A Morales-Rodriguez er al. Journal of the European Ceramic Society 27(2007)3301-3305 3305 Acknowledgements gITS= Kotow The authors would like to thank Snecma Propulsion Solide ( France)and the programs of Ayudas de perfeccionamiento de Doctores de la junta de andalucia and avudas de Ayudantes de la Universidad de Sevilla(spain) for supporting where Vr is the volume fraction of longitudinal fiber tows in the this research. We are grateful to Dr M. R'Mili for his helpful composites,Otow the tow strength, F the force operating on the discussion tow, N the nominal number of fibers/tow, ac the critical value of the ratio of the number of broken fibers N to the total number References of fibers N(when the surviving fibers are unable to carry the applied load )and r is the mean fiber radius 1. Naslain, R, Design, preparation and of non-oxide cmcs for Table 3 presents the values of ultimate strength calcu- application in engines and nuclear reactors: an overview. Comp. Sci. Tech ated from previous equations. The critical fraction of broken no.,2004,64,155-170. fibers has been calculated considering that the neighbour 2. Mizuno, M. Zhu. S, Nagano, Y. Sakaida, Y, Kagawa, Y. and Watan- overloading of fibers interact (global load sharing). The ulti- abe, M, Cyclic-fatigue behavior of Sic/SiC composites at room and high temperatures.J. Am. Ceram Soc. 1996, 79, 3065-3077 mate strength has also been calculated from single sic-fibers 3. Shuler, S. F, Holmes, J. W and Wu, X, Influence of loading frequency data(E= 180 GPa), oUTS, considering the final deformations the room-temperature fatigue of carbon-fiber/SiC-matrix composites. JAm achieved by the composites. Results from predictions collected Ceran.Soc.,1993,76,2327-2336 in Table 3 show that both tows and single fibers are accurate 4. Penas, O, Etude de composites SiC/SiBC a matrice multisequencee fatigue cyclique a hautes temperatures sous air. PhD Thesis. INSA Lyon, to predict tended illeurbanne. france. 2002. obtained than considering the mirror approach(see Sec- 5. Stinton, D P, Caputo, A.J. and Lowden, R.A, Synthesis of fiber-reinforced tion 4.1) SiC composites by chemical vapor infiltration. Am. Ceram Soc. Bul, 1986, 65,347-350. 5. Conclusions 6. Curtin, W.A, Theory of mechanical properties of ceramic-matrix compos- s.JAm.cerm.Soc.,1991,74.2837-2845 7. Melchosky, J. J, Freiman, S. W. and Rice, R. w Fracture surface analysis This work points out that the extensive fiber/matrix debond- of ceramics. J Mater Sci. 1976. 11, 1310-1319 ing could be related to the strength enhancement observed in 8. Thouless, M D, Sbazeiro, O, Sigl, L S and Evans, A G, Effect of interface statically fatigued 2D-SiCrSiC composites. The a-E curves mechanical properties on pullout in SiC-fiber-reinforced ceramic matrix indicate that multicracking of the matrix is saturated near the composites.JAm Ceram Soc., 1989, 72, 525-532. 9. Lamon, J.A., Amicromechanics-based approach to the mechanical behavior fracture of the composite. Hence, UTS of these composites of brittle- matrix composites. Comp. Sci. Technol., 2001, 61, 2259-2272. is well described by fracture behavior of bundles and statisti- Calar, V. and Lamon, J, Failure of fiber bundles. Comp. Sci. Technol. cal distribution of individual fiber failures. However, analysis 2004, 64, 701-710 based on the mirror zone of the fibers'fracture surface is less 11. Fantozzi, G, Reynaud, P and Rouby, D, Thermomechanical behaviour of ong fibres ceramic-ceramic composites. Sil. Ind. 2002, 66, 109-119A. Morales-Rodr´ıguez et al. / Journal of the European Ceramic Society 27 (2007) 3301–3305 3305 equations10: σtows UTS = Vfσtow, (5) σtow = F Nt(1 − αC)πr2 , (6) where Vf is the volume fraction of longitudinal fiber tows in the composites, σtow the tow strength, F the force operating on the tow, Nt the nominal number of fibers/tow, αC the critical value of the ratio of the number of broken fibers N to the total number of fibers Nt (when the surviving fibers are unable to carry the applied load) and r is the mean fiber radius. Table 3 presents the values of ultimate strength calcu￾lated from previous equations. The critical fraction of broken fibers has been calculated considering that the neighbour overloading of fibers interact (global load sharing).11 The ulti￾mate strength has also been calculated from single SiC-fibers data (E = 180 GPa10), σfiber UTS, considering the final deformations achieved by the composites. Results from predictions collected in Table 3 show that both tows and single fibers are accurate to predict the final composite strength tendency experimentally obtained, better than considering the mirror approach (see Sec￾tion 4.1). 5. Conclusions This work points out that the extensive fiber/matrix debond￾ing could be related to the strength enhancement observed in statically fatigued 2D-SiCf/SiC composites. The σ–ε curves indicate that multicracking of the matrix is saturated near the fracture of the composite. Hence, UTS of these composites is well described by fracture behavior of bundles and statisti￾cal distribution of individual fiber failures. However, analysis based on the mirror zone of the fibers’ fracture surface is less accurate. Acknowledgements The authors would like to thank Snecma Propulsion Solide (France) and the programs of Ayudas de Perfeccionamiento de Doctores de la Junta de Andaluc´ıa and Ayudas de Movilidad de Ayudantes de la Universidad de Sevilla (Spain) for supporting this research. We are grateful to Dr. M. R’Mili for his helpful discussion. References 1. Naslain, R., Design, preparation and properties of non-oxide CMCs for application in engines and nuclear reactors: an overview. Comp. Sci. Tech￾nol., 2004, 64, 155–170. 2. Mizuno, M., Zhu, S., Nagano, Y., Sakaida, Y., Kagawa, Y. and Watan￾abe, M., Cyclic-fatigue behavior of SiC/SiC composites at room and high temperatures. J. Am. Ceram. Soc., 1996, 79, 3065–3077. 3. Shuler, S. F., Holmes, J. W. and Wu, X., Influence of loading frequency on the room-temperature fatigue of carbon-fiber/SiC-matrix composites. J. Am. Ceram. Soc., 1993, 76, 2327–2336. 4. Penas, O., Etude de composites SiC/SiBC a matrice multis ` equenc ´ ee en ´ fatigue cyclique a hautes temp ` eratures sous air. PhD Thesis. INSA Lyon, ´ Villeurbanne, France, 2002. 5. Stinton, D. P., Caputo, A. J. and Lowden, R. A., Synthesis of fiber-reinforced SiC composites by chemical vapor infiltration. Am. Ceram. Soc. Bull., 1986, 65, 347–350. 6. Curtin, W. A., Theory of mechanical properties of ceramic-matrix compos￾ites. J. Am. Ceram. Soc., 1991, 74, 2837–2845. 7. Melchosky, J. J., Freiman, S. W. and Rice, R. W., Fracture surface analysis of ceramics. J. Mater. Sci., 1976, 11, 1310–1319. 8. Thouless, M. D., Sbazeiro, O., Sigl, L. S. and Evans, A. G., Effect of interface mechanical properties on pullout in SiC-fiber-reinforced ceramic matrix composites. J. Am. Ceram. Soc., 1989, 72, 525–532. 9. Lamon, J. A., A micromechanics-based approach to the mechanical behavior of brittle-matrix composites. Comp. Sci. Technol., 2001, 61, 2259–2272. 10. Calard, V. and Lamon, J., Failure of fiber bundles. Comp. Sci. Technol., 2004, 64, 701–710. 11. Fantozzi, G., Reynaud, P. and Rouby, D., Thermomechanical behaviour of long fibres ceramic-ceramic composites. Sil. Ind., 2002, 66, 109–119