Advertisement

Science China Technological Sciences

, Volume 61, Issue 4, pp 542–550 | Cite as

Calculation of stress intensity factor in two-dimensional cracks by strain energy density factor procedure

  • Zhao Fang
  • AiQun Li
  • HaiYing Bao
  • Hao Wang
Article
  • 43 Downloads

Abstract

In order to calculate the stress intensity factor (SIF) of crack tips in two-dimensional cracks from the viewpoint of strain energy density, a procedure to use the strain energy density factor to calculate the SIF is proposed. In this paper, the procedure is presented to calculate the SIF of crack tips in mode I cracks, mode II cracks and I+II mixed mode cracks. Meanwhile, the results are compared to those calculated by traditional approaches or other approaches based on strain energy density and verified by theoretical solutions. Furthermore, the effect of mesh density near the crack tip is discussed, and the proper location where the strain energy density factor is calculated is also studied. The results show that the SIF calculated by this procedure is close to not only those calculated by other approaches but also the theoretical solutions, thus it is capable of achieving accurate results. Besides, the mesh density around the crack tip should meet such requirements that, in the circular area created, the first layer of singular elements should have a radius about 0.05 mm and each element has a circumferential directional meshing angle to be 15°–20°. Furthermore, for a single element around the crack tip, the strain energy density factor is suggested to be calculated in the location where half of the sector element’s radius from the crack tip.

Keywords

stress intensity factor two-dimensional crack strain energy density factor averaged strain energy density 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Griffith A A. The phenomena of rupture and flow in solids. Philos Trans R Soc A-Math Phys Eng Sci, 1921, 221: 163–198CrossRefGoogle Scholar
  2. 2.
    Irwin G R. Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech, 1957, 24: 361–364Google Scholar
  3. 3.
    Bao T F, Peng Y, Cong P J, et al. Analysis of crack propagation in concrete structures with structural information entropy. Sci China Tech Sci, 2010, 53: 1943–1948CrossRefzbMATHGoogle Scholar
  4. 4.
    Sagy A, Cohen G, Reches Z, et al. Dynamic fracture of granular material under quasi-static loading. J Geophys Res, 2006, 111: 170–176CrossRefGoogle Scholar
  5. 5.
    Wang Y, Li X, Zhang B, et al. Meso-damage cracking characteristics analysis for rock and soil aggregate with CT test. Sci China Tech Sci, 2014, 57: 1361–1371CrossRefGoogle Scholar
  6. 6.
    Kong X J, Zhang Y, Zou D G, et al. Seismic cracking analyses of two types of face slab for concrete-faced rockfill dams. Sci China Tech Sci, 2017, 60: 510–522CrossRefGoogle Scholar
  7. 7.
    Anderson T L. Fracture Mechanics: Fundamentals and Applications. Boca Raton: CRC Press, 2015. 43–45Google Scholar
  8. 8.
    Kuna M. FE-techniques for crack analysis in linear-elastic structures. In: Kuna M, Ed. Finite Elements in Fracture Mechanic. Solid Mechanics and Its Applications, vol 201. Dordrecht: Springer, 2013. 193–258CrossRefGoogle Scholar
  9. 9.
    Brian R. Fracture of Brittle Solids. 2nd Ed. Cambridge: Cambridge University Press, 1993. 2–5Google Scholar
  10. 10.
    Rice J R. A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech, 1968, 35: 379–386CrossRefGoogle Scholar
  11. 11.
    Lazzarin P, Berto F, Zappalorto M. Rapid calculations of notch stress intensity factors based on averaged strain energy density from coarse meshes: Theoretical bases and applications. Int J Fatigue, 2010, 32: 1559–1567CrossRefGoogle Scholar
  12. 12.
    Sih G C, Madenci E. Crack growth resistance characterized by the strain energy density function. Eng Fract Mech, 1983, 18: 1159–1171CrossRefGoogle Scholar
  13. 13.
    Xiao Y, Liu H. Elastoplastic constitutive model for rockfill materials considering particle breakage. Int J Geomech, 2016, 17: 04016041CrossRefGoogle Scholar
  14. 14.
    Xiao Y, Sun Y, Yin F, et al. Constitutive modeling for transparent granular soils. Int J Geomech, 2016, 17: 04016150CrossRefGoogle Scholar
  15. 15.
    Bhashyam G R. ANSYS Mechanical: A Powerful Nonlinear Simulation Tool. Canonsburg, PA: ANSYS Inc, 2002Google Scholar
  16. 16.
    Sari E, Zergoug M. FEM techniques comparison for SIF computing of cracked Plate. Arab J Sci Eng, 2015, 40: 1165–1171CrossRefGoogle Scholar
  17. 17.
    Rice J R. Fracture mechanics. Appl Mech Rev, 1985, 38: 1271–1275CrossRefGoogle Scholar
  18. 18.
    Lazzarin P, Berto F, Gomez F, et al. Some advantages derived from the use of the strain energy density over a control volume in fatigue strength assessments of welded joints. Int J Fatigue, 2008, 30: 1345–1357CrossRefGoogle Scholar
  19. 19.
    Berto F, Lazzarin P. A review of the volume-based strain energy density approach applied to V-notches and welded structures. Theor Appl Fract Mech, 2009, 52: 183–194CrossRefGoogle Scholar
  20. 20.
    Lazzarin P, Berto F, Elices M, et al. Brittle failures from U- and Vnotches in mode I and mixed, I+II, mode: A synthesis based on the strain energy density averaged on finite-size volumes. Fatigue Fract Eng Mater Struct, 2009, 32: 671–684CrossRefGoogle Scholar
  21. 21.
    Sih G C, Macdonald B. Fracture mechanics applied to engineering problems-strain energy density fracture criterion. Eng Fract Mech, 1974, 6: 361–386CrossRefGoogle Scholar
  22. 22.
    Sih G C. Strain-energy-density factor applied to mixed mode crack problems. Int J Fract, 1974, 10: 305–321CrossRefGoogle Scholar
  23. 23.
    Sih G C, Faria L, Popelar C H. Fracture mechanics methodology. J Appl Mech, 1985, 52: 500CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Civil EngineeringSoutheast UniversityNanjingChina
  2. 2.Beijing Advanced Innovation Center for Future Urban DesignBeijing University of Civil Engineering and ArchitectureBeijingChina

Personalised recommendations