Damage tolerant ceramic matrix composites 1057 fail. It follows, that for such applications, the pull- 6. Curtin, w. A, Theory of mechanical properties of out energy has little importance for the conse- ceramic matrix composites. J. Am. Ceram Soc., 74 (1991) quences of failure. Therefore it can be concluded 7. Cousland, S. McK, The contribution of fibre pull-out to the work of fracture of a metal-matrix composite, for the energy,Wo, that should be optimized, but the case of non-interacting fibres. Materials Forum, 16(1993) 327-34 8. Talreja, R, Continuum modelling of damage in ceramic composites. Mechanics Materiai (1991) 6 Conclusions J. w. and Sorensen, B. F, fatigue behar of ceramic This paper has analyzed the energy absorption of mposites, eds s. V. Nair and K. Jakus. Butterworth unidirectional fibre reinforced ceramic composites Heineman, (1995)in press. A simple model has been used to assess the energy 10. Evans, A. G, Zok, F. w.& davis J, The role of inter- faccs in fiber-reinforced brittle matrix composites. Com- uptake of the individual damage mechanisms pos. Sci. Technol, 42 (1991)3-24 Special attention has been paid to separate energ I1. Prewo, K. M. Fatigue and stress rupture of silicon car- uptake by distributed and localized mechanisms bide fiber-reinforced glass-ceramics. J. Mater. Sci, 22 since they scale differently with specimen dimen (1987)2695701. 12. Mandell, J. F. Grande, D. H. Dannemann K.A sions. The distributed energy uptake, i.e. the tough High temperature testing of glass/ceramic matrix compos- ness, has bcen found to be mainly due to strain ites, Test Methods for Design Allowable for Fibrous Com- energy in the fibres(this represents more than half posites, Vol. 2, ASTM STP 1003, ed. Chamis, C.C. American Society for Testing and Materials (1989)3-15 of the energy uptake), but contributions from 13. Holmes, J w, Kotil, 'I.& Foulds, W.T., High tempera frictional sliding and distributed matrix cracking ture fatigue of Sic fibre-reinforced Si, Na ceramic con have also been found to be important, whereas the ites. In Proceedings, Symposium on High Temperatur contribution from fibre/matrix debonding has 14. Wang, S. W.& Parvizi-Majidi, A. Mechanical behaviou been found to be very small. The predictions have of Nicalon fiber reinforced calcium aluminosilicate matrix been compared to experimental values for several composites Ceram. Engng. Sci. Proc., 11(1990)1607-16 composites, and a good agreement between the 15. Kim, R.Y.& Pagano, N. J, Crack initiation in unidirec tion brittle-matrix composites. J. Am. Ceram. Soc., 74 sured values is four 1991)108290 Finally, arguments have been forwarded to con 16. Barsoum, M. w, Kangutkar, P.& Wang, A. clude that in some applications the energy uptake Matrix crack initiation in ceramic matrix cor Experiment and test results. Compos. Sc due to the distributed mechanisms should be Technol,44(1992)257-70 maximized rather than the energy for fibre pull- 17. Reyerle, D s, Spearing.S. M, Zok, F. w.& Evans out, giving the most desirable material response. matrix composites. J. Am. Ceram. Soc., 75(1992)2719-25 18. Karandikar, P.& Chou, T -w.. Characterization and modelling of microcracking and elastic moduli changes in Acknowledgement Sci. Technol,46(1993)253-6 19. Sorensen, B. F.& Talreja, R, Analysis of damage in a eramic matrix composite. Int J. Damage Mech., 2(1993) B F.S. was supported by the Riso Engineering Science Centre for Structural Characterization 20. Hertzberg, R. w, Deformation and Fracture of Engineer- and modelling of materials g Materials, 3rd Edn. Johnl Wiley and Sons, New York (1989)26 21. Kanninen, M. F.& poplar. C. H. Advanced Fracture mechanics. Oxford University Press, New York, (1985) References 2. Sakai, M. Bradt, R. C,, Fracture toughness of brittle materials. Int. Mater. Rev., 38(1993)53-78 Marshall, D. B. Evans, A. G I. Aveston, J, Cooper, G. A& Kelly, A ceramic-fiber ceramic-matrix composites. J. Am. Ceram ple fracture, The Properties of Fibre Composites, Soc,68(1985)221-31 ence Proceedings. IPC Science and Technolo 24. Holmes, J. W, A technique for tensile fatigue and creep Guildford, UK(1971)15-26 testing of fiber-reinforced ceramics. J. Compos. Mater ansky evans. A G racture in fiber-reinforced ceramics. J. Mech. Phy B. F.& holmes, J. w. effect of 34(1986)167-78 on the monotonic tensile behavior and matrix cracking 3. McCartney, L N, New theoretical model of stress transfer of a fiber-reinforced ceramic. J Am. Ceram. Soc.,(1995) etween fibre and matrix in a uniaxially fibre-reinforced compositc.Proc. R. Soc. Lond., A425(1989)21544 26. Marshall, D, B. Shaw, M. C.& morris ure- 4. Sutcu, M, Statistical fibre failure and single crack ment of interfacial debonding and slic In biaxially reinforced ceramic fiber reinforced intermetallics, Acta 5. Thouless, M. D.& Evans, A G, Effects of pull-out on 27. Sorensen, B. F, Effect of fibre roughness on the overall the mechanical properties of ceramic-matrix composites stress-transverse strain response of ceramic composites Acta Metal.,36(1988)517-22 Scrip. Metall. Mater., 28(1993)4359Damage tolerant ceramic matrix composites 1057 fail. It follows, that for such applications, the pull￾out energy has little importance for the conse￾quences of failure. Therlefore, it can be concluded that for such applications it is not the pull-out energy, W,, that should be optimized, but the toughness, U. 6. 7. 8. 6 Conclusions 9. This paper has analyzed the energy absorption of unidirectional fibre reinforced ceramic composites. A simple model has been used to assess the energy uptake of the individual damage mechanisms. Special attention has belen paid to separate energy uptake by distributed and localized mechanisms, since they scale differently with specimen dimen￾sions. The distributed en’ergy uptake, i.e. the tough￾ness, has been found to be mainly due to strain energy in the fibres (this represents more than half of the energy uptake), but contributions from frictional sliding and distributed matrix cracking have also been found to be important, whereas the contribution from fibreimatrix debonding has been found to be very small. The predictions have been compared to experimental values for several composites, and a good agreement between the predictions and the measured values is found. Finally, arguments have been forwarded to con￾clude that in some applications the energy uptake due to the distributed mechanisms should be maximized rather than the energy for fibre pull￾out, giving the most desirable material response. 10. 11. 12. 13. 14. 15. 16. 17. 18. Acknowledgement 19. B.F.S. was supported by the Riser Engineering Science Centre for Structural Characterization and Modelling of Mater:ials. 20. 21. References 1. Aveston, J., Cooper, G. A. & Kelly, A., Single and multi￾ple fracture, The Properties of Fibre Composites, Confer￾ence Proceedings. IPC Science and Technology Press, Guildford, UK (1971) 15-26. 22. 23. 24. 2. Budiansky, B., Hutchinson, J. W. & Evans, A. G., Matrix fracture in fiber-reinforced ceramics. J. Mech. Phys. Solids, 34 (1986) 167-78. 25. 3. McCartney, L. N., New theoretical model of stress transfer between fibre and matrix in a uniaxially fibre-reinforced composite. Proc. R. Sot. Land., A425 (1989) 21544. 4. Sutcu, M., Statistical fibre failure and single crack behaviour in uniaxially reinforced ceramic composites. J. Muter. Sci., 23 (1988) 928-33. 5. Thouless, M. D. & Evans, A. G., Effects of pull-out on the mechanical properties of ceramic-matrix composites. Acta Metall., 36 (1988) 517-22. 26. 27. Curtin, W. A., Theory of mechanical properties of ceramic matrix composites. J. Am. Ceram. Sot., 74 (1991) 283745. Cousland, S. McK., The contribution of fibre pull-out to the work of fracture of a metal-matrix composite, for the case of non-interacting fibres. Materials Forum, 16 (1993) 327-34. Talreja, R., Continuum modelling of damage in ceramic matrix composites. Mechanics Materials, 12 (1991) 165-80. Holmes, J. W. and Sorensen, B. F., Fatigue behavior of continuous fiber reinforced ceramic matrix composites. In Elevated Temperature Behavior of Ceramic Matrix Composites, eds S. V. Nair and K. Jakus. Butterworth Heineman, (1995) in press. Evans, A. G., Zok, F. W. & Davis, J., The role of inter￾faces in fiber-reinforced brittle matrix composites. Com￾pos. Sci. Technol.. 42 (1991) 3-24. Prewo, K. M., Fatigue and stress rupture of silicon car￾bide fiber-reinforced glass-ceramics. J. Muter. Sci., 22 (1987) 2695-701. Mandell, J. F., Grande, D. H. & Dannemann, K. A., High temperature testing of glass/ceramic matrix compos￾ites, Test Methods for Design Allowable for Fibrous Com￾posites, Vol. 2, ASTM STP 1003, ed. Chamis, C. C. American Society for Testing and Materials (1989) 3-15. Holmes, J. W., Kotil, T. & Foulds, W. T., High tempera￾ture fatigue of Sic fibre-reinforced S&N, ceramic com￾posites. In Proceedings, Symposium on High Temperature Composites. Technomic, Basel, (1989) 17686. Wang, S.-W. & Parvizi-Majidi, A., Mechanical behaviour of Nicalon fiber reinforced calcium aluminosilicate matrix composites. Ceram. Engng. Sci. Proc., 11 (1990) 1607-16. Kim, R. Y. & Pagano, N. J., Crack initiation in unidirec￾tion brittle-matrix composites. J. Am. Ceram. Sot., 74 (1991) 1082-90. Barsoum, M. W., Kangutkar, P. & Wang, A. S. D., Matrix crack initiation in ceramic matrix composites, part I. Experiment and test results. Compos. Sci. Technol., 44 (1992) 257-70. Beyerle, D. S., Spearing, S. M., Zok, F. W. & Evans, A. G., Damage and failure in unidirectional ceramic￾matrix composites. J. Am. Ceram. Sot., 75 (1992) 2719-25. Karandikar, P. & Chou, T.-W., Characterization and modelling of microcracking and elastic moduli changes in Nicalon/CAS. Compos. Sci. Technol., 46 (1993) 25363. Sorensen, B. F. & Talreja, R., Analysis of damage in a ceramic matrix composite. Znt. J. Damage Mech., 2 (1993) 246-7 1. Hertzberg, R. W., Deformation and Fracture of Engineer￾ing Materials, 3rd Edn. John Wiley and Sons, New York, (1989) 26. Kanninen, M. F. & Popelar, C. H., Advanced Fracture Mechanics. Oxford University Press, New York, (1985) 159. Sakai, M. & Bradt, R. C., Fracture toughness of brittle materials. Znt. Mater. Rev., 38 (1993) 53-78. Marshall, D. B. & Evans, A. G., Failure mechanisms in ceramic-fiber ceramic-matrix composites. J. Am. Ceram. Sot., 68 (1985) 221-31. Holmes, J. W., A technique for tensile fatigue and creep testing of fiber-reinforced ceramics. J. Compos. Mater., 26 (1992) 915-32. Sorensen, B. F. & Holmes, J. W., Effect of loading rate on the monotonic tensile behavior and matrix cracking of a fiber-reinforced ceramic. J Am. Cerum. Sot., (1995) accepted. Marshall, D. B., Shaw, M. C. & Morris, W. L., Measure￾ment of interfacial debonding and sliding resistance in fiber reinforced intermetallics. Acta Metall. Mater., 40 (1992) 443-54. Sorensen, B. F., Effect of fibre roughness on the overall stress-transverse strain response of ceramic composites. Scrip. Metall. Mater., 28 (1993) 435-9