Skip to main content
Log in

Modeling Loading/Unloading Hysteresis Behavior of Unidirectional C/SiC Ceramic Matrix Composites

  • Published:
Applied Composite Materials Aims and scope Submit manuscript

Abstract

The loading/unloading tensile behavior of unidirectional C/SiC ceramic matrix composites at room temperature has been investigated. The loading/unloading stress–strain curve exhibits obvious hysteresis behavior. An approach to model the hysteresis loops of ceramic matrix composites including the effect of fiber failure during tensile loading has been developed. By adopting a shear-lag model which includes the matrix shear deformation in the bonded region and friction in the debonded region, the matrix cracking space and interface debonded length are obtained by matrix statistical cracking model and fracture mechanics interface debonded criterion. The two-parameter Weibull model is used to describe the fiber strength distribution. The stress carried by the intact and fracture fibers on the matrix crack plane during unloading and subsequent reloading is determined by the Global Load Sharing criterion. Based on the damage mechanisms of fiber sliding relative to matrix during unloading and subsequent reloading, the unloading interface reverse slip length and reloading interface new slip length are obtained by the fracture mechanics approach. The hysteresis loops of unidirectional C/SiC ceramic matrix composites corresponding to different stress have been predicted.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Naslain, R.: Design, preparation and properties of non-oxide CMCs for application in engines and nuclear reactors: an overview. Compos. Sci. Technol. 64, 155–170 (2004). doi:10.1016/S0266-3538(03)00230-6

    Article  CAS  Google Scholar 

  2. Dalmaz, A., Reynaud, P., Rouby, D., Fantozzi, G.: Damage propagation in carbon/silicon carbide composites during tensile tests under the SEM. J. Mat. Sci. 31, 4213–4219 (1996). doi:10.1007/BF00356441

    Article  CAS  Google Scholar 

  3. Chiang, Y.C.: On fiber debonding and matrix cracking in fiber-reinforced ceramics. Compos. Sci. Technol. 61, 1743–1756 (2001). doi:10.1016/S0266-3538(01)00078-1

    Article  CAS  Google Scholar 

  4. Curtin, W.A.: Stress–strain behavior of brittle matrix composites. Comprehensive composite materials, Elsevier Science Ltd. 4, 47–76 (2000). doi:10.1016/B0-08-042993-9/00088-7

  5. Rouby, D., Reynaud, P.: Fatigue behavior related to interface modification during load cycling in ceramic-matrix fiber composites. Compos. Sci. Technol. 48, 109–118 (1993). doi:10.1016/0266-3538(93)90126-2

    Article  CAS  Google Scholar 

  6. Evans, A.G., Zok, F.W., McMeeking, R.M.: Fatigue of ceramic matrix composites. Acta Metall. Mater. 43, 859–875 (1995). doi:10.1016/0956-7151(94)00304-Z

    Article  CAS  Google Scholar 

  7. Reynaud, P.: Cyclic fatigue of ceramic-matrix composites at ambient and elevated temperatures. Compos. Sci. Technol. 56, 809–814 (1996). doi:10.1016/0266-3538(96)00025-5

    Article  CAS  Google Scholar 

  8. Mei, H., Cheng, L.F.: Comparison of the mechanical hysteresis of carbon/ceramic-matrix composites with different fiber performs. Carbon 47, 1034–1042 (2009). doi:10.1016/j.carbon.2008.12.025

    Article  CAS  Google Scholar 

  9. Kotil, T., Holmes, J.W., Comninou, M.: Origin of hysteresis observed during fatigue of ceramic-matrix composites. J. Am. Ceram. Soc. 73, 1879–1883 (1990). doi:10.1111/j.1151-2916.1990.tb05239.x

    Article  CAS  Google Scholar 

  10. Pryce, A.W., Smith, P.A.: Matrix cracking in unidirectional ceramic matrix composites under quasi-static and cyclic loading. Acta Metall. Mater. 41, 1269–1281 (1993). doi:10.1016/0956-7151(93)90178-U

    Article  CAS  Google Scholar 

  11. Keith, W.P., Kedward, K.T.: The stress–strain behavior of a porous unidirectional ceramic matrix composite. Composites 26, 163–174 (1995). doi:10.1016/0010-4361(95)91379-J

    Article  CAS  Google Scholar 

  12. Solti, J.P., Mall, S., Robertson, D.D.: Modeling damage in unidirectional ceramic-matrix composites. Compos. Sci. Technol. 54, 55–66 (1995). doi:10.1016/0266-3538(95)00041-0

    Article  Google Scholar 

  13. Ahn, B.K., Curtin, W.A.: Strain and hysteresis by stochastic matrix cracking in ceramic matrix composites. J. Mech. Phys. Solid 45, 177–209 (1997). doi:10.1016/S0022-5096(96)00081-6

    Article  Google Scholar 

  14. Li, L.B., Song, Y.D., Sun, Z.G.: Influence of interface debonding on the fatigue hysteresis loops of ceramic matrix composites. Chin. J. Solid Mech. 30, 8–14 (2009). in Chinese

    Google Scholar 

  15. Li, L.B., Song, Y.D., Sun, Z.G.: Effect of fiber Poisson contraction on fatigue hysteresis loops of ceramic matrix composites. J. Nanjing. Uni. Aero. Astron. 41, 181–186 (2009). in Chinese

    CAS  Google Scholar 

  16. Li, L.B., Song, Y.D.: An approach to estimate interface shear stress of ceramic matrix composites from hysteresis loops. Appl. Compos. Mater. 17, 309–328 (2010). doi:10.1007/s10443-009-9122-6

    Article  CAS  Google Scholar 

  17. Li, L.B., Song, Y.D.: Estimate interface frictional coefficient of ceramic matrix composites from hysteresis loops. J. Compos. Mater. 45, 989–1006 (2011). doi:10.1177/0021998310381437

    Article  CAS  Google Scholar 

  18. Fantozzi, G., Reynaud, P., Rouby, D.: Thermomechanical behavior of long fibers ceramic-ceramic composites. Silic. Ind. 66, 109–119 (2001)

    CAS  Google Scholar 

  19. Fantozzi, G., Reynaud, P.: Mechanical hysteresis in ceramic matrix composites. Mater. Sci. Eng., A 521–522, 18–23 (2009). doi:10.1016/jmsea.2008.09.128

    Google Scholar 

  20. Li, L.B., Song, Y.D.: Influence of fiber failure on fatigue hysteresis loops of ceramic matrix composites. J. Reinf. Plast. Compos. 30, 12–25 (2011). doi:10.1177/0731684410386273

    Article  Google Scholar 

  21. Kun, F., Herrmann, H.J.: Damage development under gradual loading of composites. J. Mat. Sci. 35, 4685–4693 (2000). doi:10.1023/A:1004842704921

    Article  CAS  Google Scholar 

  22. Yang, B., Mall, S.: Cohesive-shear-lag model for cycling stress–strain behavior of unidirectional ceramic matrix composites. Int. J. Damage Mech. 12, 45–64 (2003). doi:10.1177/1056789503012001003

    Article  CAS  Google Scholar 

  23. Budiansky, B., Hutchinson, J.W., Evans, A.G.: Matrix fracture in fiber-reinforced ceramics. J. Mech. Phys. Solid 34, 167–189 (1986). doi:0022-5096/86$3.00+0.00

    Article  Google Scholar 

  24. Daniel, I.M., Lee, J.W.: The behavior of ceramic matrix fiber composites under longitudinal loading. Compos. Sci. Technol. 46, 105–113 (1993). doi:10.1016/0266-3538(93)90166-E

    Article  CAS  Google Scholar 

  25. Aveston, J., Cooper, G.A., Kelly, A.: Single and multiple fracture. Properties of fiber composites: conference on proceedings. England: National Physical Laboratory, IPC. 15–26 (1971)

  26. Zok, F.W., Spearing, S.M.: Matrix crack spacing in brittle matrix composites. Acta Metall. Mater. 40, 2033–2043 (1992). doi:10.1016/0956-7151(92)90189-L

    Article  Google Scholar 

  27. Zhu, H., Weitsman, Y.: The progression of failure mechanisms in unidirectional reinforced ceramic composites. J. Mech. Phys. Solid 42, 1601–1632 (1994). doi:10.1016/0022-5096(94)90089-2

    Article  CAS  Google Scholar 

  28. Curtin, W.A.: Multiple matrix cracking in brittle matrix composites. Acta Metall. Mater. 41, 1369–1377 (1993). doi:10.1016/0956-7151(93)90246-O

    Article  CAS  Google Scholar 

  29. Hsueh, C.H.: Crack-wake interface debonding criterion for fiber-reinforced ceramic composites. Acta Mater. 44, 2211–2216 (1996). doi:10.1016/1359-6454(95)00369-X

    Article  CAS  Google Scholar 

  30. Gao, Y., Mai, Y., Cotterell, B.: Fracture of fiber-reinforced materials. J. Appl. Math. Phys. 39, 550–572 (1988). doi:10.1007/BF00948962

    Article  Google Scholar 

  31. Sun, Y.J., Singh, R.N.: The generation of multiple matrix cracking and fiber-matrix interfacial debonding in a glass composite. Acta Mater. 46, 1657–1667 (1998). doi:10.1016/S1359-6454(97)00347-9

    Article  CAS  Google Scholar 

  32. Thouless, M.D., Evans, A.G.: Effects of pull-out on the mechanical properties of ceramic matrix composites. Acta Metall. Mater. 36, 517–522 (1988). doi:10.1016/0001-6160(88)90083-1

    Article  CAS  Google Scholar 

  33. Cao, H.C., Thouless, M.D.: Tensile tests of ceramic-matrix composites: theory and experiment. J. Am. Ceram. Soc. 73, 2091–2094 (1990). doi:10.1111/j.1151-2916.1990.tb05273.x

    Article  CAS  Google Scholar 

  34. Sutcu, M.: Weibull statistics applied to fiber failure in ceramic composites and work of fracture. Acta Metall. Mater. 37, 651–661 (1989). doi:10.1016/0001-6160(89)90249-6

    Article  CAS  Google Scholar 

  35. Schwietert, H.R., Steif, P.S.: A theory for the ultimate strength of a brittle-matrix composite. J. Mech. Phys. Solid 38, 325–343 (1990). doi:10.1016/0022-5096(90)90002-L

    Article  Google Scholar 

  36. Curtin, W.A.: Theory of mechanical properties of ceramic-matrix composites. J. Am. Ceram. Soc. 74, 2837–2845 (1991). doi:10.1111/j.1151-2916.1991.tb06852.x

    Article  CAS  Google Scholar 

  37. Weitsman, Y., Zhu, H.: Multiple-fracture of ceramic composites. J. Mech. Phys. Solid 41, 351–388 (1993). doi:10.1016/0022-5096(93)90012-5

    Article  CAS  Google Scholar 

  38. Hild, F., Domergue, J.M., Leckie, F.A., Evans, A.G.: Tensile and flexural ultimate strength of fiber-reinforced ceramic-matrix composites. Int. J. Solids Struct. 31, 1035–1045 (1994). doi:10.1016/0020-7683(94)90010-8

    Article  Google Scholar 

  39. Curtin, W.A., Ahn, B.K., Takeda, N.: Modeling brittle and tough stress–strain behavior in unidirectional ceramic matrix composites. Acta Mater. 46, 3409–3420 (1998). doi:10.1016/S1359-6454(98)00041-X

    Article  CAS  Google Scholar 

  40. Paar, R., Valles, J.-L., Danzer, R.: Influence of fiber properties on the mechanical behavior of unidirectionally-reinforced ceramic matrix composites. Mater. Sci. Eng., A 250, 209–216 (1998). doi:10.1016/S0921-5093(98)00593-0

    Article  Google Scholar 

  41. Liao, K., Reifsnider, K.L.: A tensile strength model for unidirectional fiber-reinforced brittle matrix composite. Int. J. Fract. 106, 95–115 (2000). doi:10.1023/A:1007645817753

    Article  CAS  Google Scholar 

  42. Zhou, S.J., Curtin, W.A.: Failure of fiber composites: a lattice green function model. Acta Metall. Mater. 43, 3093–3104 (1995). doi:10.1016/0956-7151(95)00003-E

    Article  CAS  Google Scholar 

  43. Dutton, R.E., Pagano, N.J., Kim, R.Y.: Modeling the ultimate tensile strength of unidirectional glass-matrix composites. J. Am. Ceram. Soc. 83, 166–174 (2000). doi:10.1111/j.1151-2916.2000.tb01166.x

    Article  CAS  Google Scholar 

  44. Xia, Z., Curtin, W.A.: Toughness-to-brittle transitions in ceramic-matrix composites with increasing interfacial shear stress. Acta Mater. 48, 4879–4892 (2000). doi:10.1016/S1359-6454(00)00291-3

    Article  CAS  Google Scholar 

  45. Phoenix, S.L., Raj, R.: Scalings in fracture probabilities for a brittle matrix fiber composite. Acta Metall. Mater. 40, 2813–2828 (1992)

    Article  CAS  Google Scholar 

  46. Ramakrishnan, N., Arunachalam, V.S.: Effective elastic moduli of porous ceramic materials. J. Am. Ceram. Soc. 76, 2745–2752 (1993). doi:10.1111/j.1151-2916.1993.tb04011.x

    Article  CAS  Google Scholar 

  47. Curtin, W.A.: In situ fiber strength in ceramic-matrix composites from fracture mirrors. J. Am. Ceram. Soc. 77, 1075–1078 (1994). doi:10.1111/j.1151-2916.1994.tb07272.x

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This work is sponsored by the Postdoctoral Science Foundation of China (Grant No. 2012M511274).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Li Longbiao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Longbiao, L., Yingdong, S. & Youchao, S. Modeling Loading/Unloading Hysteresis Behavior of Unidirectional C/SiC Ceramic Matrix Composites. Appl Compos Mater 20, 655–672 (2013). https://doi.org/10.1007/s10443-012-9294-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10443-012-9294-3

Keywords

Navigation