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Shrinkage and splitting of microcracks under pressure simulated by the finite-element method

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Abstract

The two-dimensional finite-element method is applied to analyze the shrinkage and splitting of microcracks regularly arranged on or perpendicular to a grain boundary under pressure. Grain-boundary and surface diffusions are coupled by the boundary conditions at the triple point of the microcrack surface and the grain boundary. The shrinkage and splitting processes for the two kinds of microcracks are revealed by detailed finite-element analyses. For the microcrack lying on a grain boundary, it first shrinks to a small void shape, then the void is split by the grain boundary and the two split voids assume a cylindrical shape under the capillary force of the surface. For the microcrack perpendicular to the grain boundary, it is split into two segments by the grain boundary during the early stage of shrinkage. Then, the split microcracks stop shrinking and evolve into two cylindrical channels with a circular section by the capillary force of the surface. These evolution processes are controlled by the applied pressure, microcrack spacing, ratio of grain-boundary diffusion to surface diffusion, and equilibrium dihedral angle, defined by surface and grain-boundary tensions. The influences of these controlled parameters on the evolution processes are numerically clarified based on a great number of finite-element analyses.

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References

  1. J. Rödel and A.M. Glaeser: in Sintering of Advanced Ceramics, C. Handwerker, J.E. Blendell, and W.A. Kaysser, eds., The American Ceramic Society, Westerville, OH, 1990, pp. 243–57.

    Google Scholar 

  2. A.G. Evans and E.A. Charles: Acta Metall., 1997, vol. 25, pp. 919–27.

    Google Scholar 

  3. J. Rödel and A.M. Glaeser: J. Am. Ceram. Soc., 1990, vol. 73 (3), pp. 592–601.

    Article  Google Scholar 

  4. J.D. Powers and A.M. Glaeser: J. Am. Ceram. Soc., 1993, vol. 75 (9), pp. 2225–34.

    Article  Google Scholar 

  5. B.J. Wanamaker, T.F. Wong, and B. Evans: J. Geophys. Res., 1990, vol. 95 (10), pp. 1563–41.

    Article  Google Scholar 

  6. S.H. Hickman and B. Evans: Phys. Chem. Miner., 1987, vol. 15, pp. 91–102.

    Article  CAS  Google Scholar 

  7. R.N. Singh and J.L. Routbort: J. Am. Ceram. Soc., 1979, vol. 62 (3–4), pp. 128–33.

    Article  CAS  Google Scholar 

  8. M.D. Drory and A.M. Glaeser: J. Am. Ceram. Soc., 1985, vol. 68 (1), pp. C-14–C-15.

    Article  CAS  Google Scholar 

  9. J. Svoboda and H. Riedel: Acta Metall. Mater., 1995, vol. 43 (2), pp. 499–506.

    Article  CAS  Google Scholar 

  10. C. Scott and V.B. Tran: Am. Ceram. Soc. Bull., 1985, vol. 64 (8), pp. 1129–31.

    CAS  Google Scholar 

  11. J. Rödel and A.M. Glaeser: in Interfacial Structures Properties and Design, M.H. Yoo, W.A.T. Clark, and C.L. Braint, eds., Materials Research Society, Pittsburgh, PA, 1988, pp. 485–90.

    Google Scholar 

  12. Z. Suo and W. Wang: J. Appl. Phys., 1994, vol. 76 (6), pp. 3410–21.

    Article  CAS  Google Scholar 

  13. W.C. Carter and A.M. Glaeser: Acta Metall., 1987, vol. 35 (1), pp. 237–45.

    Article  Google Scholar 

  14. Q. Ma: Scripta Mater., 1997, vol. 36, pp. 77–82.

    Article  Google Scholar 

  15. J.-H. Choy, S.A. Hackney, and J.K. Lee: J. Appl. Phys., 1995, vol. 77 (11), pp. 5647–54.

    Article  CAS  Google Scholar 

  16. F.A. Nichols: Acta Metall., 1968, vol. 16, pp. 103–13.

    Article  CAS  Google Scholar 

  17. J.K. Lee and T.H. Courtney: Metall. Trans. A, 1989, vol. 20A, pp. 1385–94.

    CAS  Google Scholar 

  18. D. Hull and R.E. Rimmer: Phil. Mag., 1959, vol. 4, pp. 673–87.

    CAS  Google Scholar 

  19. T.-J. Chuang and J.R. Rice: Acta Metall., 1973, vol. 21, pp. 1625–28.

    Article  Google Scholar 

  20. T.-J. Chuang, K.I. Kagawa, J.R. Rice, and L.B. Sills: Acta Metall., 1979, vol. 27, pp. 265–84.

    Article  CAS  Google Scholar 

  21. G.M. Pharr and W.D. Nix: Acta Metall., 1979, vol. 27, pp. 1615–31.

    Article  CAS  Google Scholar 

  22. L. Martinez and W.D. Nix: Metall. Trans., 1981, vol. 13A, pp. 427–37.

    Google Scholar 

  23. Y. Takahashi, K. Takahashi, and K. Nishiguchi: Acta Mater., 1991, vol. 39 (12), pp. 3199–3216.

    Article  CAS  Google Scholar 

  24. Y. Takahashi, K. Inoue, and K. Nishiguchi: Acta Mater., 1993, vol. 41 (11), pp. 3077–84.

    Article  CAS  Google Scholar 

  25. F.A. Nichols: J. Mater. Sci., 1976, vol. 11, pp. 1077–82.

    Article  Google Scholar 

  26. C.H. Hsueh, A.G. Evans, and R.L. Coble: Acta Metall., 1982, vol. 30 (7), pp. 1269–79.

    Article  Google Scholar 

  27. W.H. Yang and D.J. Srolovitz: Phys. Rev. Lett., 1993, vol. 71 (10), pp. 1593–96.

    Article  Google Scholar 

  28. B. Sun, Z. Suo, and A.G. Evans: J. Appl. Phys. Solids, 1994, vol. 42 (11), pp. 1653–77.

    Article  CAS  Google Scholar 

  29. W. Yang and Z. Suo: Acta Mech. Sinica, 1996, vol. 12 (2), pp. 144–57.

    Article  Google Scholar 

  30. Z. Suo: Adv. Appl. Mech., 1997, vol. 33, pp. 193–294.

    Article  Google Scholar 

  31. B. Sun, Z. Suo, and A.C.F. Cocks: Materials Research Society Symposia Proceedings, Materials Research Society, Pittsburgh, PA, 1996, vol. 403, p. 71.

    Google Scholar 

  32. H.J. Frost, C.V. Thompson, and D.T. Walton: Acta Metall. Mater., 1992, vol. 40, p. 779.

    Article  CAS  Google Scholar 

  33. A.C.F. Cocks and S.P.A. Gill: Acta Mater., 1996, vol. 44 (12), pp. 4765–75.

    Article  CAS  Google Scholar 

  34. B. Sun, Z. Suo, and W. Yang: Acta Mater., 1997, vol. 45 (5), pp. 1907–15.

    Article  CAS  Google Scholar 

  35. J.M. Huang and W. Yang: Model. Simul. Mater. Sci. Eng., 1999, vol. 7, pp. 87–105.

    Article  CAS  Google Scholar 

  36. C. Herring: in The Physics of Powder Metallurgy, W.E. Kingston, ed., McGraw-Hill, New York, NY, 1951, pp. 143–79.

    Google Scholar 

  37. J. Pan and A.C.F. Cocks: Acta Mater., 1995, vol. 43 (4), pp. 1395–1406.

    Article  CAS  Google Scholar 

  38. B. Sun and Z. Suo: Acta Mater., 1997, vol. 45, pp. 4953–62.

    Article  CAS  Google Scholar 

  39. W.D. Kingery and M. Berg: J. Appl. Phys., 1955, vol. 26 (10), pp. 1205–12.

    Article  CAS  Google Scholar 

  40. W.W. Mullins: J. Appl. Phys., 1956, vol. 27 (8), pp. 77–83.

    Article  Google Scholar 

  41. P.Z. Huang, Z.H. Li, and J. Sun: Modelling Simul. Mater. Sci. Eng., 2001, vol. 9, pp. 193–206.

    Article  Google Scholar 

  42. P.Z. Huang, Z.H. Li, and J. Sun: Comput. Mater. Sci., 2001, vol. 20, pp. 66–76.

    Article  Google Scholar 

  43. J. Svoboda and H. Riedel: Acta Metall. Mater., 1992, vol. 40 (11), pp. 2829–40.

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. the School of Civil Engineering and Mechanics, Shanghai Jiaotong University, 200240, Shanghai, People’s Republic of China

    Peizhen Huang (Doctor) & Zhonghua Li (Professor)

  2. the State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xian Jiaotong University, People’s Republic of China

    Jun Sun (Professor)

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  1. Peizhen Huang
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  2. Zhonghua Li
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  3. Jun Sun
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Huang, P., Li, Z. & Sun, J. Shrinkage and splitting of microcracks under pressure simulated by the finite-element method. Metall Mater Trans A 33, 1117–1124 (2002). https://doi.org/10.1007/s11661-002-0213-3

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  • DOI: https://doi.org/10.1007/s11661-002-0213-3

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