Log in

Inclined Hole Under Different Loading Conditions: A Review of Recent Results

  • Published:
Strength of Materials Aims and scope

Three-dimensional (3D) elastic stress distributions in the vicinity of the sharp corners of an inclined diamond hole in a plate are investigated. A detailed 3D finite element model under different loading conditions is analyzed to study the intensity of different fracture modes due to the thickness effect. The stress results are compared with those provided by a recent theory which reduces the 3D governing equations of elasticity to a differential equation system, which includes a biharmonic equation and a harmonic equation. They provide the solution of the corresponding in-plane and out-of-plane notch problem, respectively, and have to be concurrently satisfied. Comparing numerical results and theoretical stress distributions, a good agreement is found.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. T. Nakamura and D. M. Parks, “Antisymmetrical 3-D stress field near the crack front of a thin elastic plate,” Int. J. Solids Struct., 25, 1411–1426 (1989).

    Article  Google Scholar 

  2. Z. H. ** and R. C. Batra, “A crack at the interface between a Kane–Mindlin plate and a rigid substrate,” Eng. Fract. Mech., 57, 343–354 (1997).

    Article  Google Scholar 

  3. M. Heyder, K. Kolk, and G. Kuhn, “Numerical and experimental investigations of the influence of corner singularities on 3D fatigue crack propagation,” Eng. Fract. Mech., 72, 2095–2105 (2005).

    Article  Google Scholar 

  4. T. R. Kane and R. D. Mindlin, “High-frequency extensional vibrations of plates,” J. Appl. Mech., 23, 277–283 (1956).

    Google Scholar 

  5. A. Kotousov, “On stress singularities at angular corners of plates of arbitrary thickness under tension,” Int. J. Fracture, 132, 29–36 (2005).

    Article  Google Scholar 

  6. A. Kotousov, “Fracture in plates of finite thickness,” Int. J. Solids Struct., 44, 8259–8273 (2007).

    Article  Google Scholar 

  7. P. Lazzarin and M. Zappalorto, “A three-dimensional stress field solution for pointed and sharply radiused V-notches in plates of finite thickness,” Fatigue Fract. Eng. Mater. Struct., 35, 1105–1119 (2012).

    Article  Google Scholar 

  8. L. P. Pook, “A finite element analysis of cracked square plates and bars under antiplane loading,” Fatigue Fract. Eng. Mater. Struct., 26, 533–541 (2003).

    Article  Google Scholar 

  9. L. P. Pook, “Finite element analysis of corner point displacements and stress intensity factors for narrow notches in square sheets and plates,” Fatigue Fract. Eng. Mater. Struct., 23, 979–992 (2000).

    Article  Google Scholar 

  10. L. P. Pook, “A note on corner point singularities,” Int. J. Fatigue, 53, 3–8 (1992).

    Google Scholar 

  11. F. Berto, P. Lazzarin, A. Kotousov, and S. Harding, “Out-of-plane singular stress fields in V-notched plates and welded lap joints induced by in-plane shear load conditions,” Fatigue Fract. Eng. Mater. Struct., 34, 291–304 (2011).

    Article  Google Scholar 

  12. M. L. Williams, “Stress singularities resulting from various boundary conditions in angular corners of plates in extension,” J. Appl. Mech., 19, 526–528 (1952).

    Google Scholar 

  13. P. Lazzarin and R. Tovo, “A unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches,” Int. J. Fracture, 78, 3–19 (1996).

    Article  Google Scholar 

  14. P. Lazzarin and R. Tovo, “A notch intensity factor approach to the stress analysis of welds,” Fatigue Fract. Eng. Mater. Struct., 21, 1089–1103 (1998).

    Article  Google Scholar 

  15. R. Gross and A. Mendelson, “Plane elastostatic analysis of V-notched plates,” Int. J. Fract. Mech., 8, 267–276 (1972).

    Article  Google Scholar 

  16. A. Seweryn and K. Molski, “Elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions,” Eng. Fract. Mech., 55, 529–556 (1996).

    Article  Google Scholar 

  17. M. Zappalorto and P. Lazzarin, “Three-dimensional elastic stress fields ahead of notches in thick plates under various loading conditions,” Eng. Fract. Mech., 108, 75–88 (2013).

    Article  Google Scholar 

  18. R. J. Hartranft and G. C. Sih, “An approximate three-dimensional theory of plates with application to crack problems,” Int. J. Eng. Sci., 8, 711–729 (1970).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to F. Berto.

Additional information

Translated from Problemy Prochnosti, No. 5, pp. 95 – 105, September – October, 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Berto, F., Afshar, R.H. Inclined Hole Under Different Loading Conditions: A Review of Recent Results. Strength Mater 48, 668–676 (2016). https://doi.org/10.1007/s11223-016-9810-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11223-016-9810-z

Keywords

Navigation