2604 Journal of the American Ceramic Society-Glime and Cawle Vol 81. No. 10 APPENDIX B Microcomposite Residual Stress Due to Thermal Expansion Mismatch Upon cooling to room temperature, thermal expansion mis- match between the SiO2 reaction product and the SiC fiber and matrix sheath leads to residual stress in the microcomposite system FEM of the residual stress that develops upon cooling from 1100C (the oxidation anneal temperature)to room tem- perature has been performed, and a contour plot of the pre dicted maximum principal stresses is provided in Fig. Bl. Lin ear expansion coefficients have been used in the model and have been selected to represent the mean value for cooll from the anneal temperature to room temperature, 4x/o( for fused SiO, 4 and 4 x 10-6/C for the sCS SiC fiber and Si sheath D.9 A maximum thermally induced tensile stress of -100 MPa is 75 predicted in the fiber. The stress in the SiO2 near the joint is imarily compressive and <150 MPa. With the local stress concentration accounted for. the stresses in the SiO, and fiber ncrease, near fracture, to-I and 2 GPa, respectively. Although 0.45 the qualitative behavior of the system is not influenced dra- matically by the thermal stresses, the ratio of tensile stress 434 the fiber to that in the SiO, at the seal is increased compared to FEM predictions that do not consider thermally induced stress Fig. B2). For the microcomposite model, considering thermal stress in the analysis decreases the predicted maximum princi- pal stress in the SiO, from 1.7 to 1.3 GPa. Fig. B2. Contour plot of maximum principal stress for the model Acknowledgments: The authors would like to thank Mark Purdy and SiC-SiC microcomposite system. Scale indicates the local stress rela- Jeff Lewis. BFGoodrich OH, for providing chemic tive to the I gPa fiber nominal stress. Arrows indicate the direction of vapor deposition, and Greg Morscher, CWRU/NASA Lewis Research Center, the maximum principal stress. References C. Cao E. Bischoff. O. Sbaizero M. Rhile. A. G. Evans. D. B. Marshall and J J. Brennan, "Efiects of Interfaces on the Properties of Fiber-Reinforced .1g2 Ceramics, J. Am. Ceram. Soc., 73 16] 1691-9 Reactivity of Silicon Carbide and Carbon with Oxygen in Thermostructural Composites, "'Carbon, 31, 6 L. Filipuzzi and R. Naslain, " Oxidation Mechanisms and Kinetics of ID- SiC/C/SiC Composite Materials: IL, Modeling, J Am. Ceram. Soc., 77 [2] 467-80(1994 Camus, and R. Naslain, " Oxidati etics of ID-SiC/C/SIC Composite Materials: I, An Experimental Approach, JAm. Ceran.Soc.,771245966(1994) mic Transactions. Vol. 28. Advances in Ceramic Matris osites. Edited 518 by N. Bansal, Ar eramic Society, Westerville, OH, 199 bF E. Heredia, J. McNulty, F w. Zok, and A G. Evans, Oxidation Em- brittlement Probe for Ceramic-Matrix Composites, "JAm Ceram Soc., 7881 R 2097-100(1995) A.G. Evans, F W. Zok, R. M. MeMeeking, and Z Z. Du, ""Models of igh-Temperature, Environmentally Assiste ment in Ceramic-Matrix Composites, J. Am. Ceram. Soc., 79 192345-52(1996). 151. Wiley-Interscience, New York, 1997. lorscher, unpublished research, NASA Lewis Research Center 135 G. Cruciani, K. E. Spear, R. E. Tressler, and C. F. Ram- -0057 IM. D. Thouless, O. Sbaizero, L.S. Sigl, and A G. Evans, ""Effect of In- terface Mechanical Properties on Pullout in a SiC-Fiber luminum Silicate Glass-Ceramic, "J. Am. Ceram. Soc, 72 [4 525-32 (1989). Evans, M Fiber Cracking in Brittle Matrix Composites, J. Am. Ceram. Soc., 72 L N. P. Bansal and R. H. Doremus(Eds ) Handbook of Glass Properties, p I4Y. S. Tolukian(Ed. ) Thermophysical Properties of Matter-TPRC Data Fig. B1. Contour plot of maximum principal stress resulting from Series, VoL. 13: P. 358. IFI/Plenum, New York, 1970 ISM. K. Brun and M. P, Borom, ""Thermomechanical Properties of ermal expansion mismatch between SiO, and SiC upon cooling from sited Silicon Carbide Filaments, J. Am. Cera. Soc 1100C to room temperature. 1993-96(1989)APPENDIX B Microcomposite Residual Stress Due to Thermal Expansion Mismatch Upon cooling to room temperature, thermal expansion mis￾match between the SiO2 reaction product and the SiC fiber and matrix sheath leads to residual stress in the microcomposite system. FEM of the residual stress that develops upon cooling from 1100°C (the oxidation anneal temperature) to room tem￾perature has been performed, and a contour plot of the pre￾dicted maximum principal stresses is provided in Fig. B1. Lin￾ear expansion coefficients have been used in the model and have been selected to represent the mean value for cooling from the anneal temperature to room temperature, 4 × 10−7/°C for fused SiO2 14 and 4 × 10−6/°C for the SCS SiC fiber and SiC sheath.15 A maximum thermally induced tensile stress of ∼100 MPa is predicted in the fiber. The stress in the SiO2 near the joint is primarily compressive and <150 MPa. With the local stress concentration accounted for, the stresses in the SiO2 and fiber increase, near fracture, to ∼1 and 2 GPa, respectively. Although the qualitative behavior of the system is not influenced dra￾matically by the thermal stresses, the ratio of tensile stress in the fiber to that in the SiO2 at the seal is increased compared to FEM predictions that do not consider thermally induced stress (Fig. B2). For the microcomposite model, considering thermal stress in the analysis decreases the predicted maximum princi￾pal stress in the SiO2 from 1.7 to 1.3 GPa. Acknowledgments: The authors would like to thank Mark Purdy and Jeff Lewis, BFGoodrich Aerospace, Brecksville, OH, for providing chemical vapor deposition, and Greg Morscher, CWRU/NASA Lewis Research Center, Cleveland, OH, for assistance in tensile testing. References 1 H. C. Cao, E. Bischoff, O. Sbaizero, M. Rhu¨le, A. G. Evans, D. B. Marshall, and J. J. Brennan, ‘‘Effects of Interfaces on the Properties of Fiber-Reinforced Ceramics,’’ J. Am. Ceram. Soc., 73 [6] 1691–99 (1990). 2 C. Vix-Guterl, J. Lahaye, and P. Ehrburger, ‘‘Reactivity of Silicon Carbide and Carbon with Oxygen in Thermostructural Composites,’’ Carbon, 31, 629– 35 (1993). 3 L. Filipuzzi and R. Naslain, ‘‘Oxidation Mechanisms and Kinetics of 1D￾SiC/C/SiC Composite Materials: II, Modeling,’’ J. Am. Ceram. Soc., 77 [2] 467–80 (1994). 4 L. Filipuzzi, G. Camus, and R. Naslain, ‘‘Oxidation Mechanisms and Ki￾netics of 1D-SiC/C/SiC Composite Materials: I, An Experimental Approach,’’ J. Am. Ceram. Soc., 77 [2] 459–66 (1994). 5 O. Unal, J. Cawley, K. Lagerlof, and S. Prybyla, ‘‘Intermittent Coatings for Continuous-Fiber-Reinforced Ceramic-Matrix Composites’’; pp. 223–34 in Ce￾ramic Transactions, Vol. 28, Advances in Ceramic Matrix Composites. Edited by N. Bansal. American Ceramic Society, Westerville, OH, 1993. 6 F. E. Heredia, J. McNulty, F. W. Zok, and A. G. Evans, ‘‘Oxidation Em￾brittlement Probe for Ceramic-Matrix Composites,’’ J. Am. Ceram. Soc., 78 [8] 2097–100 (1995). 7 A. G. Evans, F. W. Zok, R. M. McMeeking, and Z. Z. Du, ‘‘Models of High-Temperature, Environmentally Assisted Embrittlement in Ceramic-Matrix Composites,’’ J. Am. Ceram. Soc., 79 [9] 2345–52 (1996). 8 W. D. Pilkey, Peterson’s Stress Concentration Factors, 2nd ed.; pp. 122 and 151. Wiley-Interscience, New York, 1997. 9 G. N. Morscher, unpublished research, NASA Lewis Research Center, Cleveland, OH. 10C. E. Ramberg, G. Cruciani, K. E. Spear, R. E. Tressler, and C. F. Ram￾berg, ‘‘Passive-Oxidation Kinetics of High-Purity Silicon Carbide from 800° to 100°C,’’ J. Am. Ceram. Soc., 79 [11] 2897–911 (1996). 11M. D. Thouless, O. Sbaizero, L. S. Sigl, and A. G. Evans, ‘‘Effect of In￾terface Mechanical Properties on Pullout in a SiC-Fiber-Reinforced Lithium Aluminum Silicate Glass-Ceramic,’’ J. Am. Ceram. Soc., 72 [4] 525–32 (1989). 12A. G. Evans, M. Y. He, and J. W. Hutchinson, ‘‘Interface Debonding and Fiber Cracking in Brittle Matrix Composites,’’ J. Am. Ceram. Soc., 72 [12] 2300–303 (1989). 13N. P. Bansal and R. H. Doremus (Eds.), Handbook of Glass Properties; p. 226. Academic Press, Orlando, FL, 1986. 14Y. S. Tolukian (Ed.), Thermophysical Properties of Matter–TPRC Data Series, Vol. 13; p. 358. IFI/Plenum, New York, 1970. 15M. K. Brun and M. P. Borom, ‘‘Thermomechanical Properties of Chemi￾cally Vapor Deposited Silicon Carbide Filaments,’’ J. Am. Ceram. Soc., 72 [10] 1993–96 (1989). h Fig. B2. Contour plot of maximum principal stress for the model SiC–SiC microcomposite system. Scale indicates the local stress rela￾tive to the 1 GPa fiber nominal stress. Arrows indicate the direction of the maximum principal stress. Fig. B1. Contour plot of maximum principal stress resulting from thermal expansion mismatch between SiO2 and SiC upon cooling from 1100°C to room temperature. 2604 Journal of the American Ceramic Society—Glime and Cawley Vol. 81, No. 10