1572 Journal of the American Ceramic Sociery--Ogasaara et al Vol. 84. No. 7 400 003 350 ∑;=0.78 Experimental a30 002 250 200 0.01 Predicted line (t=14MPa) 0 050100150200250300350400 150200250300350400450 Peak Stress [MPa] Stress [MPa Fig. 12. Relationship between debond stress, d and peak stress, d. The Fig. 14. Relationship between the debond length, Ia, calculated with 2 normalized stress, 2i=oyap, has a constant value of 0. 78 o/o =0.78 and T= 14 MPa. The debond length, Id, at one is approximately one half that of the saturated matrix crack spacing, /,(45.4 E 400 006 300 T=18MPa 200 0.002 100 Karandikar, Chou Hutchinson Jensen 200220240260280300320 00020.40.60.81.01.214 Fig. 13. Relationship between inelastic strain index, y, and Strain [ dp. Predicted lines for friction stresses of T=10, 14, and 18 MPa have ig. 15. Comparison between predicted and experimental stress/strain been superimposed onto the data. nduced fiber clamping stresses that accompany roughne ing, as reported by Parthasarathy and Kerans.2 Predicted possess suitable interface properties with the low sidis a / SK for friction stresses of t=10.14. and 18 MPa are CMC 5 superposed onto Fig. 13, and indicate that T is approximately 14 MPa for the present composite. The predicted trend in hysteresis (4) Debond Length and Debond Energ loop width, assuming a frictional stress of T s= 14 MPa, is shown Figure 14 shows the debond length as a function of applied in Fig. 6, and indicates good agreement with the experimental data stress,o, calculated from Eq(16)with 2i=o 0,=0 By measuring the fiber fracture mirror size and pull-out length, Davies et al. estimated the sliding stress of the present composite of adjacent debond regions. The debond length, Id, at Gms is one using Curtin's theory to be t=4.94 MPa, which is approximately half that of the saturated matrix crack spacing, Is, (45. 4 um)in Fig. one third of the sliding stress, T=14 MPa, estimated by hysteresis 14, and is in agreement with the experimental results. The debond nalysis. The difference may be attributed to the stress level at energy obtained from Eq (17)is found to be 3.5-8.0 J/m and to which T is estimated, in that the matrix crack density is not be similar to that of other SiC/SiC composites. 2 saturated for the estimation of r by the hysteresis analysis, whereas Curtin's theory can only be utilized following matrix crack (5) Simulation of the Stress/Strain Behavior Simulated stress/strain curves based on the model proposed ontraction of the fiber and/or wear of the interface roughness above are shown in Fig. 15 between the fiber and the matrix may contribute to a decrease in data, indicating estimation of stress partitioning to be fairly good sliding stress throughout the entire stress/strain regime. The predicted curve The range of sliding stress in SiC fiber/SiC matrix composites using the Hutchinson and Jensen theory is almost the same as that is reported to vary widely between I and 200 MPa. 227-29 In spite by the Karandikar and Chou theory. o The stress partitioning of the coating free interface, the present composite appears to actor,A, is plotted in Fig. 16 as a function of the applied stress. Itinduced fiber clamping stresses that accompany roughness unseat￾ing, as reported by Parthasarathy and Kerans.26 Predicted trends for friction stresses of t 5 10, 14, and 18 MPa are shown superposed onto Fig. 13, and indicate that t is approximately 14 MPa for the present composite. The predicted trend in hysteresis loop width, assuming a frictional stress of t ' 14 MPa, is shown in Fig. 6, and indicates good agreement with the experimental data. By measuring the fiber fracture mirror size and pull-out length, Davies et al. 5 estimated the sliding stress of the present composite using Curtin’s theory to be t 5 4.94 MPa, which is approximately one third of the sliding stress, t 5 14 MPa, estimated by hysteresis analysis. The difference may be attributed to the stress level at which t is estimated, in that the matrix crack density is not saturated for the estimation of t by the hysteresis analysis, whereas Curtin’s theory can only be utilized following matrix crack saturation. In the latter region, it is conceivable that Poisson’s contraction of the fiber and/or wear of the interface roughness between the fiber and the matrix may contribute to a decrease in sliding stress. The range of sliding stress in SiC fiber/SiC matrix composites is reported to vary widely between 1 and 200 MPa.12,27–29 In spite of the coating free interface, the present composite appears to possess suitable interface properties with the low sliding stress resulting in excellent mechanical properties for this “NUSK” CMC.5 (4) Debond Length and Debond Energy Figure 14 shows the debond length as a function of applied stress, s#, calculated from Eq. (16) with Si 5 si /sp 5 0.78 and t 5 14 MPa. The matrix crack density saturation is due to the linking of adjacent debond regions. The debond length, ld, at s# mc is one half that of the saturated matrix crack spacing, ls, (45.4 mm) in Fig. 14, and is in agreement with the experimental results. The debond energy obtained from Eq. (17) is found to be 3.5–8.0 J/m2 and to be similar to that of other SiC/SiC composites.12 (5) Simulation of the Stress/Strain Behavior Simulated stress/strain curves based on the model proposed above are shown in Fig. 15, and agree well with the experimental data, indicating estimation of stress partitioning to be fairly good throughout the entire stress/strain regime. The predicted curve using the Hutchinson and Jensen theory9 is almost the same as that by the Karandikar and Chou theory.10 The stress partitioning factor, l, is plotted in Fig. 16 as a function of the applied stress. It Fig. 14. Relationship between the debond length, ld, calculated with Si 5 si /sp 5 0.78 and t 5 14 MPa. The debond length, ld, at s# mc is approximately one half that of the saturated matrix crack spacing, ls (45.4 mm). Fig. 15. Comparison between predicted and experimental stress/strain behavior for the orthogonal 3-D composite. Fig. 12. Relationship between debond stress, s#i , and peak stress, s# p. The normalized stress, Si 5 si /sp, has a constant value of 0.78. Fig. 13. Relationship between inelastic strain index, +, and peak stress, s# p. Predicted lines for friction stresses of t 5 10, 14, and 18 MPa have been superimposed onto the data. 1572 Journal of the American Ceramic Society—Ogasawara et al. Vol. 84, No. 7