Acta Mechanica Sinica

, Volume 35, Issue 1, pp 190–200 | Cite as

Damage and fracture model for eutectic composite ceramics

  • Jinfeng Yu
  • Xinhua NiEmail author
  • Xiequan Liu
  • Yunwei Fu
  • Zhihong Du
Research Paper


Study of damage and fracture models to analyze the fracture mechanism of eutectic composite ceramics is of considerable importance because no accurate fracture models are available for these materials. Eutectic composite ceramics are composed of microcells with random direction. We present herein a model that predicts the damage and fracture of eutectic composite ceramics based on analysis of defect stability and the damage localization band. Firstly, given the microstructure of eutectic composite ceramics, a mesodomain and a microcell model are constructed. The local stress field in the mesodomain is then analyzed based on the interaction direct derivative estimate. Secondly, the stability of a defect around particles in a microcell is analyzed, and the stress intensity factor of an annular defect under the applied stress field and the residual stress field in the particle are calculated. The stress intensity factor of a defect is controlled by the residual stress when the defect extension is small. However, it is controlled by the applied stress when the defect extension is large. Finally, a model for the damage localization band at the crack tip is constructed based on the Dugdale–Barenblatt model. The residual intensity is the important factor affecting the length of the damage localization band. When the damage variables reach their largest value, the residual intensity and the length of the damage localization band attain their minimum value. This work provides the theoretical basis for further study of the damage mechanics of eutectic composite ceramics and guides the engineering applications of these materials.


Microcell Interaction direct derivative estimate Defect stability Damage localization band 



This work was supported by the National Natural Science Foundation of China (Grant 11272355).


  1. 1.
    Llorca, J., Pastor, J., Poza, P.: Influence of the Y2O3 content and temperature on the mechanical properties of melt-grown Al2O3/ZrO2 eutectic. J. Am. Ceram. Soc. 87, 633–639 (2004)CrossRefGoogle Scholar
  2. 2.
    Pastor, J., Llorca, J., Poza, P., et al.: Mechanical properties of melt-grown Al2O3–ZrO2(Y2O3) eutectic with different microstructure. J. Eur. Soc. 25, 1215–1223 (2005)Google Scholar
  3. 3.
    Lee, J.H., Yoshikawa, A., Murayama, Y., et al.: Microstructure and mechanical properties of Al2O3/Y3Al5O12/ZrO2 ternary eutectic materials. J. Eur. Ceram. Soc. 25, 1411–1417 (2005)CrossRefGoogle Scholar
  4. 4.
    Sayir, A., Farmer, S.C.: The effect of the microstructure on mechanical properties of directionally solidified Al2O3/ZrO2(Y2O3) eutectic. Acta Mater. 48, 4691–4697 (2000)CrossRefGoogle Scholar
  5. 5.
    Zhao, Z.M., Zhang, L., Song, Y.G., et al.: Microstructures and properties of rapidly solidified Y2O3 doped Al2O3/ZrO2 composites prepared by combustion synthesis. Scripta Mater. 55, 819–822 (2006)CrossRefGoogle Scholar
  6. 6.
    Huang, Z.M., Zhang, H.S.: Current status and future trend of researches on the strength of fiber-reinforced composites—a summary of the results from a “failure Olympics”. Adv. Mech. 37, 80–98 (2007)Google Scholar
  7. 7.
    Altinkok, N., Koker, R.: Modelling of the prediction of tensile and density properties in particle reinforced metal matrix composites by using neural networks. Mater. Des. 27, 625–631 (2006)CrossRefGoogle Scholar
  8. 8.
    Moorthy, S., Ghosh, S.: A Voronoi cell finite element model for particle cracking in elastic-plastic composite materials. Comput. Methods Appl. Mech. Eng. 151, 377–400 (1998)CrossRefzbMATHGoogle Scholar
  9. 9.
    Zhao, A.H., Yu, J.L.: A micro-mechanical damage model for quasi-brittle materials. J. Tsinghua Univ. 40, 88–91 (2000)Google Scholar
  10. 10.
    Feng, X.Q., Yu, S.W.: Micromechanical modeling of softening in microcrack-weakened quasi-brittle materials. Acta Mech. Solida Sin. 8, 121–132 (1995)Google Scholar
  11. 11.
    Yao, Z.J.: Research on micromechanical damage model and macro mechanical properties for metal-matrix composites. [PhD. Thesis], Ordnance Engineering College, Shijiazhuang (2006)Google Scholar
  12. 12.
    Charles, Y., Estevez, R., Bréchet, Y., et al.: Modelling the competition between interface debonding and particle fracture using a plastic strain dependent cohesive zone. Eng. Fract. Mech. 77, 705–718 (2010)CrossRefGoogle Scholar
  13. 13.
    Monchiet, V., Gruescu, C., Cazacu, O., et al.: A micromechanical approach of crack-induced damage in orthotropic media: application to a brittle matrix composite. Eng. Fract. Mech. 83, 40–53 (2012)CrossRefGoogle Scholar
  14. 14.
    Cheng, P.Y., Jiao, G.Q., Wang, B.: Modeling oxidation damage of continuous fiber reinforced ceramic matrix composites. Acta. Mech. Sin. 27, 382–388 (2011)CrossRefGoogle Scholar
  15. 15.
    Ni, X.H., Chen, C., Ma, Y.C., et al.: The fracture strength of eutectic ceramic containing lamellar inclusion. J. Appl. Sci. 13, 1570–1575 (2013)CrossRefGoogle Scholar
  16. 16.
    Zheng, Q.S., Du, D.X.: An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution. J. Mech. Phys. Solids 49, 2765–2788 (2001)CrossRefzbMATHGoogle Scholar
  17. 17.
    Fu, Y.W.: Research on strength of eutectic composite ceramic with inherent defects. [PhD. Thesis], Ordnance Engineering College, Shijiazhuang (2016)Google Scholar
  18. 18.
    Du, Z.H., Ni, X.H., Liu, X.Q.: The damage strain field analysis of triangular symmetrical composite eutectic. World J. Eng. 13, 6–11 (2016)CrossRefGoogle Scholar
  19. 19.
    Henniche, A., Ouyang, J.H., Ma, Y.H., et al.: Microstructure and mechanical properties of ceramics obtained from chemically co-precipitated Al2O3–GdAlO3 nano-powders with eutectic composition. Ceram. Int. 43, 6996–7001 (2017)CrossRefGoogle Scholar
  20. 20.
    Henniche, A., Ouyang, J.H., Ma, Y.H., et al.: Microstructure, mechanical and thermo-physical properties of hot-pressed Al2O3–GdAlO3–ZrO2 ceramics with eutectic composition. Prog. Nat. Sci.: Mater. Int. 27, 491–497 (2017)CrossRefGoogle Scholar
  21. 21.
    Ma, W.D., Zhang, J., Su, H.J.: Microstructure transformation from irregular eutectic to complex regular eutectic in directionally solidified Al2O3/GdAlO3/ZrO2 ceramics by laser floating zone melting. J. Eur. Ceram. Soc. 36, 1447–1454 (2016)CrossRefGoogle Scholar
  22. 22.
    Xing, J.: SIF-based fracture criterion for interface cracks. Acta. Mech. Sin. 3, 491–496 (2016)MathSciNetzbMATHGoogle Scholar
  23. 23.
    Nie, Y., Zhang, M.F., Liu, Y., et al.: Microstructure and mechanical properties of Al2O3/YAG eutectic ceramic grown by horizontal directional solidification method. J. Alloys Compd. 657, 184–191 (2016)CrossRefGoogle Scholar
  24. 24.
    Fu, X.S., Fu, L.S., Chen, G.Q., et al.: High temperature deformation of non-directionally solidified Al2O3/YAG/ZrO2 eutectic bulk ceramic. Ceram. Int. 43, 1781–1787 (2017)CrossRefGoogle Scholar
  25. 25.
    Song, C., Wang, S., Liu, J., et al.: Microstructure and mechanical properties of Al2O3/Er3Al5O12 binary eutectic ceramic prepared by Bridgman method. Materials 11, 534–543 (2018)CrossRefGoogle Scholar
  26. 26.
    Lawn, B.: Fracture of Brittle Solids, 2nd edn. Higher Education Press, Beijing (2010)Google Scholar
  27. 27.
    Zhao, Z.M., Zhang, L., Zhang, S.Y., et al.: Microstructures and mechanical properties of large-scale Al2O3/ZrO2(Y2O3) self-growing ceramic plates prepared by combustion synthesis under high gravity. Proc. SPIE 6423, 64235B1–64235B8 (2007)CrossRefGoogle Scholar
  28. 28.
    Fu, Y.W.: Effective elastic property prediction of ceramic composite with inherent defect. J. Mech. Eng. 48, 46–51 (2012)CrossRefGoogle Scholar
  29. 29.
    Swain, M.V.: Structure and Properties of Ceramics. Science Press, Beijing (1998)Google Scholar
  30. 30.
    Jack, D.A., Smith, D.E.: Elastic properties of short-fiber polymer composites, derivation and demonstration of analytical forms for expectation and variance from orientation tensors. J. Compos. Mater. 42, 277–308 (2008)CrossRefGoogle Scholar
  31. 31.
    Llorca, J., Orera, V.: Directionally solidified eutectic ceramic oxides. Prog. Mater Sci. 51, 711–809 (2006)CrossRefGoogle Scholar
  32. 32.
    David, H.: Elastic field in 3D due to a spheroidal inclusion-MATLABTM code for Eshelby’s solution. Comput. Geosci. 35, 2170–2173 (2009)CrossRefGoogle Scholar
  33. 33.
    Feng, X.Q.: Micro-failure theory for brittle materials and shakedown analysis of structures with damage. [PhD. Thesis], Tsinghua University, Beijing (1995)Google Scholar
  34. 34.
    Yu, S.W., Feng, X.Q.: Damage Mechanics. Tsinghua University Press, Beijing (1997)Google Scholar
  35. 35.
    Barenblatt, G.I.: The mathematical theory of equilibrium cracks in brittle materials. Adv. Appl. Mech. 7, 55–129 (1962)CrossRefGoogle Scholar
  36. 36.
    Dugdale, D.S.: Yielding of steel sheets containing slits. Mech. Phys. Solids 8, 100–104 (1960)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Jinfeng Yu
    • 1
  • Xinhua Ni
    • 2
    Email author
  • Xiequan Liu
    • 2
  • Yunwei Fu
    • 3
  • Zhihong Du
    • 1
  1. 1.Department of Vehicle and Electric EngineeringArmy Engineering UniversityShijiazhuangChina
  2. 2.Army Infantry CollegeNanchangChina
  3. 3.Xichang Satellite Launch CenterXichangChina

Personalised recommendations