Skip to main content
SpringerLink
Log in

Cohesive Zone Modeling of Crack Propagation in FCC Single Crystals via Atomistic Simulations

  • Published:
Metals and Materials International Aims and scope Submit manuscript

Abstract

This paper presents a cohesive zone model of fracture in Cu and Ni single crystals under tension, based on an atomistic analysis. The molecular-statics approach based on the conjugate-gradient method was used to investigate the crack-growth behavior at the atomic level. The fracture toughness was evaluated on the basis of energy considerations, and the cohesive traction was calculated using the J integral and the atomic-scale separation in the cohesive zone. The cohesive traction and separation curves obtained using computational data from atomistic simulations were compared with the exponential form of continuum mechanics. The results showed that the exponential form satisfactorily represented the cohesive zone properties of Cu. However, the cohesive traction and separation curves for Ni were found to deviate from the exponential form in the softening stage, owing to small-scale nonlinear features near the cohesive zone.

Graphic Abstract

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
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. M. Mehrabian, B. Nayebi, A. Bahmani, D. Dietrich, T. Lampke, E. Ahounbar, M. Shokouhimehr, Met. Mater. Int. (2019). https://doi.org/10.1007/s12540-019-00537-3

    Article  Google Scholar 

  2. W. Jiang, H. Jiang, G. Li, F. Guan, J. Zhu, Z. Fan, Met. Mater. Int. (2020). https://doi.org/10.1007/s12540-019-00606-7

    Article  Google Scholar 

  3. X.-K. Zhu, J.A. Joyce, Eng. Fract. Mech. 85, 1 (2012)

    Google Scholar 

  4. M. Elices, G.V. Guinea, J. Gomez, J. Plana, Eng. Fract. Mech. 69, 137 (2002)

    Google Scholar 

  5. G.I. Barenblatt, J. Appl. Math. Mech. 23, 622 (1959)

    Google Scholar 

  6. D.S. Dugdale, J. Mech. Phys. Solids 8, 100 (1960)

    Google Scholar 

  7. J.R. Rice, Mathematical Analysis in the Mechanics of Fracture (Academic Press, New York, 1968)

    Google Scholar 

  8. E. Smith, Eng. Fract. Mech. 6, 213 (1974)

    Google Scholar 

  9. K. Park, G.H. Paulino, Appl. Mech. Rev. 64, 060802 (2011)

    Google Scholar 

  10. C.Y. Hui, A. Ruina, R. Long, A. Jagota, J. Adhes. 87, 1 (2011)

    CAS  Google Scholar 

  11. J.P. McGarry, E.O. Mairtin, G. Parry, G.E. Beltz, J. Mech. Phys. Solids 63, 336 (2014)

    Google Scholar 

  12. Y. Zhu, K.M. Liechti, K. Ravi-Chandar, Int. J. Solids Struct. 46, 31 (2009)

    CAS  Google Scholar 

  13. H.-G. Kim, H.B. Chew, K.-S. Kim, Int. J. Numer. Methods Eng. 91, 516 (2012)

    Google Scholar 

  14. J.L. Cribb, B. Tomkins, J. Mech. Phys. Solids 15, 135 (1967)

    Google Scholar 

  15. V.C. Li, C.-M. Chan, C.K.Y. Leung, Cem. Concr. Res. 17, 441 (1987)

    CAS  Google Scholar 

  16. B.F. Sørensen, T.K. Jacobsen, Eng. Fract. Mech. 70, 1841 (2003)

    Google Scholar 

  17. Md Meraj, S. Pal, Met. Mater. Int. 23, 272 (2017)

    CAS  Google Scholar 

  18. C.B. Cui, H.G. Beom, Met. Mater. Int. 24, 35 (2018)

    CAS  Google Scholar 

  19. A. Rajput, S.K. Paul, Met. Mater. Int. (2019). https://doi.org/10.1007/s12540-019-00475-0

    Article  Google Scholar 

  20. B. Zhou, M. Li, F. Xiong, L. Yang, Met. Mater. Int. (2019). https://doi.org/10.1007/s12540-019-00513-x

    Article  Google Scholar 

  21. Y.G. Xu, G.R. Liu, K. Behdinan, Z. Fawaz, J. Intell. Mater. Syst. Struct. 15, 933 (2004)

    CAS  Google Scholar 

  22. M. Karimi, T. Roarty, T. Kaplan, Modelling Simul. Mater. Sci. Eng. 14, 1409 (2006)

    CAS  Google Scholar 

  23. C.B. Cui, H.G. Beom, Mater. Sci. Eng. A 609, 102 (2014)

    CAS  Google Scholar 

  24. C.B. Cui, S.D. Kim, H.G. Beom, J. Mater. Res. 30, 1957 (2015)

    CAS  Google Scholar 

  25. A. Needleman, Int. J. Fract. 42, 21 (1990)

    Google Scholar 

  26. S.J. Plimpton, J. Comput. Phys. 117, 1 (1995)

    CAS  Google Scholar 

  27. J.R. Shewchuk, An Introduction to the Conjugate Gradient Method Without the Agonizing Pain (Carnegie Mellon University, Pittsburgh, 1994)

    Google Scholar 

  28. M.S. Daw, M.I. Baskes, Phys. Rev. B 29, 6443 (1984)

    CAS  Google Scholar 

  29. Y. Mishin, M.J. Mehl, D.A. Papaconstantopoulos, A.F. Voter, J.D. Kress, Phys. Rev. B 63, 224106 (2001)

    Google Scholar 

  30. Y. Mishin, D. Farkas, M.J. Mehl, D.A. Papaconstantopoulos, Phys. Rev. B 59, 3393 (1999)

    CAS  Google Scholar 

  31. G. Simons, H. Wang, Single Crystal Elastic Constants and Calculated Aggregate Properties (MIT Press, Cambridge, MA, 1977)

    Google Scholar 

  32. C.J. Smith (ed.), Metal Reference Book, 5th edn. (Butterworth, London, 1976)

    Google Scholar 

  33. R.A. Chaudhuri, Philos. Mag. 90, 2049 (2010)

    CAS  Google Scholar 

  34. M.F. Horstemeyer, M.I. Baskes, J. Eng. Mater. Technol. 121, 114 (1999)

    Google Scholar 

  35. J.A. Begley, J.D. Landes, The J integral as a fracture criterion, ASTM STP 514 (American Society for Testing and Materials, Philadelphia, 1972).

  36. B. Lawn, Fracture of Brittle Solids (Cambridge Univ. Press, Cambridge, 1993)

    Google Scholar 

  37. J.R. Willis, J. Mech. Phys. Solids 15, 151 (1967)

    Google Scholar 

  38. J.R. Rice, J. Appl. Mech. 35, 379 (1968)

    Google Scholar 

  39. S.F. Ferdous, A. Adnan, J. Nanomech. Micromech. 7, 04017010 (2017)

    Google Scholar 

  40. J. Skogsrud, C. Thaulow, Eng. Fract. Mech. 150, 153 (2015)

    Google Scholar 

  41. R.J. Swenson, Am. J. Phys. 51, 940 (1983)

    CAS  Google Scholar 

  42. A. Stukowski, Modelling Simul. Mater. Sci. Eng. 18, 015012 (2009)

    Google Scholar 

  43. X.R. Zhuo, A. Ma, H.G. Beom, Comput. Mater. Sci. 169, 109105 (2019)

    CAS  Google Scholar 

  44. A. Sazgar, M.R. Movahhedy, M. Mahnama, S. Sohrabpour, Mater. Sci. Eng. A 679, 116 (2017)

    CAS  Google Scholar 

  45. B. Paliwal, M. Cherkaoui, Int. J. Solids Struct. 50, 3346 (2013)

    CAS  Google Scholar 

  46. C.B. Cui, H.G. Beom, J. Mater. Sci. 49, 8355 (2014)

    CAS  Google Scholar 

  47. R. Komanduri, N. Chandrasekaran, L.M. Raff, Int. J. Mech. Sci. 43, 2237 (2001)

    Google Scholar 

  48. W.-P. Wu, N.-L. Li, Y.-L. Li, Comput. Mater. Sci. 113, 203 (2016)

    CAS  Google Scholar 

  49. X.R. Zhuo, J.H. Kim, H.G. Beom, Crystals 8, 441 (2018)

    Google Scholar 

Download references

Acknowledgement

This work was supported by a National Research Foundation of Korea (NRF) Grant funded by the Korean government (MSIT) (No. 2019R 1F 1A 1041818).

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Inha University, Incheon, 22212, Republic of Korea

    Gi Hun Lee, Jang Hyun Kim & Hyeon Gyu Beom

Authors
  1. Gi Hun Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jang Hyun Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hyeon Gyu Beom
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hyeon Gyu Beom.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, G.H., Kim, J.H. & Beom, H.G. Cohesive Zone Modeling of Crack Propagation in FCC Single Crystals via Atomistic Simulations. Met. Mater. Int. 27, 584–592 (2021). https://doi.org/10.1007/s12540-020-00693-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12540-020-00693-x

Keywords

Search

Navigation