Tabanfard, M. (2016). Finite Element Modeling of Strain Rate and Grain Size Dependency in Nanocrystalline Materials. Journal of Advanced Materials and Processing, 4(2), 63-74.

Minoo Tabanfard. "Finite Element Modeling of Strain Rate and Grain Size Dependency in Nanocrystalline Materials". Journal of Advanced Materials and Processing, 4, 2, 2016, 63-74.

Tabanfard, M. (2016). 'Finite Element Modeling of Strain Rate and Grain Size Dependency in Nanocrystalline Materials', Journal of Advanced Materials and Processing, 4(2), pp. 63-74.

Tabanfard, M. Finite Element Modeling of Strain Rate and Grain Size Dependency in Nanocrystalline Materials. Journal of Advanced Materials and Processing, 2016; 4(2): 63-74.

Finite Element Modeling of Strain Rate and Grain Size Dependency in Nanocrystalline Materials

^{}Department of Mechanical Engineering,Islamic Azad University of Najafabad, Isfahan, Iran

Abstract

Nanocrystalline materials show a higher strain-rate sensitivity in contrast to the conventional coarse-grained materials and a different grain size dependency. To explain these phenomenon, a finite element model is constructed that considers both grain interior and grain boundary deformation of nanocrystalline materials. The model consist of several crystalline cores with different orientations and grain boundary phase. The nonlinear behavior of the nanocrystalline core is implemented by a grain size dependent crystal plasticity. The boundary phase is assumed to have the mechanical properties of quasi-amorphous material. The constitutive equations for both grains interior and boundary phase are implemented into the finite-element software Abaqus. A calibration procedure was used to tune some parameters of the model with the previously published experimental data on the nanocrystalline copper. Then the model is used to predict the material behavior in various strain rates and grain sizes. The stresses obtained from these simulations match well with the experimental data for nanocrystalline copper at different strains and strain rates. Deviation from the Hall-Petch law and inverse Hall-Petch effect are also well illustrated by the model.

[1] R.J. Asaro, S. Suresh, "Mechanistic models for the activation volume and rate sensitivity in metals with nanocrystalline grains and nano-scale twins", Acta Mater., Vol. 53, 2005, pp. 3369-3382.

[2] H. Van Swygenhoven, P.M. Derlet, A.G. Froseth, "Nucleation and propagation of dislocations in nanocrystalline fcc metals", Acta Mater., Vol. 54, 2006, pp. 1975-1983.

[3] Z. Jiang, X. Liu, G. Li, Q. Jiang, J. Lian, "Strain rate sensitivity of a nanocrystalline Cu synthesized by electric brush plating", Appl. Phys. Lett., Vol. 88, 2006, p.143115.

[4] Z. Jiang, H. Zhang, C. Gu, Q. Jiang, J. Lian, "Deformation mechanism transition caused by strain rate in a pulse electric brush-plated nanocrystalline Cu", J. Appl. Phys., Vol. 104, 2008, p. 053505.

[5] G. Wang, J. Lian, Z. Jiang, L. Qin, Q. Jiang, "Compressive creep behavior of an electric brush-plated nanocrystalline Cu at room temperature", J. Appl. Phys., Vol. 106, 2009, p. 086105.

[6] S. Cheng, E. Ma, Y.M. Wang, L.J. Kecskes, K.M. Youssef, C.C. Koch, U.P. Trociewitz, K. Han, "Tensile properties of in situ consolidated nanocrystalline Cu", Acta Mater., Vol. 53, 2005, pp. 1521-1533.

[7] A. Giga, Y. Kimoto, Y. Takigawa, K. Higashi, "Demonstration of an inverse Hall-Petch relationship in electrodeposited nanocrystalline Ni-W alloys through tensile testing", Scr. Mater., Vol. 55, 2006, pp. 143-146.

[8] C.A. Schuh, T.G. Nieh, T. Yamasaki, "Hall-Petch breakdown manifested in abrasive wear resistance of nanocrystalline nickel", Scr. Mater., Vol. 46, 2002, pp. 735-740.

[9] V.Y. Gertsman, M. Hoffmann, H. Gleiter,R. Birringer, "The study of grain size dependence of yield stress of copper for a wide grain size range", Acta Metall. Mater., Vol. 42, 1994, pp. 3539-3544.

[10] H. Gleiter," Nanocrystalline materials", Prog. Mater Sci., Vol. 33, 1989, pp. 223-315.

[11] Y.M. Wang,E. Ma, "Strain hardening, strain rate sensitivity, and ductility of nanostructured metals", Mater. Sci. Eng., A, Vol. 375-377, 2004, pp. 46-52.

[12] X. Li, J. Zhou, R. Zhu, Y. Liu, H. Jiang., "Grain rotation dependent non-homogeneous deformation behavior in nanocrystalline materials", Mater. Sci. Eng., A, Vol. 527, 2010, pp.5677–5685.

[13] Y. Wei, A.F. Bower, H. Gao, "Enhanced strain-rate sensitivity in fcc nanocrystals due to grain-boundary diffusion and sliding", Acta Mater., Vol. 56, 2008, pp. 1741-1752.

[14] T.G. Desai, P. Millett, D. Wolf, "Is diffusion creep the cause for the inverse Hall-Petch effect in nanocrystalline materials?", Mater. Sci. Eng., A, Vol. 493, 2008, pp. 41-47.

[15] K.A. Padmanabhan, G.P. Dinda, H. Hahn, H. Gleiter, "Inverse Hall-Petch effect and grain boundary sliding controlled flow in nanocrystalline materials", Mater. Sci. Eng., A, Vol. 452-453, 2007, pp. 462-468.

[16] H.W. Song, S.R. Guo, Z.Q. Hu, "A coherent polycrystal model for the inverse Hall-Petch relation in nanocrystalline materials", Nanostruct. Mater., Vol. 11, 1999, pp. 203-210.

[17] G.J. Fan, H. Choo, P.K. Liaw, E.J. Lavernia, "A model for the inverse Hall-Petch relation of nanocrystalline materials", Mater. Sci. Eng., A, Vol. 409, 2005, pp. 243-248.

[18] X. Liu, F. Yuan, Y. We, “Grain size effect on the hardness of nanocrystal measured by the nanosize indente”, Appl. Surf. Sci., Vol. 279, 2013, pp.159–166.

[19] Y. Liu, J. Zhou, X. Ling, "Impact of grain size distribution on the multiscale mechanical behavior of nanocrystalline material", Mater. Sci. Eng., A, Vol. 527, 2010, pp.1719–1729.

[20] H.S. Kim, Y. Estrin, M.B. Bush, "Plastic deformation behaviour of fine-grained materials", Acta Mater., Vol. 48, 2000, pp.493–504.

[21] Y.J. Wei, L. Anand, "Grain-boundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metals", J. Mech. Phys. Sol., Vol. 52, 2004, pp. 2587-2616.

[22] R. Jafari Nedoushan, M. Farzin, M. Mashayekhi, "Effects of strain rate and grain size on behavior of nano crystalline materials", J. Nano Res., Vol. 17, 2012, pp. 35-51.

[23] R. Jafari Nedoushan, M. Farzin, "Effect of Hydrostatic Pressure on Nano Crystalline Materials Behavior", J. Nano Res., Vol. 18-19, 2012, pp. 27-42.

[24] P. Valentini, T. Dumitric."Microscopic theory for nanoparticle-surface collisions in crystalline silicon", Phys. Rev. B: Condens. Matter., Vol. 75, 2007, pp. 224106-1-224106-9.

[25] P. Valentini, W.W. Gerberich, T. Dumitric, "Phase-Transition Plasticity Response in Uniaxially Compressed Silicon Nanospheres", Phys. Rev. Lett., Vol. 99, 2007, pp.175701-1-175701-4.

[26] A. C. F. Cocks, "Interface reaction controlled creep", Mech. Mater., Vol. 13, 1992, pp.165-174.

[27] J. Pan, A. C. F. Cocks, "Computer simulation of superplastic deformation", Comput. Mater. Sci., Vol. 1, 1993, pp. 95-109.

[28] B. Zhu, R.J. Asaro, P. Krysl,R. Bailey, "Transition of deformation mechanisms and its connection to grain size distribution in nanocrystalline metals", Acta Mater., Vol. 53, 2005, pp. 4825-4838.

[29] Y.J. Wei, L. Anand, "Grain-boundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metals", J. Mech. Phys. Solids, Vol. 52, 2004, pp. 2587-2616.

[30] X. Qing, G. Xingming, "The scale effect on the yield strength of nanocrystalline materials", Int. J. Solids Struct., Vol. 43, 2006, pp. 7793–7799

[31] R.J. Asaro, A. Needleman, "Texture development and strain hardening in rate dependent polycrystals", Acta Metall., Vol. 33, 1985, pp. 923-953.

[32] D. Peirce, R.J. Asaro, A. Needleman, "An analysis of nonuniform and localized deformation in ductile single crystals", Acta Metall., Vol. 30, 1982, pp. 1087-1119.

[33] R. Schwaiger, B. Moser, M. Dao, N. Chollacoop, S. Suresh, "Some critical experiments on the strain-rate sensitivity of nanocrystalline nickel", Acta Mater., Vol. 51, 2003, pp. 5159–5172.

[34] S. Li, J. Zhou, L. Ma, N. Xu, R. Zhu, X. He,"Continnum level simulation on the deformation behavior of nanocrystalline nikel", Comput. Mater. Sci., Vol. 45, 2009, pp.390-397.

[35] N. Ahmed, A. Hartmaier, “A two-dimensional dislocation dynamics model of the plastic Deformation of polycrystalline metals”, J. Mech. Phys. Solids, Vol. 58, 2010, pp.2054–2064.

[36] S. Gollapudi, K.V. Rajulapat, I. Charit, C.C. Kocha, R.O. Scattergood, K.L. Murty, "Creep in nanocrystalline materials: Role of stress assisted grain growth", Mater. Sci. Eng., A, Vol. 527, 2010, pp.5773–5781.

[37] C.F.O. Dahlberg, J. Faleskog, "Strain gradient plasticity analysis of the influence of grain size and distribution on the yield strength in polycrystals", Eur. J. Mech. A/Solid., Vol. 44, 2014, pp.1–16.