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Weibull statistical fracture theory for the fracture of ceramics

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Abstract

The Weibull statistical fracture theory is widely applied to the fracture of ceramic materials. The foundations of the Weibull theory for brittle fracture are reviewed. This theory predicts that brittle fracture strength is a function of size, stress distribution, and stress state. Experimental multiaxial loading results for A12O3 tubes are compared to the stress state predictions of the Weibull theory. For the most part, the Weibull theory yields reasonable predictions, although there may be some difficulties in dealing with shear stress effects on fracture.

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References

  1. W. Weibull: “A Statistical Theory of the Strength of Materials”, Ingenioersvetenskapsakad., Handl., 1939, no. 151, 45 pp.

    Google Scholar 

  2. W. Weibull: “The Phenomenon of Rupture in Solids”, Ingenioersvetenskapsakad., Handl., 1939, no. 153, 55 pp.

    Google Scholar 

  3. J.J. Petrovic and M.G. Stout: “Fracture of A12O3 in Combined Tension/Torsion: I. Experiments”,J. Amer. Ceram. Soc, 1981, vol. 64, pp. 656–60.

    Article  CAS  Google Scholar 

  4. J. J. Petrovic and M.G. Stout: “Fracture of A12O3 in Combined Tension/Torsion: II. Weibull Theory”,J. Amer. Ceram. Soc, 1981, vol. 64, pp. 661–66.

    Article  CAS  Google Scholar 

  5. M. G. Stout and J. J. Petrovic: “Multiaxial Loading Fracture of A12O3 Tubes: I. Experiments”,J. Amer. Ceram. Soc, 1984, vol 67, pp. 14–18.

    Article  Google Scholar 

  6. J. J. Petrovic and M. G. Stout: “Multiaxial Loading Fracture of A12O3 Tubes: II. Weibull Theory and Analysis”,J. Amer. Ceram. Soc, 1984, vol. 67, pp. 18–23.

    Article  Google Scholar 

  7. S. B. Batdorf and J. G. Crose: “A Statistical Theory for the Fracture of Brittle Structures Subjected to Non-Uniform Polyaxial Stresses”,J. Appl. Mech., 1974, vol. 41, pp. 459–64.

    Google Scholar 

  8. A. G. Evans: “A General Approach for the Statistical Analysis of Multiaxial Fracture”,J. Amer. Ceram. Soc, 1978, vol. 61, pp. 302–08.

    Article  CAS  Google Scholar 

  9. Fracture, An Advanced Treatise, H. Liebowitz, ed., Academic Press, New York, NY, 1968, vol. II, p. 615.

    Google Scholar 

  10. E. K. Priddle: “Effect of Multiaxial Stresses on the Fracture Strength of Silicon Carbide”,J. Strain Anal., 1969, vol. 4, pp. 81–87.

    Google Scholar 

  11. J.J. Petrovic and M.G. Mendiratta: “Mixed-Mode Fracture From Controlled Surface Flaws in Hot-Pressed Si2N4,J. Amer. Ceram. Soc, 1976, vol. 59, pp. 163–67.

    Article  CAS  Google Scholar 

  12. J. J. Petrovic and M. G. Mendiratta: “Correction of Mixed-Mode Fracture From Controlled Surface Flaws in Hot-Pressed Si2N4”,J. Amer. Ceram. Soc, 1977, vol. 60, p. 463.

    Article  Google Scholar 

  13. S.W. Freiman, A.C. Gonzalez, and J.J. Mecholsky: “Mixed-Mode Fracture in Soda-Lime Glass”,J. Amer. Ceram. Soc, 1979, vol. 62, pp. 206–08.

    Article  CAS  Google Scholar 

  14. J.J. Petrovic: “Controlled Surface Flaw Fracture in Tension and Torsion”, inFracture Mechanics of Ceramics, R. C. Bradt, A. G. Evans, D. P. H. Hasselman, and F. F. Lange, eds., Plenum Press, New York, NY, 1983, vol. 6, pp. 63–75.

    Google Scholar 

  15. D.B. Marshall: “Mechanisms of Failure from Surface Flaws in Mixed-Mode Loading”,J. Amer. Ceram. Soc, 1984, vol. 67, pp. 110–16.

    Article  Google Scholar 

  16. J. J. Petrovic: “Mixed-Mode Fracture of Hot-Pressed Si2N4”,J. Amer. Ceram. Soc, 1985, vol. 68, pp. 348–55.

    Article  CAS  Google Scholar 

  17. D. K. Shetty, A. R. Rosenfield, and W. H. Duckworth: “Mixed-Mode Fracture of Ceramics in Diametral Compression”,J. Amer. Ceram. Soc, 1986, vol. 69, pp. 437–43.

    Article  CAS  Google Scholar 

  18. S. B. Batdorf and H. L. Heinisch, Jr.:“Weakest Link Theory Reformulated for Arbitrary Fracture Criterion”,J. Amer. Ceram. Soc, 1978, vol. 61, pp. 355–58.

    Article  Google Scholar 

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Authors and Affiliations

  1. Group MST-6: Materials Technology, Metallurgy and Ceramics, Materials Science and Technology Division, Los Alamos National Laboratory, 87545, Los Alamos, NM

    J. J. Petrovic (Associate Group Leader)

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  1. J. J. Petrovic
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Additional information

This paper is based on a presentation made at the symposium “Stochastic Aspects of Fracture” held at the 1986 annual AIME meeting in New Orleans, LA, on March 2-6, 1986, under the auspices of the ASM/MSD Flow and Fracture Committee.

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Petrovic, J.J. Weibull statistical fracture theory for the fracture of ceramics. Metall Trans A 18, 1829–1834 (1987). https://doi.org/10.1007/BF02647012

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