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Grain boundary strengthening of FCC polycrystals

Published online by Cambridge University Press:  13 March 2019

R. Arturo Rubio ,
Sarra Haouala  and
Javier LLorca
R. Arturo Rubio
Affiliation:
IMDEA Materials Institute, Getafe, Madrid 28906, Spain
Sarra Haouala
Affiliation:
IMDEA Materials Institute, Getafe, Madrid 28906, Spain
Javier LLorca*
Affiliation:
IMDEA Materials Institute, Getafe, Madrid 28906, Spain; and Department of Materials Science, Polytechnic University of Madrid, Madrid 28040, Spain
*
a)Address all correspondence to this author. e-mail: [email protected]
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Abstract

The effect of grain size on the flow strength of FCC polycrystals was analyzed by means of computational homogenization. The mechanical behavior of each grain was dictated by a dislocation-based crystal plasticity model in the context of finite strain plasticity and takes into the account the formation of pile-ups at grain boundaries. All the model parameters have a clear physical meaning and were identified for different FCC metals from dislocation dynamics simulations or experiments. It was found that the influence of the grain size on the flow strength of FCC polycrystals was mainly dictated by the similitude coefficient K that establishes the relationship between the dislocation mean free path and the dislocation density in the bulk. Finally, the modeling approach was validated by comparison with experimental results of the effect of grain size on the flow strength of Ni, Al, Cu, and Ag.

Keywords

grain sizestrengthpolycrystal
Type
Invited Paper
Information
Journal of Materials Research , Volume 34 , Issue 13: Focus Issue: Intrinsic and Extrinsic Size Effects in Materials , 15 July 2019 , pp. 2263 - 2274
Copyright
Copyright © Materials Research Society 2019 

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References

Hall, E.O.: The deformation and aging of mild steel: III. Discussion of results. Proc. Phys. Soc., London, Sect. B 64, 747–753 (1951).CrossRefGoogle Scholar
Petch, N.J.: The cleavage strength of polycrystals. J. Iron Steel Inst. Jpn. 174, 25–28 (1953).Google Scholar
Raj, S.V. and Pharr, G.M.: A compilation and analysis of data for the stress dependence of the subgrain size. Mater. Sci. Eng., A 81, 217–237 (1986).CrossRefGoogle Scholar
Dunstan, D.J. and Bushby, A.J.: The scaling exponent in the size effect of small scale plastic deformation. Int. J. Plast. 40, 152–162 (2013).CrossRefGoogle Scholar
Dunstan, D.J. and Bushby, A.J.: Gran size dependence of the strength of metals: The Hall–Petch effect does not scale as the inverse of the square root of the grain size. Int. J. Plast. 53, 55–65 (2014).CrossRefGoogle Scholar
Li, Y., Bushby, A.J., and Dustan, D.J.: A compilation and analysis of data for the stress dependence of the subgrain size. Proc. R. Soc. A 472, 20150890 (2016).CrossRefGoogle Scholar
Bieler, T.R., Eisenlohr, P., Zhang, C., Phukan, H.J., and Crimp, M.M.A.: Grain boundaries and interfaces in slip transfer. Curr. Opin. Solid State Mater. Sci. 18, 212–226 (2014).CrossRefGoogle Scholar
Hémery, T., Nizou, P., and Villechaise, P.: In situ SEM investigation of slip transfer in Ti–6Al–4V: Effect of applied stress. Mater. Sci. Eng., A 709, 277–284 (2018).CrossRefGoogle Scholar
Bieler, T.R., Alizadeh, R., and LLorca, J.: An analysis of (the lack of) slip transfer between near-cube oriented grains in pure Al. Int. J. Plast. (2019), https://doi.org/10.1016/j.ijplas.2019.02.014.CrossRefGoogle Scholar
Ashby, M.: The deformation of plastically non-homogeneous materials. Philos. Mag. 21, 399–424 (1970).CrossRefGoogle Scholar
Kocks, U.: The relation between polycrystal deformation and single crystal deformation. Metall. Trans. 1, 1121–1143 (1970).CrossRefGoogle Scholar
Hirth, J.P.: The influence of grain boundaries on mechanical properties. Metall. Trans. 3, 3047–3067 (1972).CrossRefGoogle Scholar
Segurado, J., Lebensohn, R.A., and LLorca, J.: Computational homogenization of polycrystal. Adv. Appl. Mech. 51, 1–114 (2018).CrossRefGoogle Scholar
Evers, L.P., Parks, D.M., Brekelmans, W.A.M., and Geers, M.G.D.: Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation. J. Mech. Phys. Solid. 50, 2403–2424 (2002).CrossRefGoogle Scholar
Cheong, K.S., Busso, E.P., and Arsenlis, A.: A study of microstructural length scale effects on the behavior of FCC polycrystals using strain gradient concepts. Int. J. Plast. 21, 1797–1814 (2005).CrossRefGoogle Scholar
Lebensohn, R.A. and Needleman, A.: Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms. J. Mech. Phys. Solid. 97, 333–351 (2016).CrossRefGoogle Scholar
Lim, H., Lee, M., Kim, J., Adams, B., and Wagoner, R.: Simulation of polycrystal deformation with grain and grain boundary effects. Int. J. Plast. 27, 1328–1354 (2011).CrossRefGoogle Scholar
Mayeur, J., Beyerlein, I., Bronkhorst, C., and Mourad, H.: Incorporating interface affected zones into crystal plasticity. Int. J. Plast. 65, 206–225 (2015).CrossRefGoogle Scholar
Su, Y., Zambaldi, C., Mercier, D., Eisenlohr, P., Bieler, T., and Crimp, M.: Quantifying deformation processes near grain boundaries in α titanium using nanoindentation and crystal plasticity modeling. Int. J. Plast. 86, 170–186 (2016).CrossRefGoogle Scholar
Haouala, S., Segurado, J., and LLorca, J.: An analysis of the influence of grain size on the strength of FCC polycrystals by means of computational homogenization. Acta Mater. 148, 72–85 (2018).CrossRefGoogle Scholar
Taylor, G.I.: The mechanism of plastic deformation of crystals. Proc. R. Soc. A 165, 362–387 (1934).CrossRefGoogle Scholar
Kocks, U. and Mecking, H.: Physics and phenomenology of strain hardening: The FCC case. Prog. Mater. Sci. 48, 171–273 (2003).CrossRefGoogle Scholar
Lefebvre, S.: Etude expérimentale et simulation numérique du comportement mécanique de structures sub-micrométriques de cuivre: Application aux interconnexions dans les circuits intégrés. Ph.D. thesis, Ecole Centrale de Paris, Paris, 2006.Google Scholar
Kocks, U.F., Argon, A.S., and Ashby, M.A.: Thermodynamics and kinetics of slip. Prog. Mater. Sci. 19, 1–281 (1975).Google Scholar
Kubin, L.P. and Louchet, F.: Description of low-temperature interstitial hardening of the b.c.c. lattice from in situ experiments. Philos. Mag. A 38, 205–221 (1978).CrossRefGoogle Scholar
Franciosi, P., Berveiller, M., and Zaoui, A.: Latent hardening in copper and aluminium single crystals. Acta Metall. 28, 273–283 (1980).CrossRefGoogle Scholar
Devincre, B., Hoc, T., and Kubin, L.: Dislocation mean free paths and strain hardening of crystals. Science 320, 1745–1748 (2008).CrossRefGoogle ScholarPubMed
Bertin, N., Capolungo, L., and Beyerlein, I.J.: Hybrid dislocation dynamics based strain hardening constitutive model. Int. J. Plast. 49, 119–144 (2013).CrossRefGoogle Scholar
Zaefferer, S., Kuo, J-C., Zhao, Z., Winning, M., and Raabe, D.: On the influence of the grain boundary misorientation on the plastic deformation of aluminum bicrystals. Acta Mater. 51, 4719–4735 (2003).CrossRefGoogle Scholar
de Sansal, C., Devincre, B., and Kubin, L.P.: Grain size strengthening in microcrystalline copper: A three-dimensional dislocation dynamics simulation. Key Eng. Mater. 423, 25–32 (2010).CrossRefGoogle Scholar
Kocks, U.F. and Mecking, H.: Kinetics of flow and strain-hardening. Acta Metall. 29, 1865–1875 (1981).Google Scholar
Sauzay, M. and Kubin, L.: Scaling laws for dislocation microstructures in monotonic and cyclic deformation of fcc metals. Prog. Mater. Sci. 56, 725–784 (2011).CrossRefGoogle Scholar
DREAM.3D (2016). Available at: http://www.dream3d.bluequartz.net.Google Scholar
Abaqus: Analysis User’s Manual, Dassault Systèmes.Google Scholar
Alankar, A., Mastorakos, I.N., and Field, D.P.: A dislocation-density-based 3D crystal plasticity model for pure aluminum. Acta Mater. 57, 5936–5946 (2009).CrossRefGoogle Scholar
Castelluccio, G.M. and McDowell, D.L.: Mesoscale cyclic crystal plasticity with dislocation substructures. Int. J. Plast. 57, 1–26 (2017).CrossRefGoogle Scholar
Mohazzabi, P.: Temperature dependence of the elastic constants of copper, gold and silver. J. Phys. Chem. Solid. 46, 147–150 (1985).CrossRefGoogle Scholar
Martinez-Mardones, J., Walgraef, D., and Wörner, C.: Materials Instabilities (World Scientific, 2000).CrossRefGoogle Scholar
Arsenlis, A. and Parks, D.M.: Modeling the evolution of crystallographic dislocation density in crystal plasticity. J. Mech. Phys. Solid. 50, 1979–2009 (2002).CrossRefGoogle Scholar
Paus, P., Kratochvíl, J., and Benes, M.: A dislocation dynamics analysis of the critical cross-slip annihilation distance and the cyclic saturation stress in fcc single crystals at different temperatures. Acta Mater. 61, 7917–7923 (2013).CrossRefGoogle Scholar
Zaiser, M. and Sandfeld, S.: Scaling properties of dislocation simulations in the similitude regime. Model. Simulat. Mater. Sci. Eng. 22, 065012 (2014).CrossRefGoogle Scholar
El-Awady, J.A.: Unraveling the physics of size-dependent dislocation-mediated plasticity. Nat. Commun. 6, 5926 (2015).CrossRefGoogle Scholar
Hansen, N.: The effect of grain size and strain on the tensile flow stress of aluminium at room temperature. Acta Metall. 25, 863–869 (1977).CrossRefGoogle Scholar
Narutani, T. and Takamura, J.: Grain-size strengthening in terms of dislocation density measured by resistivity. Acta Metall. Mater. 39, 2037–2049 (1991).CrossRefGoogle Scholar
Carreker, R.P.: Tensile deformation of silver as a function of temperature, strain rate, and grain size. JOM 9, 112–115 (1957).CrossRefGoogle Scholar
Hansen, N. and Ralph, B.: The strain and grain size dependence of the flow stress of copper. Acta Metall. 30, 411–417 (1982).CrossRefGoogle Scholar