SpringerLink
Log in

Three-Dimensional Computational Analysis of Stress State Transition in Through-Cracked Plates

  • Published:
Mathematics in Computer Science Aims and scope Submit manuscript

Abstract

Stress state is a main parameter within fracture mechanics. It has a major influence on different phenomena, namely those involving diffusion, plastic deformation, and brittle fracture. As is well-known, in the near-surface regions of a crack front, the plane stress state dominates, while at interior positions the plane strain state prevails. The main objective here is to examine the extent of surface regions in through-cracked planar geometries subjected to cyclic loading. Two constitutive material models were developed to characterise the stress state along the crack front. A new criterion based on the h stress triaxiality parameter was proposed to define the transition between surface and near-surface regions. Finally, a linear relation between the stable value of the extent of surface region and the maximum stress intensity factor was established.

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

Access this article

Log in via an institution

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cayón, A., Alvarez, J.A., Gutiérrez-Solana, F.: Influence of microstructure and triaxial stress states on hydrogen induced cracking. Anales de Mecanica de la Fractura 20, 273–8 (2003)

    Google Scholar 

  2. Webster, G.A., Ainsworth, R.A.: High temperature component life assessment.: Chapman Hall, UK (1994)

  3. Tong, J., Byrne, J., Hall, R., Aliabadi, M.H.: A comparison of corner notched and compact tension specimens for high temperature fatigue testing. In: Proc. conference engineering against fatigue, University of Sheffield, UK (1997)

  4. Antunes, F.V., Ferreira, J.A.M., Branco, C.M., Byrne, J.: Influence of stress state on high temperature fatigue crack growth in Inconel 718. Fatigue Fract. Eng. Mater. Struct. 24, 127–135 (2001)

    Article  Google Scholar 

  5. Van Stone, R.H., Cox, T.B., Low, J.R., Psioda, J.A.: Microstructural aspects of fracture by dimple rupture. Int Metal Rev 30, 157–179 (1985)

    Google Scholar 

  6. Branco, R., Costa, J.D., Antunes, F.V.: Low-cycle fatigue behaviour of 34CrNiMo6 high strength steel. Theoretical and Applied Fracture Mechanics 58, 28–34 (2012)

    Article  Google Scholar 

  7. Clausmeyer, H., Kussmaul, K., Roos, E.: Influence of stress state on the failure behaviour of cracked components made of steel. ASME. Appl Mech Rev 44, 77–92 (1991)

    Article  Google Scholar 

  8. Kim, J., Gao, X., Srivatsan, S.: Modelling of void growth in ductile solids: effects of stress triaxiality and initial porosity. Eng Fract Mech 71, 379–400 (2004)

    Article  Google Scholar 

  9. Fleck, N.A., Smith, R.A.: Crack closure - is it just a surface phenomenon? Int J Fract 4, 157–159 (1982)

    Google Scholar 

  10. Antunes, F.V., Chegini, A.G., Branco, R., Camas, D.: A numerical study of plasticity induced crack closure under plane strain conditions. International Journal of Fatigue 71, 75–86 (2015)

    Article  Google Scholar 

  11. Pippan, R., Kolednik, O., Lang, M.: A mechanism for plasticity-induced crack closure under plane strain conditions. Fatigue Fract Eng Mater Struct 17, 721–726 (1994)

    Article  Google Scholar 

  12. Antunes, F.V., Branco, R., Costa, J.D., Rodrigues, D.M.: Plasticity induced crack closure in Middle-Crack Tension specimen: numerical versus experimental. Fatigue & Fracture of Engineering Materials & Structures 33, 673–686 (2010)

    Article  Google Scholar 

  13. ASTM E399-09e2, Standard test method for linear-elastic plane-strain Fracture toughness K\(_{{\rm IC}}\) of metallic materials. ASTM Volume 03.01 metals (2009). doi:10.1520/E0399-09E02

  14. Wang, B., Hu, N., Kurobane, Y., Makino, Y., Lie, S.T.: Damage criterion and safety assessment approach to tubular joints. Engineering Structures 22, 424–434 (2000)

    Article  Google Scholar 

  15. Chen, C.R., Kolednik, O., Heerens, J., Fischer, F.D.: Three-dimensional modeling of ductile crack growth: Cohesive zone parameters and crack tip triaxiality. Engineering Fracture Mechanics 72, 2072–2094 (2005)

    Article  Google Scholar 

  16. Anvari, M., Scheider, I., Thaulow, C.: Simulation of dynamic ductile crack growth using strain-rate and triaxiality-dependent cohesive elements. Engineering Fracture Mechanics 73, 2210–2228 (2006)

    Article  Google Scholar 

  17. Kim, Y.-J., Kim, J.-S., Cho, S.-M.: 3-D constraint effects on J testing and crack tip constraint in M(T), SE(B), SE(T) and C(T) specimens: numerical study. Engineering Fracture Mechanics 71, 1203–1218 (2004)

    Article  Google Scholar 

  18. Mirone, G.: Role of stress triaxiality in elastoplastic characterization and ductile failure prediction. Engineering Fracture Mechanics 74, 1203–1221 (2007)

    Article  Google Scholar 

  19. Bakker, A.: Three-dimensional constraint effects on stress intensity distributions in plate geometries with through-thickness cracks. Fatigue and Fracture of Engineering Materials and Structures 15, 1051–1069 (1992)

    Article  Google Scholar 

  20. Kotousov, A., Wang, C.H.: Three dimensional stress constraint in an elastic plate with a notch. International Journal of Solids and Structures 39, 4311–4326 (2002)

    Article  MATH  Google Scholar 

  21. Berto, F., Lazzarin, P., Wang, C.: Three-dimensional linear elastic distributions of stress and strain energy density ahead of V-shaped notched in plates of arbitrary thickness. International Journal of Fracture 127, 265–282 (2004)

    Article  MATH  Google Scholar 

  22. Branco, R., Antunes, F.V., Costa, J.D.: Notched M(T) specimen for plane strain studies. International Journal of Fatigue 58, 28–39 (2014)

    Article  Google Scholar 

  23. Guo, W.: Three-dimensional analyses of plastic constraint for through-thickness cracked bodies. Engineering Fracture Mechanics 62, 383–407 (1999)

    Article  Google Scholar 

  24. She, C., Guo, W.: The out-of-plane constraint of mixed-mode cracks in thin elastic plates. Intermational Journal of Solids and Structures 44, 3021–3034 (2007)

    Article  MATH  Google Scholar 

  25. Zhao, J., Guo, W., She, C.: The in-plane and out-of-plane stress constraint factors and K-T-Tz description of stress field near the border of a semi-elliptical surface crack. International Journal of Fatigue 29, 435–443 (2007)

    Article  MATH  Google Scholar 

  26. Zhang, B., Guo, W.: Three-dimensional stress state around quarter-elliptical corner cracks in elastic plates subjected to uniform tension loading. Engineering Fracture Mechanics 74, 386–398 (2007)

    Article  Google Scholar 

  27. Yang, Z.: Stress and strain concentration factors for tension bars of circular cross-section with semicircular groove. Engineering Fracture Mechanics 76, 1683–1690 (2009)

    Article  Google Scholar 

  28. Yu, P., She, C., Guo, W.: Equivalent thickness conception for corner cracks. International Journal of Solids and Structures 47, 2123–2130 (2010)

    Article  MATH  Google Scholar 

  29. Burton, W.S., Sinclair, G.B., Solecki, J.S., Swedlow, J.L.: On the implications for LEFM of the three-dimensional aspects in some crack/surface intersection problems. International Journal of Fracture 25, 3–32 (1984)

    Article  Google Scholar 

  30. Narayana, K.B., Dattaguru, B., Ramamurthy, T.S., Vijayakumar, K.: A General procedure for modified crack closure integral in 3D problems with cracks. Engineering Fracture Mechanics 48, 167–176 (1994)

    Article  Google Scholar 

  31. Antunes, F.V., Ferreira, J.A.M., Branco, C.M., Byrne, J.: Stress intensity factor solutions for corner cracks under mode I loading. Fatigue and Fracture of Engineering Materials and Structures 23, 81–90 (2000)

    Article  Google Scholar 

  32. Camas, D., Garcia-Manrique, J., Gonzalez-Herrera, A.: Numerical study of the thickness transition in bi-dimensional specimen cracks. International Journal of Fatigue 33, 921–928 (2011)

    Article  Google Scholar 

  33. Lopez-Crespo, P., Withers, P.J., Yusof, F., Dai, H., Steuwer, A., Kelleher, J.F., Buslaps, T.: Overload effects on fatigue crack-tip fields under plane stress conditions: surface and bulk analysis. Fatigue Fract Engng Mater Struct 36, 75–84 (2012)

    Article  Google Scholar 

  34. Saverio F.: Three-dimensional modelling of plasticity induced crack closure in the propagation of a fatigue crack in 304L steel. Ecole Nationale Supérieure de Mécanique et d’Aérotechnique, ENSMA, France [in French] (2014)

  35. von Mises, R.V.: Mechanik der festen korper im plastic-deformablen zustand. Nachrichten vos der koniglichen gellesschaft des winssenschaftenzu Gottingen. Mathematisch-physikalische klasse, 582–592 (1913)

  36. Swift, H.W.: Plastic instability under plane stress. J Mech Phys Solids 1, 1–18 (1952)

    Article  Google Scholar 

  37. Branco, R., Antunes, F.V., Costa, J.D.: Lynx: A user-friendly computer application for simulating fatigue growth of planar cracks using FEM. Computer Applications in Engineering Education 22, 375–569 (2014)

    Article  Google Scholar 

  38. Menezes, L.F., Teodosiu, C.: Three-dimensional numerical simulation of the deep drawing process using solid finite elements. J Mater Process Technol 97, 100–106 (2000)

    Article  Google Scholar 

  39. Oliveira, M.C., Alves, J.L., Menezes, L.F.: Algorithms and Strategies for Treatment of Large Deformation Frictional Contact in the Numerical Simulation of Deep Drawing Process. Arch Comput Method E 15, 113–162 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  40. Branco, R., Antunes, F.V., Costa, J.D.: Lynx: New tool to model mode-I fatigue crack propagation. Proceedings of 4th International Conference on Crack Paths (CP2012), pages 735-742, 19-21 September, Gaeta, Italy, ISBN: 9788895940441 (2012)

  41. Antunes, F.V., Rodrigues, D.M.: Numerical simulation of plasticity induced crack closure: Identification and discussion of parameters. Engineering Fracture Mechanics 75, 3101–3120 (2008)

    Article  Google Scholar 

  42. Kotousov, A., Lazzarin, P., Berto, F., Harding, S.: Effect of the thickness on elastic deformation and quasi-brittle fracture of plate components. Engineering Fracture Mechanics 77, 1665–1681 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CEMUC, Department of Mechanical Engineering, University of Coimbra, Coimbra, Portugal

    Rúben Maia, F. V. Antunes & M. C. Oliveira

  2. Department of Mechanical Engineering, ISEC, Polytechnic Institute of Coimbra, Coimbra, Portugal

    Ricardo Branco

  3. School of Mechanical Engineering, The University of Adelaide, Adelaide, SA, 5005, Australia

    Andrei Kotousov

Authors
  1. Rúben Maia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ricardo Branco
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. V. Antunes
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. C. Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Andrei Kotousov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ricardo Branco.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maia, R., Branco, R., Antunes, F.V. et al. Three-Dimensional Computational Analysis of Stress State Transition in Through-Cracked Plates. Math.Comput.Sci. 10, 343–352 (2016). https://doi.org/10.1007/s11786-016-0267-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11786-016-0267-z

Keywords

Mathematics Subject Classification

Search

Navigation