Skip to main content
SpringerLink
Log in

Numerical investigation of fracture behavior of nanostructured Cu with bimodal grain size distribution

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Nanostructured metals with bimodal grain size distribution, composed of coarse grain (CG) and nanograin (NG) regions, have proved to have high strength and good ductility. Here, numerical investigation, based on the mechanism-based strain gradient plasticity theory and the Johnson–Cook failure model, focuses on effects of (1) distribution characteristics of the CG regions and (2) the constitutive relation of the NG with different grain sizes on fracture behavior in a center-cracked tension specimen of bimodal nanostructured Cu. High strain rate simulations show that both of them directly influence load response and energy history, and importantly, they are closely related to the fracture pattern. This study shows that both CG region bridging and crack deflection toughen the bimodal nanostructured Cu significantly, while debonding enhances the overall ductility moderately. Simulations also show that with volume fraction of the CG regions increasing, both structural strength and ductility of the bimodal nanostructured Cu specimen can be improved.

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

Similar content being viewed by others

References

  1. Tellkamp V.L., Lavernia E.J., Melmed A.: Mechanical behavior and microstructure of a thermally stable bulk nanostructured Al alloy. Metall. Mater. Trans. A 32, 2335–2343 (2001)

    Article  Google Scholar 

  2. Wang Y., Chen M., Zhou F., Ma E.: High tensile ductility in a nanostructured metal. Nature 419, 912–915 (2002)

    Article  Google Scholar 

  3. Han B.Q., Lee Z., Witkin D., Nutt S., Lavernia E.J.: Deformation behavior of bimodal nanostructured 5083 Al alloys. Metall. Mater. Trans. A 36, 957–965 (2005)

    Article  Google Scholar 

  4. Fan G.J., Choo H., Liaw P.K., Lavernia E.J.: Plastic deformation and fracture of ultrafine-grained Al–Mg alloys with a bimodal grain size distribution. Acta Mater. 54, 1759–1766 (2006)

    Article  Google Scholar 

  5. Lee Z., Radmilovic V., Ahn B., Lavernia E.J., Nutt S.R.: Tensile deformation and fracture mechanism of bulk bimodal ultrafine-grained Al–Mg alloy. Metall. Mater. Trans. A 41, 795–801 (2010)

    Article  Google Scholar 

  6. Bui Q.H.: Heterogeneous plastic deformation in bimodal bulk ultrafine-grained nickel. J. Mater. Sci. 47, 1902–1909 (2012)

    Article  MathSciNet  Google Scholar 

  7. Ye R.Q., Han B.Q., Lavernia E.J.: Simulation of deformation and failure process in bimodal Al alloys. Metall. Mater. Trans. A 36, 1833–1840 (2005)

    Article  Google Scholar 

  8. ABAQUS/Explicit. ABAQUS Example Problems Manual, version 6.10. Dassault, Providence, RI (2012)

  9. Zhai J., Tomar V., Zhou M.: Micromechanical simulation of dynamic fracture using the cohesive finite element method. J. Eng. Mater. Tech. 126, 179–191 (2004)

    Article  Google Scholar 

  10. Zhu L.L., Ruan H.H., Li X.Y., Dao M., Gao H.J., Lu J.: Modeling grain size dependent optimal twin spacing for achieving ultimate high strength and related high ductility in nanotwinned metals. Acta Mater. 59, 5544–5557 (2011)

    Article  Google Scholar 

  11. Gao H., Huang Y., Nix W.D., Hutchinson J.W.: Mechanism-based strain gradient plasticity—I. Theory. J. Mech. Phys. Solids 47, 1239–1263 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  12. Huang Y., Qu S., Hwang K.C., Li M., Gao H.J.: A conventional theory of mechanism-based strain gradient plasticity. Int. J. Plast. 20, 753–782 (2004)

    Article  MATH  Google Scholar 

  13. Zhu L.L., Lu J.: Modelling the plastic deformation of nanostructured metals with bimodal grain size distribution. Int. J. Plast. 30-31, 166–184 (2012)

    Article  Google Scholar 

  14. Kocks U.F., Mecking H.: The physics and phenomenology of strain hardening. Prog. Mater. Sci. 48, 171–273 (2003)

    Article  Google Scholar 

  15. Capolungo L., Jochum C., Cherkaoui M., Qu J.: Homogenization method for strength and inelastic behavior of nanocrystalline materials. Int. J. Plast. 21, 67–82 (2005)

    Article  MATH  Google Scholar 

  16. Weng G.J.: Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions. Int. J. Eng. Sci. 22, 845–856 (1984)

    Article  MATH  Google Scholar 

  17. Johnson, G.R., Cook, W.H.: A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the 7th International Symposium on Ballistics. The Hague, The Netherlands (1983)

  18. Johnson G.R., Cook W.H.: Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng. Fract. Mech. 21, 31–48 (1985)

    Article  Google Scholar 

  19. Dabboussi W., Nemes J.A.: Modeling of ductile fracture using the dynamic punch test. Int. J. Mech. Sci. 47, 1282–1299 (2005)

    Article  Google Scholar 

  20. Borvik T., Langseth M., Hopperstad O.S., Malo K.A.: Ballistic penetration of steel plates. Int. J. Impact Eng. 22, 855–886 (1999)

    Article  Google Scholar 

  21. Gupta N.K., Iqbal M.A., Sekhon G.S.: Experimental and numerical studies on the behavior of thin aluminum plates subjected to impact by blunt- and hemispherical-nosed projectiles. Int. J. Impact Eng. 32, 1921–1944 (2006)

    Article  Google Scholar 

  22. Teng X., Wierzbicki T.: Evaluation of six fracture models in high velocity perforation. Eng. Fract. Mech. 73, 1653–1678 (2006)

    Article  Google Scholar 

  23. Li B.W., Zhao H.P., Qin Q.H., Feng X.Q., Yu S.W.: Numerical study on the effects of hierarchical wavy interface morphology on fracture toughness. Comput. Mater. Sci. 57, 14–22 (2012)

    Article  Google Scholar 

  24. Gleiter H.: Nanostructured materials: basic concepts and microstructure. Acta Mater. 48, 1–29 (2000)

    Article  Google Scholar 

  25. Wang G.F., Feng X.Q., Yu S.W., Nan C.W.: Interface effects on effective elastic moduli of nanocrystalline materials. Mater. Sci. Eng. A 363, 1–8 (2003)

    Article  Google Scholar 

  26. Guo X., Leung A.Y.T., Chen A.Y., Ruan H.H., Lu J.: Investigation of non-local cracking in layered stainless steel with nanostructured interface. Scripta Mater. 63, 403–406 (2010)

    Article  Google Scholar 

  27. Guo X., Weng G.J., Soh A.K.: Ductility enhancement of layered stainless steel with nanograined interface layers. Comput. Mater. Sci. 55, 350–355 (2012)

    Article  Google Scholar 

  28. Su Y., Du J.N.: Effect of intrinsic surface stress on single-vertex structure of polarization in ferroelectric nanoparticles. Appl. Phys. Lett. 96, 162905 (2010)

    Article  Google Scholar 

  29. Su Y., Chen H., Li J.J., Soh A.K., Weng G.J.: Effects of surface tension on the size-dependent ferroelectric characteristics of free-standing BaTiO3 nano-thin films. J. Appl. Phys. 110, 084108 (2011)

    Article  Google Scholar 

  30. Liu N., Su Y., Weng G.J.: A phase-field study on the hysteresis behaviors and domain patterns of nanocrystalline ferroelectric polycrystals. J. Appl. Phys. 113, 204106 (2013)

    Article  Google Scholar 

  31. Su Y.: On the dynamics of vortex structure in ferroelectric nanoparticles. Acta Mech. 224, 1175–1184 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  32. Guo X., Chang K., Chen L.Q., Zhou M.: Determination of fracture toughness of AZ31 Mg alloy using the cohesive finite element method. Eng. Fract. Mech. 96, 401–415 (2012)

    Article  Google Scholar 

  33. Guo X., Su R.K.L., Young B.: Numerical investigation of the bilinear softening law in the cohesive crack model for normal-strength and high-strength concrete. Adv. Struct. Eng. 15, 373–388 (2012)

    Article  Google Scholar 

  34. Guo X., Zhang W.J., Zhu L.L., Lu J.: Mesh dependence of transverse cracking in laminated metals with nanograined interface layers. Eng. Fract. Mech. 105, 211–220 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Tianjin University, Tianjin, 300072, China

    X. Guo & X. Y. Dai

  2. Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin, 300072, China

    X. Guo

  3. Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, 310027, Zhejiang Province, China

    L. L. Zhu

  4. Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Hong Kong, China

    J. Lu

Authors
  1. X. Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. X. Y. Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. L. Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to X. Guo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guo, X., Dai, X.Y., Zhu, L.L. et al. Numerical investigation of fracture behavior of nanostructured Cu with bimodal grain size distribution. Acta Mech 225, 1093–1106 (2014). https://doi.org/10.1007/s00707-013-1050-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-013-1050-8

Keywords

Search

Navigation