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Hall-Petch analysis of dislocation pileups in thin material layers and in nanopolycrystals

Published online by Cambridge University Press:  06 March 2013

Ronald W. Armstrong*
Affiliation:
Department of Mechanical Engineering, Center for Energetic Concepts Development, University of Maryland, College Park, Maryland 20742
*
a)Address all correspondence to this author. e-mail: [email protected]
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Abstract

A potential order-of-magnitude increase in Hall-Petch (H-P)-based strength level for nanoscale grain-size structures is an important enabler of electronic thin film material design applications. Dislocation pileups of smaller lengths in such thin film materials are blocked in a screw orientation at the through-thickness grain boundaries of relatively larger grains. For fully nanopolycrystalline materials, both strength and strain rate sensitivity measurements exhibit complementary H-P reciprocal square root of grain size dependencies. An additional increase in strength level is predicted for transition from a pileup to a single dislocation loop expanding against the grain boundary obstacle. In opposition, disordered grain boundaries are responsible for a reduced H-P stress intensity, kε. And at the limiting high stresses reached at lower-limiting nanoscale grain sizes, reversed H-P dependences are obtained both for the strength and strain rate sensitivity.

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Articles
Copyright
Copyright © Materials Research Society 2013 

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References

REFERENCES

Head, A.K.: The interaction of dislocations with boundaries and surface films. Aust. J. Phys. 13, 278283 (1959).CrossRefGoogle Scholar
Armstrong, R.W. and Head, A.K.: Dislocation queuing and fracture in an elastically anisotropic material. Acta Metall. 13, 759764 (1965).CrossRefGoogle Scholar
Head, A.K.: Dislocation group dynamics VI. The release of a pile-up. Philos. Mag. 27(3), 531539 (1973).CrossRefGoogle Scholar
Armstrong, R.W., Coffey, C.S., and Elban, W.L.: Adiabatic heating at a dislocation pile-up avalanche. Acta Metall. 30, 21112116 (1982).CrossRefGoogle Scholar
Armstrong, R.W.: Dislocation pile-up model for the strength of polycrystals, in International Symposium On Materials For Enabling Nanodevices (ISMEN 2012); K-N. Tu, T.F. Liu, and P. Sheng eds.; UCLA, 27–29 Aug., 2012; p. 12.Google Scholar
Armstrong, R.W.: Dislocation Pile-ups: From {110} cracking in MgO to model strength evaluations. Mater. Sci. Eng., A 409, 2431 (2005).CrossRefGoogle Scholar
Griffin, A.J. Jr., Brotzen, F.R., and Dunn, C.: Hall-Petch relation in thin film metallizations. Scr. Metall. 20, 12711272 (1986).CrossRefGoogle Scholar
Brotzen, F.R.: Mechanical testing of thin films. Int. Mater. Rev. 39(1), 2445 (1994).CrossRefGoogle Scholar
Armstrong, R.W.: Hall-Petch analysis for nanopolycrystals, in Nanometals – Status and Perspective, Faester, S., Hansen, N., Huang, X., Juul Jensen, D., and Ralph, B., eds (Danish Technical University, Risoe Campus, Roskilde, 2012); pp. 181199.Google Scholar
Fleischer, R.L. and Hosford, W.F. Jr.: Easy glide and grain boundary effects in polycrystalline aluminum. Trans. TMS-AIME 221, 244247 (1961).Google Scholar
Hansen, N.: Effect of grain size and strain on the tensile flow stress of aluminum at room temperature. Acta Metall. 25(8), 863869 (1977).CrossRefGoogle Scholar
Armstrong, R.W.: On size effects in polycrystal plasticity. J. Mech. Phys. Sol. 9, 196199 (1961).CrossRefGoogle Scholar
Voscoboinikov, R.E.: Equilibrium of a screw dislocation near the interface in a coated solid. Phys. Met. Metall. 113(5), 448454 (2012) [in Russian].CrossRefGoogle Scholar
Keller, C., Hug, E., Retoux, R., and Feaugas, X.: TEM study of dislocation patterns in near-surface and core regions of deformed nickel polycrystals with few grains across the cross section. Mech. Mater. 42, 4454 (2010).CrossRefGoogle Scholar
Brittain, C.P., Armstrong, R.W., and Smith, G.C.: Hall-Petch dependence for ultrafine grain size electrodeposited chromium material. Scr. Metall. 19, 8991 (1985).CrossRefGoogle Scholar
Bull, S.J., Sanderson, L., Moharrami, N., and Oila, A.: Effect of microstructure on hardness of submicrometre thin films and nanostructured devices. Mater. Sci. Tech. 28(9–10), 11771185 (2012).CrossRefGoogle Scholar
Chicot, D., Gil, L., Silva, K., Roudet, F., Puchi-Cabrera, E.S., Staia, M.H., and Teer, D.G.: Thin film hardness determination using indentation loading curve modeling. Thin Solid Films 518, 55655571 (2010).CrossRefGoogle Scholar
Carreker, R.P. Jr. and Hibbard, W.R. Jr.: Tensile deformation of aluminum as a function of temperature, strain rate and grain size. Trans. TMS-AIME 209, 11571163 (1957).Google Scholar
Tsuji, N., Ito, Y., Saito, Y., and Minamino, Y.: Strength and ductility of ultrafine-grained aluminum and iron produced by ARB and annealing. Scr. Mater. 47(12), 893899 (2002).CrossRefGoogle Scholar
Hansen, N. and Ralph, B.: The strain and grain size dependence of the flow stress of copper. Acta Metall. 30, 411417 (1982).CrossRefGoogle Scholar
Lu, L., Chen, X., Huang, X., and Lu, K.: Revealing the maximum strength in nanotwinned copper. Science 323, 607610 (2009).CrossRefGoogle ScholarPubMed
Keller, C. and Hug, E.: Hall-Petch behavior of Ni polycrystals with a few grains per thickness. Mater. Lett. 62, 17181720 (2008).CrossRefGoogle Scholar
Torrents, A., Yang, H., and Mohammed, F.: Effect of annealing on hardness and the modulus of elasticity in bulk nanocrystalline nickel. Metall. Mater. Trans. A 41, 621630 (2010).CrossRefGoogle Scholar
Armstrong, R.W.: Dislocation queuing analysis for the plastic deformation of aluminum polycrystals, in Physics of Materials; A Festschrift for Dr. Walter Boas on the Occasion of His 75th Birthday, edited by Borland, D.W., Clarebrough, L.M., and Moore, A.J.W. (University of Melbourne, Australia, 1979); pp. 111.Google Scholar
Li, J.C.M. and Liu, G.C.T.: Circular dislocation pileups: 1. Strength of ultrafine polycrystalline aggregates. Philos. Mag. 15, 10591063 (1967).CrossRefGoogle Scholar
Armstrong, R.W.: Theory of the tensile ductile-brittle behavior of polycrystalline hcp materials; with application to beryllium. Acta Metall. 16, 347355 (1968).CrossRefGoogle Scholar
Armstrong, R.W.: Strength and ductility of metals. Trans. Indian J. Met. 50, 521531 (1997).Google Scholar
Armstrong, R.W., Conrad, H., and Nabarro, F.R.N.: Meso- to nanoscopic 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. 791, Warrendale, PA, 2004); pp. 6977.Google Scholar
Armstrong, R.W.: Grain boundary structural influences on nanopolycrystal strength and strain rate sensitivity. Emerg. Mater. Res. 1(S1), 3137 (2012).Google Scholar
Conrad, H.: Grain-size dependence of the flow stress of copper from millimeters to nanometers. Metall. Mater. Trans. A 35, 26812695 (2004).CrossRefGoogle Scholar
Armstrong, R.W.: Thermal activation strain rate analysis (TASRA) for polycrystalline metals. J. Sci. Indust. Res. 32(11), 591598 (1973) [in Indian].Google Scholar
Prasad, Y.V.R.K. and Armstrong, R.W.: Polycrystal versus single-crystal strain rate sensitivity of cadmium. Philos. Mag. 29(6), 14211425 (1974).CrossRefGoogle Scholar
Rodriguez, P., Armstrong, R.W., and Mannan, S.L.: The dependence of activation area on grain size in cadmium. Trans. Indian Inst. Met. 56(3), 189196 (2003).Google Scholar
Armstrong, R.W. and Rodriguez, P.: Flow stress/grain size/strain rate coupling for fcc nanopolycrystals. Philos. Mag. 86, 57875796 (2006).CrossRefGoogle Scholar
Narutani, T. and Takamura, J.: Grain size strengthening in terms of dislocation density measured by resistivity. Acta Metall. Mater. 39(8), 20372049 (1991).CrossRefGoogle Scholar
Asaro, R.J. and Suresh, S.: Mechanistic models for the activation volume and rate sensitivity in metals with nanocrystalline grain sizes. Acta Mater. 53, 33693382 (2005).CrossRefGoogle Scholar
Rodriguez, P.: Grain size dependence of the activation parameters for plastic deformation: Influence of crystal structure, slip system and rate-controlling dislocation mechanism. Metall. Mater. Trans. A 35(9), 26972705 (2004).CrossRefGoogle Scholar
Conrad, H. and Narayan, J.: Mechanisms for grain size hardening and softening in zinc. Acta Mater. 50, 50675078 (2002).CrossRefGoogle Scholar
Langdon, T.G.: Grain boundary sliding revisited: Developments in sliding over four decades. J. Mater. Sci. 41, 597609 (2006).CrossRefGoogle Scholar
Ogawa, K. and Tanaka, K.: Effect of grain size on the strength of polycrystalline zinc, in Proceedings of 23rd Japan Congress on Materials Research (Soc. Mater. Sci., Japan, 1980); pp. 3945.Google Scholar