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Consistent application of path-independent interaction integrals to arbitrary curved crack faces

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Abstract

The interaction integral (I-integral) method is a numerical technique based on the theory of path-independent energy conservation integrals, efficiently and accurately yielding stress intensity factors (SIF) for crack loading analyses. The drawback of the method, however, is that the requirement of auxiliary fields, which are commonly taken from asymptotic crack tip solutions, impedes a straightforward application to curved crack paths unless the integration contour is contracted to the crack tip. Thus, in hitherto available literature, fracture mechanical analyses based on the I-integral have been restricted to straight cracks under mixed-mode loading. This paper presents consistent approaches for the calculation of the I-integral in homogeneous, plane structures with arbitrary curved cracks based on finite integration contours. Relations between both coordinates I k of the interaction integral and SIF are derived. If crack face integrals are necessary to maintain path independence, special numerical treatment is required. Results are presented and verified by comparing the loading quantities from the I-integral to values calculated by conventional methods.

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References

  1. Barsoum R.: On the use of isoparametric finite elements in linear fracture mechanics. Int. J. Numer. Methods Eng. 10, 25–37 (1976)

    Article  MATH  Google Scholar 

  2. Bergez D.: Determination of stress intensity factors by use of path-independent integrals. Mech. Res. Commun. 1, 179–180 (1974)

    Article  MATH  Google Scholar 

  3. Budiansky B., Rice J.: Conservation laws and energy-release rates. J. Appl. Mech. 40, 201–203 (1973)

    Article  MATH  Google Scholar 

  4. Cherepanov G.: Crack propagation in continuous media. J. Appl. Math. Mech. 31, 476–488 (1967)

    Article  Google Scholar 

  5. Eshelby J.: The force on an elastic singularity. Philos. Trans. A 244, 87–112 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  6. Eshelby J.: The elastic energy-momentum tensor. J. Elast. 5, 321–335 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gosz M., Moran B.: An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions. Eng. Fract. Mech. 66, 299–319 (2002)

    Article  Google Scholar 

  8. Gosz M., Dolbow J., Moran B.: Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks. Int. J. Solids Struct. 35, 1763–1783 (1998)

    Article  MATH  Google Scholar 

  9. Gross D., Seelig T.: Fracture Mechanics. 2nd edn. Springer, Berlin (2011)

    Book  Google Scholar 

  10. Henshell R., Shaw K.: Crack tip finite elements are unnecessary. Int. J. Numer. Methods Eng. 9, 495–507 (1975)

    Article  MATH  Google Scholar 

  11. Herrmann A.G., Herrmann G.: On energy release rates for a plane crack. J. Appl. Mech. 48, 525–528 (1981)

    Article  MATH  Google Scholar 

  12. Judt P., Ricoeur A.: Accurate loading analyses of curved cracks under mixed-mode conditions applying the J-integral. Int. J. Fract. 182, 53–66 (2013)

    Article  Google Scholar 

  13. Kim J., Paulino G.: The interaction integral for fracture of orthotropic functionally graded materials: evaluation of stress intensity factors. Int. J. Solids Struct. 40, 3967–4001 (2003)

    Article  MATH  Google Scholar 

  14. Kuna M.: Finite Elements in Fracture Mechanics. Springer, Dordrecht (2013)

    Book  MATH  Google Scholar 

  15. Moës N., Gravouil A., Belytschko T.: Non-planar 3d crack growth by the extended finite element and level sets—part i: mechanical model. Int. J. Numer. Methods Eng. 53, 2549–2568 (2002)

    Article  MATH  Google Scholar 

  16. Moghaddam A., Ghajar R., Alfano M.: Finite element evaluation of stress intensity factors in curved non-planar cracks in fgms. Mech. Res. Commun. 38, 17–23 (2011)

    Article  MATH  Google Scholar 

  17. Muskhelishvili N.: Some Basic Problems of the Mathematical Theory of Elasticity. Nordhoff International Publishing, Leyden (1977)

    Book  Google Scholar 

  18. Rice J.: A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35, 379–386 (1968)

    Article  Google Scholar 

  19. Rouzegar S., Mirzaei M.: A comparative study on 2D crack modelling using the extended finite element method. Mechanika 19, 390–397 (2013)

    Article  Google Scholar 

  20. Rybicki E., Kanninen M.: A finite element calculation of stress intensity factors by a modified crack closure integral. Eng. Fract. Mech. 9, 931–938 (1977)

    Article  Google Scholar 

  21. Stern M., Becker E., Dunham R.: A contour integral computation of mixed-mode stress intensity factors. Int. J. Fract. 12, 359–368 (1976)

    Google Scholar 

  22. Walters M., Paulino G., Dodds R.: Interaction integral procedures for 3-D curved cracks including surface tractions. Eng. Fract. Mech. 72, 1635–1663 (2005)

    Article  Google Scholar 

  23. Wang S., Yau J., Corten H.: A mixed-mode crack analysis of rectilinear anisotropic solids using conservation laws of elasticity. Int. J. Fract. 16, 247–259 (1980)

    Article  MathSciNet  Google Scholar 

  24. Williams M.: On the stress distribution at the base of a stationary crack. J. Appl. Mech. 24, 109–114 (1957)

    MathSciNet  MATH  Google Scholar 

  25. Yu H., Wu L., Guo L., Wu H., Du S.: An interaction integral method for 3D curved cracks in nonhomogeneous materials with complex interfaces. Int. J. Solids Struct. 47, 2178–2189 (2010)

    Article  MATH  Google Scholar 

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  1. Institute of Mechanics, University of Kassel, 34125, Kassel, Germany

    Paul O. Judt & Andreas Ricoeur

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  1. Paul O. Judt
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  2. Andreas Ricoeur
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Correspondence to Paul O. Judt.

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Judt, P.O., Ricoeur, A. Consistent application of path-independent interaction integrals to arbitrary curved crack faces. Arch Appl Mech 85, 13–27 (2015). https://doi.org/10.1007/s00419-014-0897-z

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