete debonding (PP) and (s) sliding stress immediately following complete debonding (Pl ) for YAG fiber system, as a function of embedded fiber length (L) (coating thicknesses of (a) 2 mm and (b) 9 mm). December 1997 Control of Interfacial Properties through Fiber Coatings: Monazite Coatings 2993