Acta Mechanica Solida Sinica

, Volume 22, Issue 5, pp 453–464 | Cite as

Thermal Fracture of Functionally Graded Plate with Parallel Surface Cracks

  • Yuezhong Feng
  • Zhihe JinEmail author


This work examines the fracture behavior of a functionally graded material (FGM) plate containing parallel surface cracks with alternating lengths subjected to a thermal shock. The thermal stress intensity factors (TSIFs) at the tips of long and short cracks are calculated using a singular integral equation technique. The critical thermal shock ΔTc that causes crack initiation is calculated using a stress intensity factor criterion. Numerical examples of TSIFs and ΔTc for an Al2O3/Si3N4 FGM plate are presented to illustrate the effects of thermal property gradation, crack spacing and crack length ratio on the TSIFs and ΔTc. It is found that for a given crack length ratio, the TSIFs at the tips of both long and short cracks can be reduced significantly and ΔTc can be enhanced by introducing appropriate material gradation. The TSIFs also decrease dramatically with a decrease in crack spacing. The TSIF at the tips of short cracks may be higher than that for the long cracks under certain crack geometry conditions. Hence, the short cracks instead of long cracks may first start to grow under the thermal shock loading.

Key words

functionally graded material thermal fracture parallel cracks alternating lengths stress intensity factor 


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  1. [1]
    Gupta, T.K., Strength degradation and crack propagation in thermally shocked Al2O3. Journal of the American Ceramic Society, 1972, 43: 249–253.CrossRefGoogle Scholar
  2. [2]
    Geyer, J.F. and Nemat-Nasser, S., Experimental investigation of thermally induced interacting cracks in brittle solids. International Journal Solids and Structures, 1982, 18: 349–356.CrossRefGoogle Scholar
  3. [3]
    Bahr, H.A., Fischer, G. and Weiss, H.J., Thermal shock crack patterns explained by single and multiple crack growth. Journal of Materials Science, 1986, 21: 2716–2720.CrossRefGoogle Scholar
  4. [4]
    Nemat-Nasser, S., Keer, L.M. and Parihar, K.S., Unstable growth of thermally induced interacting cracks in brittle solids. International Journal of Solids Structures, 1978, 14: 409–430.CrossRefGoogle Scholar
  5. [5]
    Bahr, H.A., Weiss, H.J., Maschke, H.G. and Meissner, F., Multiple crack propagation in a strip caused by thermal shock. Theoretical and Applied Fracture Mechanics, 1988, 10: 219–226.CrossRefGoogle Scholar
  6. [6]
    Rizk, A.A. Transient thermal stress intensity factors for periodic array of cracks in a half-plane due to convective cooling. Journal of Thermal Stresses, 2003, 26:443–456.CrossRefGoogle Scholar
  7. [7]
    Rizk, A.A., Convective thermal shock of an infinite plate with periodic edge cracks. Journal of Thermal Stresses, 2005, 28: 103–119.CrossRefGoogle Scholar
  8. [8]
    Jin, Z.H. and Feng, Y.Z., An array of parallel edge cracks with alternating lengths in a strip subjected to a thermal shock. Journal of Thermal Stresses, 2009, 32: 431–447.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Kawasaki, A. and Watanabe, R., Fabrication of disk-shaped functionally gradient materials by hot pressing and their thermomechanical performance. In J.B. Holt, M. Koizumi, T. Hirai, Z.A. Munir (Eds.), Ceramic Transactions, Vol. 34, American Ceramic Society, Westerville, OH, 1993, pp. 157–164.Google Scholar
  10. [10]
    Kokini, K., DeJonge, J., Rangaraj, S. and Beardsley, B., Thermal shock of functionally graded thermal barrier coatings. In K. Trumble, K. Bowman, I. Reimanis and S. Sampath (Eds.), Ceramic Transactions, Vol. 114, American Ceramic Society, Westerville, OH, 2001, 213–221.Google Scholar
  11. [11]
    Jin, Z.H. and Noda, N., An edge crack in a nonhomogeneous material under thermal loading. Journal of Thermal Stresses, 1994, 17: 591–599.CrossRefGoogle Scholar
  12. [12]
    Jin, Z.H. and Batra, R.C., Stress intensity relaxation at the tip of an edge crack in a functionally graded material subjected to a thermal shock. Journal of Thermal Stresses, 1996, 19: 317–339.CrossRefGoogle Scholar
  13. [13]
    Erdogan, F. and Wu, B.H., Crack problems in FGM layers under thermal stresses. Journal of Thermal Stresses, 1996, 19(3): 237–265.CrossRefGoogle Scholar
  14. [14]
    Nemat-Alla, M. and Noda, N., Edge crack problem in a semi-infinite FGM plate with a bi-directional coefficient of thermal expansion under two-dimensional thermal leading. Acta Mechanica, 2000, 114(3–4): 211–229.CrossRefGoogle Scholar
  15. [15]
    Fujimoto, T. and Noda, N., Crack propagation in a functionally graded plate under thermal shock. Archive of Applied Mechanics, 2000, 70(6): 377–386.CrossRefGoogle Scholar
  16. [16]
    Jin, Z.H. and Paulino, G.H., Transient thermal stress analysis of an edge crack in a functionally graded material. International Journal of Fracture, 2001, 107: 73–98.CrossRefGoogle Scholar
  17. [17]
    Yildirim, B. and Erdogan, F., Edge crack problems in homogenous and functionally graded material thermal barrier coatings under uniform thermal loading. Journal of Thermal Stresses, 2004, 27(4): 311–329.CrossRefGoogle Scholar
  18. [18]
    Yildirim, B., Dag, S. and Erdogan, E., Three dimensional fracture analysis of FGM coatings under thermomechanical loading. International journal of Fracture, 2005, 132(4): 369–395.CrossRefGoogle Scholar
  19. [19]
    Jin, Z.H. and Luo, W.J., Thermal shock residual strength of functionally graded ceramics. Materials Science and Engineering A, 2006, 435–436: 71–77.CrossRefGoogle Scholar
  20. [20]
    Noda, N. and Guo, L.C., Thermal shock analysis for a functionally graded plate with a surface crack. Acta Mechanica, 2008, 195: 157–166.CrossRefGoogle Scholar
  21. [21]
    El-Borgi, S., Djemel, M.F. and Abdelmoula, R., A surface crack in a graded coating bonded to a homogeneous substrate under thermal loading. Journal of Thermal Stresses, 2008, 31(2): 176–194.CrossRefGoogle Scholar
  22. [22]
    Bao, G. and Wang, L., Multiple cracking in functionally graded ceramic-metal coatings. International Journal of Solids and Structures, 1995, 32: 2853–2871.CrossRefGoogle Scholar
  23. [23]
    Erdogan, F. and Ozturk, M., Periodic cracking of functionally graded coatings. International Journal of Engineering Science, 1995, 33: 2179–2195.MathSciNetCrossRefGoogle Scholar
  24. [24]
    Afsar, A.M. and Sekine, H., Cracking spacing effect on the brittle fracture characteristics of semi-infinite functionally graded materials with periodic edge cracks. International journal of fracture, 2000, 102: 61–66.CrossRefGoogle Scholar
  25. [25]
    Rangaraj, S. and Kokini, K., Multiple surface cracking and its effect on interface cracks in functionally graded thermal barrier coatings under thermal shock. ASME Journal of Applied Mechanics, 2003, 70: 234–245.CrossRefGoogle Scholar
  26. [26]
    Han, H.C. and Wang, B.L., Thermal shock resistance enhancement of functionally graded materials by multiple cracking. Acta Materialia, 2006, 54(4): 963–973.MathSciNetCrossRefGoogle Scholar
  27. [27]
    Jin, Z.H. and Feng, Y.Z., Thermal fracture resistance of a functionally graded coating with periodic edge cracks. Surface & Coatings technology, 2008, 202: 4189–4197.CrossRefGoogle Scholar
  28. [28]
    Jin, Z.H. and Feng, Y.Z., Effects of multiple cracking on the residual strength behavior of thermally shocked functionally graded ceramics. International Journal of Solids and Structures, 2008, 45: 5973–5986.CrossRefGoogle Scholar
  29. [29]
    Jin, Z.H., An asymptotic solution of temperature field in a strip a functionally graded material. International Communication in Heat and Mass Transfer, 2002, 29: 887–895.CrossRefGoogle Scholar
  30. [30]
    Erdogan, F., Gupta, G.D. and Cook, T.S., Numerical solution of singular integral equations. In Sih, G.C. (ed.), Mechanics of Fracture, Vol. 1: Methods of Analysis and Solutions of Crack Problems, Leyden, The Netherlands: Noordhoff International Publishing, 1973.Google Scholar
  31. [31]
    Jin, Z.H. and Batra, R.C., Some basic fracture mechanics concepts in functionally graded materials. Journal of the Mechanics and Physics of Solids, 1996, 44: 1221–1235.CrossRefGoogle Scholar
  32. [32]
    Reiter, T. and Dvorak, G.J., Micromechanical models for graded composite materials. Journal of the Mechanics and Physics of Solids, 1997, 45(8): 1281–1302.CrossRefGoogle Scholar
  33. [33]
    Aboudi, J., Pindera, M.J. and Arnold, S.M., Higher-order theory for functionally graded materials. Composites Part B — Engineering, 1999, 30: 777–832.CrossRefGoogle Scholar
  34. [34]
    Christensen, R.M., Mechanics of Composite Materials, New York: John Wiley & Sons, 1979.Google Scholar
  35. [35]
    Munz, D. and Fett, T., Ceramics, Berlin: Springer, 1999.CrossRefGoogle Scholar
  36. [36]
    Delale, F. and Erdogan, F., The crack problem for a non-homogeneous plane. ASME Journal of Applied Mechanics, 1983, 50(3): 609–614.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2009

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of MaineOronoUSA

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