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Relationship of stress intensity factors for plane cracks in isotropic and transversally isotropic media

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Abstract

An interrelationship between the stress intensity factors for plane cracks in isotropic and transversally isotropic media is found for symmetric and obliquely symmetric force and symmetric temperature loadings. It is shown that the stress intensity factors for a plane crack in a transversally isotropic material can be obtained using standard formulas for the transition from the stress intensity factor for the corresponding problem in the case of an isotropic material. As examples, stress intensity factors are found for a circular crack, for a periodic system of circular cracks in a transversally isotropic material under force and temperature loading, etc.

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References

  1. A. E. Andreikov,Spatial Problems in the Fracture Theory [in Russian], Kiev (1982).

  2. R. V. Gol’dshtein and V. M. Entov,Qualitative Methods in Continuum Mechanics [in Russian], Moscow (1989).

  3. V. S. Kirilyuk, “Interrelation of problems in the theories of elasticity and thermoelasticity for isotropic and transversally isotropic media with coplanar cracks under symmetric loading,”Prikl. Mekh.,31, No. 12, 51–60 (1995).

    MathSciNet  Google Scholar 

  4. Yu. M. Kobzar’, “Representation of solutions of static problems in the thermoelasticity of transversally isotropic bodies,” in:Proc. XI-th Conf. of Young Scientists of the Institute of Mechanics of the Ukrainian Academy of Sciences, Kiilov, May 27–30, 1986, pp. 492–495. Deposited in VINITI, July 28, 1986, No. 5507-V.

  5. V. V. Panasyuk (ed.),Fracture Mechanics and the Strength of Materials: A Handbook in 4 Volumes [in Russian], Kiev (1988), M. P. Savruk, Vol. 2,Stress Intensity Factors in Media with Cracks (1988).

  6. Yu. N. Podil’chuk, “Stressed and thermally stressed state of transversally isotropic bodies with elliptical and parabolic cracks,”Prikl. Mekhanika. 29, No. 10, 26–36 (1993).

    Google Scholar 

  7. Yu. N. Podil’chuk, “Exact analytic solutions of three dimensional boundary value problems in the statics of transversally isotropic bodies of canonical form (A review),”Prikl. Mekh.,33, No. 10, 3–30 (1997).

    MathSciNet  Google Scholar 

  8. Yu. Murakami (ed.),Handbook of Stress Intensity Factors, Vol 2, [Russian translation], Moscow (1990).

  9. H. A. Ellior, “Three-dimensional stress distributions in hexagonal aeolotropic crystals,”Proc. Cambridge Soc. 44, 522–533 (1948).

    Article  Google Scholar 

  10. M. K. Kassir and G. C. Sih,Three-Dimensional Crack Problems, (Mechanics of Fracture, Vol. 2), Leyden (1975).

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Authors
  1. V. S. Kirilyuk
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Additional information

Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 3–16, 1999.

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Kirilyuk, V.S. Relationship of stress intensity factors for plane cracks in isotropic and transversally isotropic media. J Math Sci 101, 2727–2736 (2000). https://doi.org/10.1007/BF02918822

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  • DOI: https://doi.org/10.1007/BF02918822

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