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Weight functions for multiple axial cracks in a coated hollow cylinder

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Abstract

In this paper, the weight functions for multiple axial cracks in a coated hollow cylinder have been investigated. The stress intensity factors (SIFs) for two reference loading cases were computed via the finite element method, which was then used to derive the weight functions. Dimensional analysis was carried out to reveal the dependence of dimensionless weight function on various important quantities such as normalized crack depth, crack spacing, and material constants. The results of such parameters dependence were presented in graphical forms and were eventually expressed by an empirical formula through a decoupled fitting method. Comparison was made on the SIF determination by the derived weight function and by other methods in literature, and an excellent agreement was found. The derived weight functions are expected to facilitate SIF calculation for a coated hollow cylinder with multiple axial cracks.

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Abbreviations

a :

Inner radius of the hollow cylinder

b :

Outer radius of the hollow cylinder

D 1, D 2, D 3 :

The coefficients of weight function to be determined

E 1, E 2 :

Young’s modulus

\({\overline{{E}}, \overline{{E}}_{1}}\) :

Plane strain modulus

F, F P, \({F_{\sigma}}\) :

Dimensionless shape factors

f(z):

The formula for a decoupled fitting method

G :

Shear modulus

h (x, l):

Weight function

l :

Crack depth

K, K I, K IP, \({K_{{\rm I}\sigma}}\) :

Stress intensity factors

n :

Crack number

P :

A single pair of force per thickness loaded at the crack mouth x = 0

P 1 :

Internal pressure of hollow cylinder

r q :

The distance from quarter point to the crack tip

s :

Crack spacing

t :

Thickness of coating

u q y :

The y-directional displacement for the quarter point on the free face of the crack

x :

The x-coordinate along the crack face

\({\mu_{1}}\), \({\mu_{2}}\) :

Poisson’s ratio

\({\sigma}\) :

Constant stress loaded at the crack face

\({\sigma_{\rm P}}\), \({\sigma_{\sigma}}\) :

The stress along the crack in the un-cracked body

\({\alpha}\), \({\beta}\) :

Dundurs’ elastic mismatch parameters

References

  1. Rooke D.P., Baratta F.I., Cartwright D.J.: Simple methods of determining stress intensity factors. Eng. Fract. Mech. 14, 397–426 (1981)

    Article  Google Scholar 

  2. Ehlers R.: Stress intensity factors and crack opening areas for axial through cracks in hollow cylinders under internal pressure loading. Eng. Fract. Mech. 25, 63–77 (1986)

    Article  Google Scholar 

  3. Perl M., Ashkenazi A.: Radial cracking of a thick-walled cylinder due to an internal thermal shock. Eng. Fract. Mech. 41, 597–605 (1992)

    Article  Google Scholar 

  4. Shahani A.R., Habibi S.E.: Stress intensity factors in a hollow cylinder containing a circumferential semi-elliptical crack subjected to combined loading. Int. J. Fract. 29, 128–140 (2007)

    MATH  Google Scholar 

  5. Li C.Q., Yang S.T.: Stress intensity factors for high aspect ratio semi-elliptical internal surface cracks in pipes. Int. J. Press. Vessel. Pip. 96–97, 13–23 (2012)

    Article  Google Scholar 

  6. Predan J., Mocilnik V., Gubeljak N.: Stress intensity factors for circumferential semi-elliptical surface cracks in a hollow cylinder subjected to pure torsion. Eng. Fract. Mech. 105, 152–168 (2013)

    Article  Google Scholar 

  7. Baratta F.I.: Stress intensity factors for internal multiple cracks in thick-walled cylinders stressed by internal pressure using load relief factors. Eng. Fract. Mech. 10, 691–697 (1978)

    Article  Google Scholar 

  8. Hutchinson J.W., Suo Z.: Mixed mode cracking in layered materials. Adv. Appl. Mech. 29, 63–191 (1992)

    Article  MATH  Google Scholar 

  9. Underwood J.H., Park A.P., Vigllante G.N., Cote P.J.: Thermal damage, cracking and rapid erosion of cannon bore coatings. J. Press. Vessel. Technol. 125, 299–304 (2003)

    Article  Google Scholar 

  10. Swanson S.R.: Finite-element solutions for a cracked two-layered elastic cylinder. Eng. Fract. Mech. 3, 283–289 (1971)

    Article  Google Scholar 

  11. Tang R.J., Erdogan F.: Stress intensity factors in a reinforced thick-walled cylinder. Int. J. Eng. Sci. 22, 867–879 (1984)

    Article  MATH  Google Scholar 

  12. Chen X.J., Zhang K., Chen G.N., Luo G.X.: Multiple axial cracks in a coated hollow cylinder due to thermal shock. Int. J. Solids Struct. 43, 6424–6435 (2006)

    Article  MATH  Google Scholar 

  13. Chen X.J., Chen G.N.: On the thermally induced cracking of a segmented coating deposited on the outer surface of a hollow cylinder. Surf. Coat. Technol. 203, 1114–1120 (2009)

    Article  Google Scholar 

  14. Bueckner H.F.: A novel principle for the computation of stress intensity factors. ZAMM 50, 529–546 (1970)

    MATH  MathSciNet  Google Scholar 

  15. Zheng X.J., Kiciak A., Glinka G.: Weight functions and stress intensity factors for internal surface semi-elliptical crack in thick-walled cylinder. Eng. Fract. Mech. 58, 207–221 (1997)

    Article  Google Scholar 

  16. Jones I.S., Rothwell G.: Reference stress intensity factors with application to weight functions for internal circumferential cracks in cylinders. Eng. Fract. Mech. 68, 435–454 (2001)

    Article  Google Scholar 

  17. Shahani A.R., Nabavi S.M.: Transient thermal stress intensity factors for an internal longitudinal semi-elliptical crack in a thick-walled cylinder. Eng. Fract. Mech. 74, 2585–2602 (2007)

    Article  Google Scholar 

  18. Nabavi S.M., Ghajar R.: Analysis of thermal stress intensity factors for cracked cylinders using weight function method. Int. J. Eng. Sci. 48, 1811–1823 (2010)

    Article  MATH  Google Scholar 

  19. Oliveira R., Wu X.R.: Stress intensity factors for axial cracks in hollow cylinders subjected to thermal shock. Eng. Fract. Mech. 27, 185–197 (1987)

    Article  Google Scholar 

  20. Fett T., Diegele E., Munz D., Rizzi G.: Weight functions for edge cracks in thin surface layers. Int. J. Fract. 81, 205–215 (1996)

    Article  Google Scholar 

  21. Schulze G.W., Erdogan F.: Periodic cracking of elastic coatings. Int. J. Solids Struct. 35, 3615–3634 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  22. Guo H.B., Vaben R., Stover D.: Atmospheric plasma sprayed thick thermal barrier coatings with high segmentation crack density. Surf. Coat. Technol. 186, 353–363 (2004)

    Article  Google Scholar 

  23. Zhou B., Kokini K.: Effect of preexisting surface cracks on the interfacial thermal fracture of thermal barrier coatings: an experimental study. Surf. Coat. Technol. 187, 17–25 (2004)

    Article  Google Scholar 

  24. Guo H.B., Kuroda S., Murakami H.: Segmented thermal barrier coatings produced by atmospheric plasma spraying hollow powders. Thin Solid Films 506-507, 136–139 (2006)

    Article  Google Scholar 

  25. Li H., Chen G., Zhang G., Zhang K., Luo G., Ye Z.: Degradation failure features of chromium-plated gun barrels with a laser-discrete-quenched substrate. Surf. Coat. Technol. 201, 9558–9564 (2007)

    Article  Google Scholar 

  26. Fett T., Mattheck C., Munz D.: On the calculation of crack opening displacement from the stress intensity factor. Eng. Fract. Mech. 27, 697–715 (1987)

    Article  Google Scholar 

  27. Fett T.: Direct determination of weight functions from reference loading cases and geometrical conditions. Eng. Fract. Mech. 42, 435–444 (1992)

    Article  Google Scholar 

  28. Tan Q.M.: Dimensional Analysis. University of Science and Technology of China, Hefei (2007)

    Google Scholar 

  29. Dundurs J.: Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading. J. Appl. Mech. 36, 650–652 (2007)

    Article  Google Scholar 

  30. Lynn P.P., Ingraffea A.R.: Transition elements to be used with quadratic point crack tip elements. Int. J. Numer. Meth. Eng. 12, 1031–1038 (1978)

    Article  Google Scholar 

  31. Bowie O.L., Freese C.E.: Elastoplastic plane-strain analysis for a circular hole in a uniaxial tensile field. Eng. Fract. Mech. 4, 315–320 (1972)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mechanics, University of Science and Technology Beijing, No. 30 Xueyuan Road, Beijing, 100083, People’s Republic of China

    Xuejun Chen & Yi You

  2. State Grid Xinjiang Electric Power Scientific Research Institute, No. 66 Changchunzhong Road, Urumqi, 830011, Xinjiang, People’s Republic of China

    Yi You

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  1. Xuejun Chen
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Correspondence to Xuejun Chen.

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Chen, X., You, Y. Weight functions for multiple axial cracks in a coated hollow cylinder. Arch Appl Mech 85, 617–628 (2015). https://doi.org/10.1007/s00419-014-0973-4

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  • DOI: https://doi.org/10.1007/s00419-014-0973-4

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