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Surface effect investigation for static bending of nanowiresresting on elastic substrate using Timoshenko beam theory in tandem with the Laplace-Youngequation

Published online by Cambridge University Press:  16 November 2012

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Abstract

In the present study, an enriched continuum mechanics framework is employed to study thesurface effects on bending behavior of silver nanowires (NWs) resting on elasticsubstrate. The Timoshenko beam theory and the Laplace-Young equation are employed toinvestigate static behavior of silver NWs lying on Winkler-Pasternak elastic substrate.Three types of boundary conditions are considered as doubly simply supported (S-S), doublyclamped (C-C) and cantilevered (C-F). Analytical solutions are obtained for NWs withsurface crystallographic orientation of [001] subjected to a concentrated external force.By defining different normalized contact stiffness, extensive numerical results arecarried out to study the influence of effective parameters such as substrate, surface,aspect ratio (L/D) and diameter onthe stiffness of NWs. According to the obtained results, the effect of surface and itsrate of variation on stiffness of NWs lying on Winkler and Winkler-Pasternak elasticfoundation models are more significant in (C-F) type of boundary condition compared to theNWs without foundation. By increasing the modulus of elastic substrate, the effect ofshear deformation increases which it is more considerable in (C-C) and (S-S) NWs restingon the Winkler-Pasternak and Winkler substrate models, respectively.

Type
Research Article
Copyright
© AFM, EDP Sciences 2012

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References

Références

Lieber, C.M., Nanoscale science and technology : building a big future from small things, MRS Bull 28 (2003) 486491 CrossRefGoogle Scholar
Xia, Y., Yang, P., Sun, Y., Wu, Y., Mayers, B., Gates, B., Yin, Y., Kim, F., Yan, H., One-dimensional nanostructures : synthesis, characterization, and applications, Adv. Mater. 15 (2003) 353389 CrossRefGoogle Scholar
Lieber, C.M., Wang, Z.L., Functional Nanowires, MRS Bull. 32 (2007) 99108 CrossRefGoogle Scholar
Canham, L.T., Silicon quantum wire array fabricated by electrochemical and chemical dissolution of wafers, Appl. Phys. Lett. 57 (1990) 104648 CrossRefGoogle Scholar
Wong, E.W., Sheehan, P.E., Lieber, C.M., Nanobeam mechanics : elasticity, strength, and toughness of nanorods and nanotubes, Science 277 (1997) 197175 CrossRefGoogle Scholar
Kacem, N., Baguet, S., Hentz, S., Dufour, R., Nonlinear phenomena in nanomechanical resonators : mechanical behaviors and physical limitations, Mécanique & Industries 11 (2010) 521529 CrossRefGoogle Scholar
Cui, Y., Zhong, Z., Wang, D., Wang, W.U., Lieber, C.M., High performance silicon nanowire field effect transistors, Nano. Lett. 3 (2003) 149152 CrossRefGoogle Scholar
M. Cahay, J.P. Leburton, D.J. Lockwood, S. Bondyopadhyay, J.S. Harris, Quantum confinement VI : nanostructured materials and devices, Electrochemical Society, inc. USA, 2001
H. Haug, S.W. Koch, Quantum theory of the optical and electronic properties of semiconductors, World Scientific, Singapore, 2004
Shenoy, V.B., Atomistic calculations of elastic properties of metallic fcc crystal surfaces, Phys. Rev. B. 71 (2005) 09410411 CrossRefGoogle Scholar
Craighead, H.G., Nanoelectromechanical systems, Science 290 (2000) 153235 CrossRefGoogle ScholarPubMed
Ekinci, K.L., M.L. Roukes, Nanoelectromechanical systems. Rev. Sci. Instrum. 76 (2005) 06110112 CrossRefGoogle Scholar
R. Michael, S.C. Wolfram, Handbook of theoretical and computational nanotechnology, American Scientific, 2005, Vol. 1
Diao, J., Gall, K., Dunn, M.L., Atomistic simulation of the structure and elastic properties of gold nanowires, J. Mech. Phys. Sol. 52 (2004) 19351962 CrossRefGoogle Scholar
Wu, H.A., Molecular dynamics study on mechanics of metal nanowire, Mech. Res. Commun. 33 (2006) 916 CrossRefGoogle Scholar
Z.L. Wang, Mechanical properties of nanowires and nanobelts, Dekker Encyclopedia of Nanoscience and Nanotechnology (2004) 1773–1786, DOI : 10.1081/E-ENN.120013387
Jing, G.Y., Duan, H.L., Sun, X.M., Zhang, Z.S., Xu, J., Li, Y.D., Wang, J.X., Yu, D.P., Surface effects on elastic properties of silver nanowires : Contact atomic-force microscopy, Phys. Rev. B 73 (2006) 2354096 CrossRefGoogle Scholar
Chen, Y.X., Dorgan, B.L., McIlroy, D.N., Aston, D.E., On the importance of boundary conditions on nanomechanical bending behavior and elastic modulus determination of silver nanowires, J. Appl. Phys. 100 (2006) 1043017 CrossRefGoogle Scholar
Chen, C.Q., Zhang, Y.S., Zhu, J., Yan, Y.J., Size dependence of Young’s modulus in ZnO nanowires, Phys. Rev. Lett. 96 (2006) 0755054 CrossRefGoogle ScholarPubMed
Miller, R.E., Shenoy, V.B., Size-dependent elastic properties of nanosized structural elements, Nanotechnology 11 (2000) 139147 CrossRefGoogle Scholar
Guo, J.-G., Zhao, Y.-P., The size-dependent bending elastic properties of nanobeams with surface effects, Nanotechnology 18 (2007) 2957016 CrossRefGoogle Scholar
Li, X.F., Wang, B.L., Lee, K.Y., Size effects of the bending stiffness of nanowires, J. Appl. Phys. 105 (2009) 0743066 CrossRefGoogle Scholar
Gurtin, M.E., Murdoch, A.I., A continuum theory of elastic material surfaces, Arch. Rational. Mech. Anal. 57 (1975) 291323 CrossRefGoogle Scholar
Dingreville, R., Qu, J., Cherkaoui, M., Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films, J. Mech. Phys. Solids 53 (2005) 18271854 CrossRefGoogle Scholar
Duan, H.L., Wang, J., Huang, Z.P., Karihaloo, B.L., Eshelby formalism for nano-inhomogeneities, Proc. R. Soc. A 461 (2005) 33353353 CrossRefGoogle Scholar
Duan, H.L., Wang, J., Huang, Z.P., Karihaloo, B.L., Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress, J. Mech. Phys. Solids 53 (2005) 15741596 CrossRefGoogle Scholar
Duan, H.L., Yi, X., Huang, Z.P., Wang, J., A unified scheme for prediction of effective moduli of multiphase composites with interface effects, Part I : Theoretical framework, Mech. Mater. 39 (2007) 8193 CrossRefGoogle Scholar
Sharma, P., Ganti, S., Bhate, N., Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities, Appl. Phys. Lett. 82 (2003) 535537 CrossRefGoogle Scholar
Sharma, P., Ganti, S., Size-dependent Eshelby’s tensor for embedded nano-inclusions incorporating surface/interface energies, ASME J. Appl. Mech. 71 (2004) 66371 CrossRefGoogle Scholar
Yvonnet, J., Quang, H.L., He, Q.-C., An XFEM/level set approach to modelling surface/interface effects and to computing the size-dependent effective properties of nanocomposites, Comput. Mech. 42 (2008) 119131 CrossRefGoogle Scholar
Yvonnet, J., Mitrushchenkov, A., Chambaud, G., He, Q.-C., Finite element model of ionic nanowires with size-dependent mechanical properties determined by ab initio calculations, Comput. Methods. Appl. Mech. Eng. 200 (2011) 614625 CrossRefGoogle Scholar
Wang, G.F., Feng, X.Q., Effects of surface elasticity and residual surface tension on the natural frequency of microbeams, Appl. Phys. Lett. 90 (2007) 231904 CrossRefGoogle Scholar
Wang, G.F., Feng, X.Q., Effects of surface stresses on contact problems at nanoscale, J. Appl. Phys. 101 (2007) 0135106 CrossRefGoogle Scholar
Wang, G.F., Feng, X.Q., Surface effects on buckling of nanowires under uniaxial compression, Appl. Phys. Lett. 94 (2009) 141913 CrossRefGoogle Scholar
Wang, G.F., Feng, X.Q., Timoshenko beam model for buckling and vibration of nanowires with surface effects, J. Phys. 42 (2009) 155411 Google Scholar
He, J., Lilley, C.M., Surface effect on the elastic behavior of static bending nanowires, Nano Lett. 8 (2008) 17981802 CrossRefGoogle ScholarPubMed
Jiang, L.Y., Yan, Z., Timoshenko beam model for static bending of nanowires with surface effects, Physica E : Low-dimens. Syst. Nanostruct. 42 (2010) 2274 CrossRefGoogle Scholar
Wang, M.C.P., Gates, B.D., Directed assembly of nanowires, Mater. Today 12 (2009) 3443 CrossRefGoogle Scholar
Lu, W., Lieber, C.M., Nanoelectronics from the bottom up, Nat. Mater. 6 (2007) 541850 CrossRefGoogle ScholarPubMed
Ru, C.Q., Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium, J. Mech. Phys. Solids 49 (2001) 126579 CrossRefGoogle Scholar
Pradhan, S.C., Kumar, A., Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method, Comput. Mater. Sci. 50 (2010) 239245 CrossRefGoogle Scholar
Mohammadimehr, M., Saidi, A.R., A. Ghorbanpour Arani, A. Arefmanesh, Q. Han, Torsional buckling of a DWCNT embedded on Winkler and Pasternak foundations using nonlocal theory, J. Mech. Sci. Technol. 24 (2010) 12891299 CrossRefGoogle Scholar
R.F. Scott, Foundation Analysis, Prentice-Hall : Englewood Cliffs N.J, 1981
A.C. Ugural, S.K. Fenster, Advanced strength and applied elasticity, Printice Hall : USA, 2003
P.L. Pasternak, On a new method of analysis of an elastic foundation by means of two foundation constants, Goz Izd Lip Po Strait i Arkh : Moscow (in Russian), 1954
Cammarata, R.C., Surface and interface stress effects in thin films, Prog. Surf. Sci. 46 (1994) 138 CrossRefGoogle Scholar
Hutchinson, J.R., Shear coefficients for timoshenko beam theory, J. Appl. Mech. Trans : ASME 68 (2001) 8792 CrossRefGoogle Scholar
Ghani razaqpur, A., Shah, K.R., Exact analysis of beams on two-parameter elastic foundations, Int. J. Solids Struct. 27 (1991) 43554 CrossRefGoogle Scholar
Liew, K.M., He, X.Q., Kitipornchai, S., Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix, Acta. Mater. 54 (2006) 42294236 CrossRefGoogle Scholar
Murmu, T., Pradhan, S.C., Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Physica E : Low-dimens. Syst. Nanostruct. 41 (2009) 12321239 CrossRefGoogle Scholar
Li, X.F., Fei, G.T., Zhou, W.F., Zhang, L.D., A convenient method to determine the bulk modulus of nanowires and its temperature dependence based on X-ray diffraction measurement, Solid. State. Commun. 150 (2010) 11171119 CrossRefGoogle Scholar