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Interpreting the softening of nanomaterials through gradient plasticity

Published online by Cambridge University Press:  10 June 2011

Xu Zhang  and
Katerina E. Aifantis
Xu Zhang
Affiliation:
School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China; and Laboratory of Mechanics and Materials, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
Katerina E. Aifantis*
Affiliation:
Laboratory of Mechanics and Materials, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece; and Physics Department, Michigan Technological University, Houghton, Michigan 49931
*
a)Address all correspondence to this author. e-mail: [email protected]
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Abstract

Experimental and simulation studies have shown that decreasing the grain size below a critical value results in softening rather than hardening in both the yield stress and flow stress of nanomaterials. In this work, a gradient plasticity framework is presented that can capture this softening behavior by treating grain boundaries as a separate phase with a finite thickness. The theoretical expression obtained for the yield stress as a function of the grain size can capture numerous experimental data that exhibit this “normal” to “abnormal” Hall–Petch transition, and an analytical equation is obtained that can predict the grain size at which this transition occurs. Furthermore, analytical expressions are obtained for the flow stress in nanomaterials, and they are in precise agreement with atomistic simulations on nanocrystalline Cu, which predict that below a critical grain size the flow stress decreases proportional to it.

Keywords

NanoscaleNanostructure
Type
Articles
Information
Journal of Materials Research , Volume 26 , Issue 11 , 14 June 2011 , pp. 1399 - 1405
Copyright
Copyright © Materials Research Society 2011

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References

REFERENCES

1.Sanders, P.G., Eastman, J.A., and Weertman, J.R.: Elastic and tensile behavior of nanocrystalline copper and palladium. Acta Mater. 45, 4019 (1997).CrossRefGoogle Scholar
2.Liu, X.D., Hu, Z.Q., and Ding, B.Z.: Hall-Petch relation in nanocrystalline Fe-Mo-Si-B alloys. Nanostruct. Mater. 2, 545 (1993).CrossRefGoogle Scholar
3.Volpp, T., Göring, E., Kuschke, W.M., and Arzt, E.: Grain size determination and limits to Hall-Petch behavior in nanocrystalline NiAl powders. Nanostruct. Mater. 8, 855 (1997).CrossRefGoogle Scholar
4.Narayan, J., Venkatesan, R.K., and Kvit, A.: Structure and properties of nanocrystalline zinc films. J. Nanopart. Res. 4, 265 (2002).CrossRefGoogle Scholar
5.Venkatesan, R., Kvit, A., Wei, Q., and Narayan, J.: Novel tungsten carbide nanocrystalline composites by pulsed laser deposition, in Structure and Mechanical Properties of Nanophase Materials—Theory and Computer Simulations vs. Experiment, edited by Farkas, D., Kung, H., Mayo, M., Van Swygenhoven, H., and Weertman, J. (Mater. Res. Soc. Symp. Proc. 634, Warrendale, PA, 2000), B6.1.1.Google Scholar
6.Chokshi, A.H., Rosen, A., Karch, J., and Gleiter, H.: On the validity of the Hall-Petch relationship in nanocrystalline materials. Scr. Metall. 23, 1679 (1989).CrossRefGoogle Scholar
7.Palumbo, G., Erb, U., and Aust, K.T.: Triple line disclination effects on the mechanical behaviour of materials. Scr. Metall. Mater. 24, 2347 (1990).CrossRefGoogle Scholar
8.Zhao, M., Li, J.C., and Jiang, Q.: Hall–Petch relationship in nanometer-size range. J. Alloy. Comp. 361, 160 (2003).Google Scholar
9.Lu, L., Chen, X., Huang, X., and Lu, K.: Revealing the maximum strength in nanotwinned copper. Science 323, 607 (2009).CrossRefGoogle ScholarPubMed
10.Meyers, M., Mishra, A., and Benson, D.: Mechanical properties of nanocrystalline materials. Prog. Mater. Sci. 51, 427 (2006).CrossRefGoogle Scholar
11.Pande, C.S. and Cooper, K.P.: Nanomechanics of Hall–Petch relationship in nanocrystalline materials. Prog. Mater. Sci. 54, 689 (2009).CrossRefGoogle Scholar
12.Saada, G. and Dirras, G.: Chapter 90 Mechanical properties of nanograined metallic polycrystals, in Dislocations in Solids Volume 15, edited by Hirth, J.P. and Kubin, L. (Elsevier, Amsterdam, 2009), p. 199.CrossRefGoogle Scholar
13.Carsley, J.E., Ning, J., Milligan, W.W., Hackney, S.A., and Aifantis, E.C.: A simple, mixtures-based model for the grain size dependence of strength in nanophase metals. Nanostruct. Mater. 5, 441 (1995).Google Scholar
14.Konstantinidis, D.A. and Aifantis, E.C.: On the “anomalous” hardness of nanocrystalline materials. Nanostruct. Mater. 10, 1111 (1998).CrossRefGoogle Scholar
15.Aifantis, K.E. and Konstantinidis, A.A.: Hall–Petch revisited at the nanoscale. Mater. Sci. Eng., B 163, 139 (2009).CrossRefGoogle Scholar
16.Aifantis, K.E. and Konstantinidis, A.A.: Yielding and tensile behavior of nanocrystalline copper. Mater. Sci. Eng., A 503, 198 (2009).CrossRefGoogle Scholar
17.Aifantis, K.E. and Willis, J.R.: The role of interfaces in enhancing the yield strength of composites and polycrystals. J. Mech. Phys. Solids 53, 1047 (2005).Google Scholar
18.Schiotz, J., Vegge, T., Di Tolla, F.D., and Jacobsen, K.W.: Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Phys. Rev. B 60, 11971 (1999).CrossRefGoogle Scholar
19.Li, J.C.M.: Grain boundary impurity and porosity effects on the yield strength of nanocrystalline materials. Appl. Phys. Lett. 90, 041912 (2007).CrossRefGoogle Scholar
20.Armstrong, R.W., Conrad, H., and Nabarro, F.R.N.: Meso-to-nano-scopic polycrystal/composite strengthening, in Mechanical Properties of Nanostructured Materials and Nanocomposites, edited by Ovid'ko, I., Pande, C.S., Krishnamoorti, R., Lavernia, E., and Skandan, G. (Mater. Res. Soc. Symp. Proc. 791, Warrendale, PA, 2004), p. 69.Google Scholar
21.Ke, M., Hackney, S.A., Milligan, W.W., and Aifantis, E.C.: Observation and measurement of grain rotation and plastic strain in nanostructured metal thin films. Nanostruct. Mater. 5, 689 (1995).Google Scholar
22.Ovid'ko, I.A. and Sheinerman, A.G.: Enhanced ductility of nanomaterials through optimization of grain boundary sliding and diffusion processes. Acta Mater. 57, 2217 (2009).Google Scholar
23.Kim, H.S., Estrin, Y., and Bush, M.B.: Constitutive modelling of strength and plasticity of nanocrystalline metallic materials. Mater. Sci. Eng., A 316, 195 (2001).CrossRefGoogle Scholar
24.Kim, H.S., Estrin, Y., and Bush, M.B.: Plastic deformation behaviour of fine-grained materials. Acta Mater. 48, 493 (2000).CrossRefGoogle Scholar
25.Armstrong, R.W.: Plasticity: Grain size effects II, in Encyclopedia of Materials: Science and Technology, edited by Buschow, K.H.J., Robert, W.C., Merton, C.F., Bernard, I., Edward, J.K., Subhash, M., and Patrick, V. (Elsevier, Oxford, England, 2005), p. 1.Google Scholar
26.Fu, H.H., Benson, D.J., and Meyers, M.A.: Analytical and computational description of effect of grain size on yield stress of metals. Acta Mater. 49, 2567 (2001).CrossRefGoogle Scholar
27.Meyers, M.A. and Ashworth, E.: A model for the effect of grain size on the yield stress of metals. Philos. Mag. A 46, 737 (1982).CrossRefGoogle Scholar
28.Gutkin, M.Y., Ovid’ko, I.A., and Skiba, N.V.: Strengthening and softening mechanisms in nanocrystalline materials under superplastic deformation. Acta Mater. 52, 1711 (2004).CrossRefGoogle Scholar
29.Ovid’ko, I.A.: Superplasticity and ductility of superstrong nanomaterials. Rev. Adv. Mater. Sci. 10, 89 (2005).Google Scholar
30.Padmanabhan, K.A. and Gleiter, H.: Optimal structural superplasticity in metals and ceramics of microcrystalline- and nanocrystalline-grain sizes. Mater. Sci. Eng., A 381, 28 (2004).CrossRefGoogle Scholar
31.Aifantis, K. and Ngan, A.: Modeling dislocation—grain boundary interactions through gradient plasticity and nanoindentation. Mater. Sci. Eng., A 459, 251 (2007).Google Scholar
32.Tabor, D.: The Hardness of Metals (Oxford University Press, 2000).CrossRefGoogle Scholar
33.Argon, A.S. and Yip, S.: The strongest size. Philos. Mag. Lett. 86, 713 (2006).CrossRefGoogle Scholar
34.Zhang, X. and Aifantis, K.E.: Accounting for grain boundary thickness in the sub-micron and nano scales. Rev. Adv. Mater. Sci. 26, 74 (2010).Google Scholar
35.Aifantis, E.C.: On the microstructural origin of certain inelastic models. Trans. ASME, J. Eng. Mat. Techn. 106, 326 (1984).CrossRefGoogle Scholar