Skip to main content
SpringerLink
Log in

Micromechanical modeling of fatigue crack initiation in polycrystals

  • Article
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

Fatigue is an important mechanism for the failure of components in many engineering applications and a significant proportion of the fatigue life is spent in the crack initiation phase. Although a large number of research work addresses fatigue life and fatigue crack growth, the problem of modeling crack initiation remains a major challenge in the scientific and engineering community. In the present work, a micromechanical model is developed and applied to study fatigue crack initiation. In particular, the effect of different hardening mechanisms on fatigue crack initiation is investigated. To accomplish this, a model describing the evolution of the particular dislocation structures observed under cyclic plastic deformation is implemented and applied on randomly generated representative microstructures to investigate fatigue crack initiation. Finally, a method is presented to calculate the S-N curve for the polycrystalline materials. With this work, it is demonstrated how the micromechanical modeling can support the understanding of damage and failure mechanisms occurring during fatigue.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

FIG. 1
FIG. 2
FIG. 3
FIG. 4
FIG. 5
FIG. 6
FIG. 7

Similar content being viewed by others

References

  1. H. Mughrabi: Microstructural fatigue mechanisms: Cyclic slip irreversibility, crack initiation, non-linear elastic damage analysis. Int. J. Fatigue 57, 2–8 (2013).

    Article  Google Scholar 

  2. K.J. Miller: The short crack problem. Fatigue Fract. Eng. Mater. Struct. 5 (3), 223–232 (1982).

    Article  Google Scholar 

  3. K. Tokaji, T. Ogawa, Y. Harada, and Z. Ando: Limitations of linear elastic fracture mechanics in respect of small fatigue cracks and microstructure. Fatigue Fract. Eng. Mater. Struct. 9 (1), 1–14 (1986).

    Article  Google Scholar 

  4. H-J. Christ and H. Mughrabi: Cyclic stress-strain response and microstructure under variable amplitube loading. Fatigue Fract. Eng. Mater. Struct. 19 (2–3), 335–348 (1996).

    Article  CAS  Google Scholar 

  5. K.J. Miller: The three thresholds for fatigue crack propagation. In Fatigue and Fracture Mechanics, Vol. 27, Robert S. Piascik, James C. Newman, Jr., and Norman E. Dowling, eds. (ASTM International, Conshohocken, Pennsylvania, 1997), pp. 267–286.

    Google Scholar 

  6. C. Bathias and P.C. Paris: Gigacycle Fatigue in Mechanical Practice, Vol. 185 (CRC Press, Boca Raton, Florida, 2004).

    Book  Google Scholar 

  7. H. Mughrabi: On the life-controlling microstructural fatigue mechanisms in ductile metals and alloys in the gigacycle regime. Fatigue Fract. Eng. Mater. Struct. 22 (7), 633–641 (1999).

    Article  CAS  Google Scholar 

  8. H. Mughrabi: On multi-stage fatigue life diagrams and the relevant life-controlling mechanisms in ultrahigh-cycle fatigue. Fatigue Fract. Eng. Mater. Struct. 25 (8–9), 755–764 (2002).

    Article  Google Scholar 

  9. D.L. McDowell, K. Gall, M.F. Horstemeyer, and J. Fan: Microstructure-based fatigue modeling of cast A356-T6 alloy. Eng. Fract. Mech. 70 (1), 49–80 (2003).

    Article  Google Scholar 

  10. D.L. McDowell: Multiaxial small fatigue crack growth in metals. Int. J. Fatigue 19 (93), 127–135 (1997).

    Article  Google Scholar 

  11. J. Lankford and F.N. Kusenberger: Initiation of fatigue cracks in 4340 steel. Metall. Trans. 4 (2), 553–559 (1973).

    Article  CAS  Google Scholar 

  12. H. Mughrabi: Cyclic slip irreversibilities and the evolution of fatigue damage. Metall. Mater. Trans. B 40 (4), 431–453 (2009).

    Article  CAS  Google Scholar 

  13. K. Tokaji and T. Ogawa: The growth behaviour of microstructurally small fatigue cracks in metals. Short Fatigue Cracks, ESIS 13, 85–99 (1992).

    CAS  Google Scholar 

  14. S. Suresh: Fatigue of Materials (Cambridge University Press, Cambridge, United Kingdom, 1998).

    Book  Google Scholar 

  15. V. Bennett and D.L. McDowell: Polycrystal orientation effects on microslip and mixed-mode behavior of microstructurally small cracks. In Mixed-mode Crack Behavior, K.J. Miller and D.L. McDowell, eds. (ASTM International, Conshohocken, Pennsylvania 1999), pp. 203–228.

    Chapter  Google Scholar 

  16. I. Simonovski, K-F. Nilsson, and L. Cizelj: The influence of crystallographic orientation on crack tip displacements of microstructurally small, kinked crack crossing the grain boundary. Comput. Mater. Sci. 39 (4), 817–828 (2007).

    Article  CAS  Google Scholar 

  17. S. Groh and H.M. Zbib: Advances in discrete dislocations dynamics and multiscale modeling. J. Eng. Mater. Technol. 131 (4), 41209 (2009).

    Article  Google Scholar 

  18. B. Künkler, O. Düber, P. Köster, U. Krupp, C-P. Fritzen, and H-J. Christ: Modelling of short crack propagation—Transition from stage I to stage II. Eng. Fract. Mech. 75 (3), 715–725 (2008).

    Article  Google Scholar 

  19. H. Mughbrabi, F.U. Ackermann, and K. Herz: Persistent slipbands in fatigued face-centered and body-centered cubic metals. In Fatigue Mechanisms, Jeffrey T. Fong, ed. (ASTM, Philadelphia, Pennsylvania 1979), pp. 69–95.

    Chapter  Google Scholar 

  20. R. Wang and H. Mughrabi: Secondary cyclic hardening in fatigued copper monocrystals and polycrystals. Mater. Sci. Eng. 63 (2), 147–163 (1984).

    Article  CAS  Google Scholar 

  21. G.M. Castelluccio: A Study on the Influence of Microstructure on Small Fatigue Cracks. PhD thesis, George W. Woodruff School of Mechanical Engineering, Georigia Institute of Technology, Atlanta, Georgia, 2012.

  22. M.A.M. Sharaf: The Microstructure Influence on Fatigue Life Variability in Structural Steels. PhD thesis. RWTH Aachen University, Aachen, Germany, 2015.

    Google Scholar 

  23. D.L. McDowell and F.P.E. Dunne: Microstructure-sensitive computational modeling of fatigue crack formation. Int. J. Fatigue 32 (9), 1521–1542 (2010).

    Article  CAS  Google Scholar 

  24. F.P.E. Dunne, A.J. Wilkinson, and R. Allen: Experimental and computational studies of low cycle fatigue crack nucleation in a polycrystal. Int. J. Plast. 23 (2), 273–295 (2007).

    Article  CAS  Google Scholar 

  25. C.P. Przybyla and D.L. McDowell: Microstructure-sensitive extreme value probabilities for high cycle fatigue of {Ni}-base superalloy {IN100}. Int. J. Plast. 26 (3), 372–394 (2010).

    Article  CAS  Google Scholar 

  26. U. Krupp, O. Düber, H-J. Christ, B. Künkler, A. Schick, and C-P. Fritzen: Application of the EBSD technique to describe the initiation and growth behaviour of microstructurally short fatigue cracks in a duplex steel. J. Microsc. 213 (3), 313–320 (2004).

    Article  CAS  Google Scholar 

  27. K. Tanaka and T. Mura: A dislocation model for fatigue crack initiation. J. Appl. Mech. 48 (1), 97–103 (1981).

    Article  Google Scholar 

  28. M. Boeff: Micromechanical modelling of fatigue crack initiation and growth. PhD thesis, Department of Mechanical Engineering, Ruhr Universität Bochum, Bochum, Germany, 2016.

    Google Scholar 

  29. E. Kröner: Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Arch. Ration. Mech. Anal. 4 (1), 273–334 (1959).

    Article  Google Scholar 

  30. E.H. Lee and D.T. Liu: Finite-strain elastic–plastic theory with application to plane-wave analysis. J. Appl. Phys. 38 (1), 19–27 (1967).

    Article  CAS  Google Scholar 

  31. E.H. Lee: Elastic–plastic deformation at finite strains. J. Appl. Mech. 36 (1), 1–6 (1969).

    Article  Google Scholar 

  32. J. Bonet and R.D. Wood: Nonlinear Continuum Mechanics for Finite Element Analysis (Cambridge University Press, 2008).

    Book  Google Scholar 

  33. A. Koester, A. Ma, and A. Hartmaier: Atomistically informed crystal plasticity model for body-centered cubic iron. Acta Mater. 60 (9), 3894–3901 (2012).

    Article  CAS  Google Scholar 

  34. F. Roters, P. Eisenlohr, L. Hantcherli, D.D. Tjahjanto, T.R. Bieler, and D. Raabe: Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Mater. 58 (4), 1152–1211 (2010).

    Article  CAS  Google Scholar 

  35. J.R. Rice: Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19 (6), 433–455 (1971).

    Article  Google Scholar 

  36. J.W. Hutchinson: Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. London, Ser. A 348 (1652), 101–127 (1976).

    Article  CAS  Google Scholar 

  37. H. Mughrabi: The long-range internal stress field in the dislocation wall structure of persistent slip bands. Phys. Status Solidi 104 (1), 107–120 (1987).

    Article  Google Scholar 

  38. T. Mayama and K. Sasaki: Investigation of subsequent viscoplastic deformation of austenitic stainless steel subjected to cyclic preloading. Int. J. Plast. 22 (2), 374–390 (2006).

    Article  CAS  Google Scholar 

  39. P. Evrard, I. Alvarez-Armas, V. Aubin, and S. Degallaix: Polycrystalline modeling of the cyclic hardening/softening behavior of an austenitic-ferritic stainless steel. Mech. Mater. 42 (4), 395–404 (2010).

    Article  Google Scholar 

  40. P. Evrard, V. Aubin, S. Degallaix, and D. Kondo: Formulation of a new single crystal law for modeling the cyclic softening. Mech. Res. Commun. 35 (8), 589–594 (2008).

    Article  Google Scholar 

  41. A. Manonukul and F.P.E. Dunne: High-and low-cycle fatigue crack initiation using polycrystal plasticity. Proc. R. Soc. London, Ser. A 460 (2047), 1881–1903 (2004).

    Article  CAS  Google Scholar 

  42. M. Boeff, F. Gutknecht, P.S. Engels, A. Ma, and A. Hartmaier: Formulation of nonlocal damage models based on spectral methods for application to complex microstructures. Eng. Fract. Mech. 147, 373–387 (2015).

    Article  Google Scholar 

  43. Sandia National Laboratories, CUBIT 13.2., 2013.

  44. K. Inal, J.L. Lebrun, and M. Belassel: Second-order stresses and strains in heterogeneous steels: Self-consistent modeling and X-ray diffraction analysis. Metall. Mater. Trans. A 35 (8), 2361–2369 (2004).

    Article  Google Scholar 

  45. S. Mahmoody: Micromechanical Modeling of Dual-Phase Steel Using a Rate-Dependet Crystal Plasticity Model (McGill University, Montreal, Canada, 2007).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-Universität Bochum, Bochum, 44801, Germany

    Martin Boeff, Hamad ul Hassan & Alexander Hartmaier

Authors
  1. Martin Boeff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamad ul Hassan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexander Hartmaier
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamad ul Hassan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Boeff, M., ul Hassan, H. & Hartmaier, A. Micromechanical modeling of fatigue crack initiation in polycrystals. Journal of Materials Research 32, 4375–4386 (2017). https://doi.org/10.1557/jmr.2017.384

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2017.384

Search

Navigation