Skip to main content
SpringerLink
Log in

On the numerical modeling of nucleation and growth of microstructurally short cracks in polycrystals under cyclic loading

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

Abstract

In the scope of this work, a micromechanical model based on the crystal plasticity finite element method is proposed and applied to describe the nucleation and growth of microstructurally short fatigue cracks in polycrystalline materials under cyclic loads. The microstructure is generated in the form of a representative volume element of a polycrystalline material with equiaxed grains having columnar structure along thickness and random crystallographic texture. With this model, we investigate the influence of loading amplitude on the crack growth behavior. It is shown that for smaller strain amplitudes, a single crack nucleates and propagates, while for larger strain amplitudes several independent crack nucleation sites form, from which microcracks start propagating. It is also observed that the global plastic strain amplitude decreases from the initial to the final cycle, during total strain-controlled loading. However, this can even increase the crack growth rate because the crack advance is governed by the local plastic slip which accumulates at the crack tip over the number of cycles. With this work, it is shown that micromechanical modeling can strongly improve our understanding of the mechanisms of short-crack nucleation and growth under fatigue loading.

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

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8

Similar content being viewed by others

References

  1. H.J. Christ, C.P. Fritzen, and P. Köster: Micromechanical modeling of short fatigue cracks. Curr. Opin. Solid State Mater. Sci. 18, 205 (2014).

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. O. Aslan, S. Quilici, and S. Forest: Numerical modeling of fatigue crack growth in single crystals based on microdamage theory. Int. J. Damage Mech. 20, 681 (2011).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  6. K. Tokaji and T. Ogawa: The growth behaviour of microstructurally small fatigue cracks in metals. Mech. Eng. Publ. 13, 85 (1992).

    CAS  Google Scholar 

  7. S. Suresh: Fatigue of Materials (Cambridge University Press, Cambridge, U.K., 1998).

    Book  Google Scholar 

  8. V. Bennett and D.L. McDowell: Mixed-Mode Crack Behavior (ASTM International, West Conshohocken, Pennsylvania, 1999); pp. 203–228.

    Book  Google Scholar 

  9. 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, 817 (2007).

    Article  CAS  Google Scholar 

  10. 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, 313 (2004).

    Article  CAS  Google Scholar 

  11. 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, 372 (2010).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  13. Y. Li, V. Aubin, C. Rey, and P. Bompard: Microstructural modeling of fatigue crack initiation in austenitic steel 304L. Procedia Eng. 31, 541 (2012).

    Article  CAS  Google Scholar 

  14. N. Marchal, S. Forest, L. Rémy, and S. Duvinage: Fatigue and creep. Local Approach to Fracture EUROMECH-MECAMAT 2006, 9th European Mechanics of Materials Conference, D.S.J. Besson and D. Moinereau, ed. (Presses des Mines de Paris, Moret Sur Loing, France, 2006); pp. 353–358.

    Google Scholar 

  15. L.G. Zhao, N.P. O’Dowd, and E.P. Busso: A coupled kinetic-constitutive approach to the study of high temperature crack initiation in single crystal nickel-base superalloys. J. Mech. Phys. Solids 54, 288 (2006).

    Article  CAS  Google Scholar 

  16. L.G. Zhao, J. Tong, and J. Byrne: The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited. Fatigue Fract. Eng. Mater. Struct. 27, 19 (2004).

    Article  Google Scholar 

  17. J. Tong, B. Lin, Y.W. Lu, K. Madi, Y.H. Tai, J.R. Yates, and V. Doquet: Near-tip strain evolution under cyclic loading: In situ experimental observation and numerical modelling. Int. J. Fatigue 71, 45 (2015).

    Article  CAS  Google Scholar 

  18. J.D. Carroll, W. Abuzaid, J. Lambros, and H. Sehitoglu: High resolution digital image correlation measurements of strain accumulation in fatigue crack growth. Int. J. Fatigue 57, 140 (2013).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  20. 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 (1986).

    Article  Google Scholar 

  21. J.R. Rice: Tensile crack tip fields in elastic-ideally plastic crystals. Mech. Mater. 6, 317 (1987).

    Article  Google Scholar 

  22. K. Gall, H. Sehitoglu, and Y. Kadioglu: FEM study of fatigue crack closure under double slip. Acta Mater. 44, 3955 (1996).

    Article  CAS  Google Scholar 

  23. G.R. Leverant and M. Gell: The influence of temperature and cyclic frequency on the fatigue fracture of cube oriented nickel-base superalloy single crystals. Metall. Trans. A 6, 367 (1975).

    Article  Google Scholar 

  24. J.S. Crompton and J.W. Martin: Crack tip plasticity and crack growth in a single-crystal superalloy at elevated temperatures. Mater. Sci. Eng. 64, 37 (1984).

    Article  CAS  Google Scholar 

  25. P.B. Aswath: Effect of orientation on crystallographic cracking in notched nickel-base superalloy single crystal subjected to far-field cyclic compression. Metall. Mater. Trans. A 25, 287 (1994).

    Article  Google Scholar 

  26. A.L. Gurson: Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99, 2 (1977).

    Article  Google Scholar 

  27. V. Tvergaard and A. Needleman: Analysis of the cup-cone fracture in a round tensile bar. Acta Metall. 32, 157 (1984).

    Article  Google Scholar 

  28. R. Mahnken: Theoretical, numerical and identification aspects of a new model class for ductile damage. Int. J. Plast. 18, 801 (2002).

    Article  Google Scholar 

  29. R. Lillbacka, E. Johnson, and M. Ekh: A model for short crack propagation in polycrystalline materials. Eng. Fract. Mech. 73, 223 (2006).

    Article  Google Scholar 

  30. B. Künkler, C-P. Fritzen, O. Düber, U. Krupp, and H-J. Christ: Simulation of short crack propagation—Transition from stage I to stage II. Proc. Appl. Math. Mech. 5, 341 (2005).

    Article  Google Scholar 

  31. O. Düber, B. Künkler, U. Krupp, H.J. Christ, and C.P. Fritzen: Experimental characterization and two-dimensional simulation of short-crack propagation in an austenitic-ferritic duplex steel. Int. J. Fatigue 28, 983 (2006).

    Article  CAS  Google Scholar 

  32. G.M. Castelluccio: A Study on the Influence of Microstructure on Small Fatigue Cracks (Georigia Institute of Technology, 2012).

  33. J.L. Bouvard, J.L. Chaboche, F. Feyel, and F. Gallerneau: A cohesive zone model for fatigue and creep–fatigue crack growth in single crystal superalloys. Int. J. Fatigue 31, 868 (2009).

    Article  CAS  Google Scholar 

  34. M. Boeff: Micromechanical modelling of fatigue crack initiation and growth. Ph.D. thesis, Ruhr Universität Bochum, Germany, 2016.

    Google Scholar 

  35. M. Boeff, H.U. Hassan, and A. Hartmaier: Micromechanical modeling of fatigue crack initiation in polycrystals. J. Mater. Res. 32, 4375 (2017).

    Article  CAS  Google Scholar 

  36. Cubit 13.2 by (Sandia National Laboratories, Albuquerque, New Mexico, 2013).

  37. J.R. Rice: Inelastic constitutive relations for solids: Theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433 (1971).

    Article  Google Scholar 

  38. J.W. Hutchinson: Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. A 348, 101 (1976).

    CAS  Google Scholar 

  39. 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, 1152 (2010).

    Article  CAS  Google Scholar 

  40. 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, 2361 (2004).

    Article  Google Scholar 

  41. S. Mahmoody: Micromechanical Modeling of Dual-Phase Steel Using a Rate-Dependent Crystal Plasticity Model (McGill University, Montreal, Canada, 2003).

    Google Scholar 

  42. D.L. McDowell: Simulation-based strategies for microstructure-sensitive fatigue modeling. Mater. Sci. Eng., A 468–470 (Spec. Iss.), 4 (2007).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  44. G. Pijaudier-Cabot and Z. Bazant: Nonlocal damage theory. J. Eng. Mech. 113, 1512–1533 (1987).

    Article  Google Scholar 

  45. R.H.J. Peerlings: Enhanced Damage Modelling for Fracture and Fatigue (Technische Universiteit Eindhoven, Eindhoven, Netherlands, 1999).

    Google Scholar 

  46. J. Polák, T. Kruml, K. Obrtlík, J. Man, and M. Petrenec: Short crack growth in polycrystalline materials. Procedia Eng. 2, 883 (2010).

    Article  CAS  Google Scholar 

  47. M. Schlesinger: Experimentelle Untersuchung Des Zeitabhängigen Rissfortschritts Unter Thermomechanischer Ermüdung in Nickellegierungen Und Mechanismenbasierte Modelle Zur Lebensdauerbewertung (Shaker Verlag, Aachen, 2014).

    Google Scholar 

Download references

Acknowledgments

The authors thank Michael Schlesinger from the Fraunhofer Institute for mechanics of materials (IWM) Freiburg for providing the experimental results for the qualitative comparison of our numerical model.

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., Hassan, H.u. & Hartmaier, A. On the numerical modeling of nucleation and growth of microstructurally short cracks in polycrystals under cyclic loading. Journal of Materials Research 34, 3523–3534 (2019). https://doi.org/10.1557/jmr.2019.270

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2019.270

Search

Navigation