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Influence of grain boundary conditions on modeling of size-dependence in polycrystals

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Abstract

In this paper, a gradient crystal plasticity model in a polycrystalline grain structure is investigated. Hereby, the focus is on the influence of the grain boundary conditions. A new type of grain boundary conditions is introduced, the so-called micro-flexible boundary condition. In particular, it is compared to existing grain boundary conditions of plastic slip. Numerical results are given for the stress–strain response as well as for the plastic slip field in the grain structure.

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References

  1. Acharya A., Tang H., Saigal S., Bassani J.L.: On boundary conditions and plastic strain-gradient discontinuity in lower-order gradient plasticity. J. Mech. Phys. Solids 52, 1793–1826 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ashby M.F.: The deformation of plastically non-homogeneous materials. Phil. Mag. 21, 399–424 (1970)

    Article  Google Scholar 

  3. Bieler T.R., Eisenlohr P., Roters F., Kumar D., Mason D.E., Crimp M.A., Raabe D.: The role of heterogeneous deformation on damage nucleation at grain boundaries in single phase metals. Int. J. Plast. 25, 1655–1683 (2009)

    Article  MATH  Google Scholar 

  4. Ekh M., Grymer M., Runesson K., Svedberg T.: Gradient crystal plasticity as part of the computational modeling of polycrystals. Int. J. Numer. Methods Eng. 72, 197–220 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ertürk I., van Dommelen J.A.W., Geers M.G.D.: Energetic dislocation interactions and thermodynamical aspects of strain gradient crystal plasticity theories. J. Mech. Phys. Solids 57, 1801–1814 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Evers L.P., Brekelmans W.A.M., Geers M.G.D.: Scale dependent crystal plasticity framework with dislocation density and grain boundary effects. Int. J. Solids Struct. 41, 5209–5230 (2004)

    Article  MATH  Google Scholar 

  7. Fredriksson P., Gudmundson P.: Size-dependent yield strength of thin films. Int. J. Plast. 21, 1834–1854 (2005)

    Article  MATH  Google Scholar 

  8. Geers M.G.D., Brekelmans W.A.M., Janssen P.J.M.: Size effects in miniaturized polycrystalline FCC samples: strengthening versus weakening. Int. J. Solids Struct. 43, 7304–7321 (2008)

    Article  Google Scholar 

  9. Gurtin M.E.: A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin. J. Mech. Phys. Solids 52, 2545–2568 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gurtin M.E., Needleman A.: Boundary conditions in small-deformation, single-crystal plasticity that account for the Burgers vector. J. Mech. Phys. Solids 53, 1–31 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. Gurtin M.E.: A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation. J. Mech. Phys. Solids 56, 640–662 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Gurtin M.E., Anand L.: Nanocrystalline grain boundaries that slip and separate: a gradient theory that accounts for grain-boundary stress and conditions at a triple-junction. J. Mech. Phys. Solids 56, 184–199 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kuroda M., Tvergaard V.: On the formulations of higher-order strain gradient crystal plasticity models. J. Mech. Phys. Solids 56, 1591–1608 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Lee T.C., Robertson I.M., Birnbaum H.K.: An in situ transmission electronmicroscope deformation study of the slip transfer mechanisms in metals. Metall. Trans. A Phys. Metall. Mater. Sci. 21, 2437–2447 (1990)

    Article  Google Scholar 

  15. Lee T.C., Robertson I.M., Birnbaum H.K.: TEM in situ deformation study of the interaction of lattice dislocations with grain-boundaries in metals. Phil. Mag. A Phys. Condens. Matter Struct. Defects Mech. Prop. 62, 131–153 (1990)

    Google Scholar 

  16. Lele S.P., Anand L.: A small-deformation strain-gradient theory for isotropic viscoplastic materials. Phil. Mag. 88(30–32), 3655–3689 (2008)

    Article  Google Scholar 

  17. Nicola L., Van der Giessen E., Gurtin M.E.: Effect of defect energy on strain-gradient predictions of confined single-crystal plasticity. J. Mech. Phys. solids 53, 1280–1294 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  18. Nye J.F.: Some geometrical relations in dislocated crystals. Acta Metall. 1, 153–162 (1953)

    Article  Google Scholar 

  19. Ohno N., Okumura D.: Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations. J. Mech. Phys. Solids 55, 1879–1898 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  20. Puri, S., Acharya, A., Rollett, A.D.: Controlling plastic flow across grain boundaries in a continuum model. Metall. Mater. Trans. A (2010). doi:10.1007/s11661-010-0257-8

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

    Article  MATH  Google Scholar 

  22. Shi J., Zikry M.A.: Grain–boundary interactions and orientation effects on crack behavior in polycrystalline aggregates. Int. J. Solids Struct. 46, 3914–3925 (2009)

    Article  MATH  Google Scholar 

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Correspondence to Swantje Bargmann.

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Ekh, M., Bargmann, S. & Grymer, M. Influence of grain boundary conditions on modeling of size-dependence in polycrystals. Acta Mech 218, 103–113 (2011). https://doi.org/10.1007/s00707-010-0403-9

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  • DOI: https://doi.org/10.1007/s00707-010-0403-9

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