Skip to main content

Dislocation Density-Based Modeling of Crystal Plasticity Finite Element Analysis

  • Living reference work entry
  • First Online:

Abstract

Dislocations play a major role in plastic deformation and fracture of metallic materials. A number of metallographic aspects such as grain boundaries, precipitates, and others contribute to the dislocations’ behavior, and therefore, we have to consider their effects too when we intend to understand the mechanical behavior of metals with microstructure. Finite element method is a powerful tool to express the shape and arrangement of metal microstructures and analyze the deformation under a prescribed boundary and loading conditions. We tried to develop models for the movement, interaction, and accumulation of dislocations during plastic slip deformation in metal microstructure and implemented them to the framework of finite element method. Models originate from physics of discrete dislocations and are brought to dislocation density-based numerical models. In this chapter, the physical pictures and expressions of dislocation density-based models are shown. Some examples of analyses are also shown.

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

References

  1. Hull D, Bacon DJ. Introduction to dislocations. 4th ed. Oxford: Butterworth Heinemann; 2001.

    Google Scholar 

  2. Ohashi T, Kawamukai M, Zbib H. A multiscale approach for modeling scale-dependent yield stress in polycrystalline metals. Int J Plast. 2007;23:897–914.

    Article  MATH  Google Scholar 

  3. Zbib HM, Diaz T, Rubia D. A multiscale model of plasticity. Int J Plast. 2002;18:1133–63.

    Article  MATH  Google Scholar 

  4. Ashby MF. The deformation of plastically non-homogeneous materials. Philos Mag. 1970;21:399–424.

    Article  Google Scholar 

  5. Kocks UF. Laws for work-hardening and low-temperature creep. Trans ASME J Eng Mat Tech. 1976;98:76–85.

    Article  Google Scholar 

  6. Mecking H, Kocks UF. Kinetics of flow and strain-hardening. Acta Metall. 1981;29:1865–75.

    Article  Google Scholar 

  7. Yasnikov IS, Vinogradov A, Estrin Y. Revisiting the Considere criterion from the viewpoint of dislocation theory fundamentals. Scr Mater. 2014;76:37–40.

    Article  Google Scholar 

  8. Ohashi T. Numerical modelling of plastic multislip in metal crystals of f . c . c . type. Philos Mag A. 1994;70:793–803.

    Google Scholar 

  9. Ohashi T. A new model of scale dependent crystal plasticity analysis. In: Kitagawa H, Shibutani Y, editors. IUTAM symposium on mesoscopic dynamics of fracture process and materials strength. Osaka: Kluwer; 2003;97–106.

    Google Scholar 

  10. Ohashi T. Crystal plasticity analysis of dislocation emission from micro voids. Int J Plast. 2005;21:2071–88.

    Article  MATH  Google Scholar 

  11. Kuhlmann-Wilsdorf D. Theory of plastic deformation: - properties of low energy dislocation structures. Mater Sci Eng A. 1989;113:1–41.

    Article  Google Scholar 

  12. Taylor GI. The mechanism of plastic deformation of crystals. part I. theoretical. Proc R Soc A Math Phys Eng Sci. 1934;145:362–87.

    Article  MATH  Google Scholar 

  13. Mott NF. A theory of work-hardening of metal crystals. Phil Mag Ser. 7. 1952;43:1151–78.

    Article  Google Scholar 

  14. Okuyama Y, Ohashi T. Numerical modeling for strain hardening of two-phase alloys with dispersion of hard fine spherical particles. Tetsu-to-Hagane. 2016;102:396–404

    Google Scholar 

  15. Yasuda Y, Ohashi T. Crystal plasticity analysis considering dislocations’ behavior in ferrite/cementite lamellar structure. ISIJ Int. 2017;57:573–580.

    Google Scholar 

  16. Fleck N, Muller G, Ashby M, Hutchinson J. Strain gradient plasticity: Theory and experiment. Acta Metall Mater. 1994;42:475–87.

    Article  Google Scholar 

  17. Gurtin ME, Ohno N. A gradient theory of small-deformation, single-crystal plasticity that accounts for GNDinduced interactions between slip systems. J Mech Phys Solids. 2011;59:320–43.

    Article  MATH  MathSciNet  Google Scholar 

  18. Ohashi T. Computer simulation of non-uniform multiple slip in face centered cubic bicrystals. Trans JIM. 1987;28:906–15.

    Article  Google Scholar 

  19. Jackson PJ, Basinski ZS. Latent hardening and the flow stress in copper single crystals. Can J Phys. 1967;45:707–35.

    Article  Google Scholar 

  20. Hiura F, Niewczas M. Latent hardening effect under self- and coplanar dislocation interactions in Mg single crystals. Scr Mater. 2015;106:8–11.

    Google Scholar 

  21. Hansen N. Hall–Petch relation and boundary strengthening. Scr Mater. 2004;51:801–6.

    Google Scholar 

  22. Yasuda Y, Ohashi T. Crystal plasticity analyses of scale dependent mechanical properties of ferrite/cementite lamellar structure model in pearlite steel wire with bagaryatsky or pitsch-petch orientation relationship. ISIJ Int. 2016;56:2320–6.

    Article  Google Scholar 

  23. Hill R. J Mech Phys Solids. Generalized constitutive relations for incremental deformation of metal crystals by multislip. J Mech Phys Solids. 1966;14:95–102.

    Google Scholar 

  24. Ohashi T, Amagai R, Okuyama Y, Kawano Y, Mayama T. Crystal plasticity finite element analysis of slip deformation in the polycrystal models of textured Ti alloys. In: JSME M&M 2016 conference. Kobe, Japan: Japan Society of Mechanical Engineers; 2016:8–10.

    Google Scholar 

  25. Inoue H. Texture of Ti and Ti alloys. Mater Sci Technol “Kinzoku” (in Japanese). 1999;69:30–38.

    Google Scholar 

  26. Bridier F, McDowell DL, Villechaise P, Mendez J. Crystal plasticity modeling of slip activity in Ti-6Al-4V under high cycle fatigue loading. Int J Plast. 2009;25:1066–82.

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work was partly supported by the Council for Science, Technology and Innovation (CSTI), Cross-ministerial Strategic Innovation Promotion Program (SIP), “Fundamentals for fatigue and fracture in structural metals” (funding agency: JST).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tetsuya Ohashi .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Ohashi, T. (2018). Dislocation Density-Based Modeling of Crystal Plasticity Finite Element Analysis. In: Schmauder, S., Chen, CS., Chawla, K., Chawla, N., Chen, W., Kagawa, Y. (eds) Handbook of Mechanics of Materials. Springer, Singapore. https://doi.org/10.1007/978-981-10-6855-3_74-1

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-6855-3_74-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6855-3

  • Online ISBN: 978-981-10-6855-3

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics