2992 Journal of the American Ceramic Sociefy-Kuo et al. Vol. 80. No. 12 Table IL. Parameters of Interfacial Properties (A, aclamping eters has been reduced to four by using the calculated pr value and T) Extracted from Curve-Fitting the LH Model to as an a-priori input to the LH equations. Further reduction in Pushout Data for Al,O3 and YAG Fiber Systems the number of parameters has been accomplished by noting that Pure Mode ll the asperity term, To. is mechanistically related to the asperity Coefficient of Clamping pressure, pressure, Asperity, through a Coulombic friction law (m) To- poa AL,, fiber system(B,=0.107 and B2=0.947) Thus, Eq (1)is reduced to a simplified form that is amer 0.27 to more-robust curve fitting: YAG fiber system(B,= 0.149 and B2=0.926) expl*一 BR BI 0.18 16.5 17.7 where o is equal to the sum Nr and all the other terms remain as defined in Eq.(1 ex Although Eq (6)reduced the number of adjustable param- to three T In effect, the interface may separate from the fiber and thereby quite sensitive to the initial settings of the parameters. To re- lessen the absolute magnitude of the roughness-induced clamp- duce the number of parameters even further, a modified form Ing pressure of Eq (4)was used to fit the immediate post-debond pushout (4) Estimating T stress over a range of specimen thicknesses. Equation (4)was The LH model was used to fit the experimental pushout data which resulted in simplified by assuming a Coulombic asperity law(Eq(5)), both before and after complete interfacial debonding(Eqs. (1) and (4)). These fits were made by recording the peak debond B,PR stress(Pp)and the stress immediately following complete fiber P (exp 5a-D) debonding(P). Averages of five pushout tests were plotted B, functions of the specimen thickness and used as data for fitting Two parameters were extracted from curve-fitting Eq. (7)to the LH equations(Fig. 6). This process was repeated for each the sliding portion of the experimental data: H and o of several coating thicknesses The LH formulation has five key parameters that can be immediate pre-debond stress values, which resulted in an esti- extracted from fits to experimental data: Ti, PR, NR, To, and p. mate of T To do so, Eq. (7) was applied to experimental However, such a large number of parameters presents consid- results over a range of specimen thicknesses. values of u and erable difficulties in conducting reliable/repeatable curve fits to Clamping were then used in Eq (6)to fit experimental values of the experimental data. Thus, the number of adjustable param- Pp as a function of the specimen thickness. The results of the 40(a 3000 250 u-0.24 174 L1⊥⊥, 1.2 Embedded Fiber Length, L(mm) r18 3000 5从-0.27 Embedded Fiber Length, L(mm) Fig. 6. Variations of peak debond stress(O) just before complete debonding(Pp)and (O)sliding stress immediately following complete debonding(P) for the Al,O, fiber system, as a function of embedded fiber length(L)(coating thicknesses of(a)6.5 um and(b)16 umIn effect, the interface may separate from the fiber and thereby lessen the absolute magnitude of the roughness-induced clamp￾ing pressure. (4) Estimating Gi The LH model was used to fit the experimental pushout data both before and after complete interfacial debonding (Eqs. (1) and (4)). These fits were made by recording the peak debond stress (PP) and the stress immediately following complete fiber debonding (Pl ). Averages of five pushout tests were plotted as functions of the specimen thickness and used as data for fitting the LH equations (Fig. 6). This process was repeated for each of several coating thicknesses. The LH formulation has five key parameters that can be extracted from fits to experimental data: Gi , PR, NR, t0, and m. However, such a large number of parameters presents consid￾erable difficulties in conducting reliable/repeatable curve fits to the experimental data. Thus, the number of adjustable param￾eters has been reduced to four by using the calculated PR value as an a-priori input to the LH equations. Further reduction in the number of parameters has been accomplished by noting that the asperity term, t0, is mechanistically related to the asperity pressure, sasperity, through a Coulombic friction law:33 t0 4 msasperity (5) Thus, Eq. (1) is reduced to a simplified form that is amenable to more-robust curve fitting: PP = PR + 2S Gi Ef B2Rf D 1/2 exp z* + sclamping B1 ~exp z* − 1! (6) where sclamping is equal to the sum sasperity + NR and all the other terms remain as defined in Eq. (1). Although Eq. (6) reduced the number of adjustable param￾eters to three (Gi , sclamping, and m), the curvefitting was still quite sensitive to the initial settings of the parameters. To re￾duce the number of parameters even further, a modified form of Eq. (4) was used to fit the immediate post-debond pushout stress over a range of specimen thicknesses. Equation (4) was simplified by assuming a Coulombic asperity law (Eq. (5)), which resulted in Pl = S sclamping − B1PR B1 D ~exp zd − 1! (7) Two parameters were extracted from curve-fitting Eq. (7) to the sliding portion of the experimental data: m and sclamping. The resulting parameters were then used in Eq. (6) to fit the immediate pre-debond stress values, which resulted in an esti￾mate of Gi . To do so, Eq. (7) was applied to experimental results over a range of specimen thicknesses. Values of m and sclamping were then used in Eq. (6) to fit experimental values of PP as a function of the specimen thickness. The results of the Table II. Parameters of Interfacial Properties (µ, sclamping, and Gi ) Extracted from Curve-Fitting the LH Model to Pushout Data for Al2O3 and YAG Fiber Systems Coating thickness, t (mm) Coefficient of friction, m Clamping pressure, sclamping (MPa) Pure Mode II interfacial fracture energy, Gi (J/m2 ) Al2O3 fiber system (B1 4 0.107 and B2 4 0.947) 6.5 0.24 174 47 16 0.27 211 18 23.5 0.20 232 11 YAG fiber system (B1 4 0.149 and B2 4 0.926) 2 0.18 421 16.2 9 0.18 464 15.5 16.5 0.19 405 17.7 Fig. 6. Variations of peak debond stress (d) just before complete debonding (PP) and (s) sliding stress immediately following complete debonding (Pl ) for the Al2O3 fiber system, as a function of embedded fiber length (L) (coating thicknesses of (a) 6.5 mm and (b) 16 mm). 2992 Journal of the American Ceramic Society—Kuo et al. Vol. 80, No. 12