Analysis of micro/nanobridge test based on nonlocal elasticity

International Journal of Solids and Structures

Volumn 49, Issue 15-16, 2012, Pages 2168-2176

  Fan, Cuiying ^a   Zhao, Minghao ^a   Zhu, Yongjie ^a   Liu, Haitao ^a   Zhang, Tong Yi ^b  

^a ZHENGZHOU UNIVERSITY   (China)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Analytical solution; Compliant substrate; Deflection; Micro nanobridge; Nonlocal elasticity; Timoshenko beam

Indexed keywords

ANALYTIC SOLUTION; APPLIED LOADS; BEAM DEFLECTION; COMPLIANT SUBSTRATES; CONTACT DEFORMATION; EXPLICIT FORMULA; INDENTERS; MICRO/NANOBRIDGE; NONLOCAL; NONLOCAL ELASTICITY; PHASE ANGLES; STRAIN GRADIENTS; SUBSTRATE DEFORMATION; TIMOSHENKO BEAM THEORY; TIMOSHENKO BEAMS;

DEFLECTION (STRUCTURES); DEFORMATION; PARTICLE BEAMS;

ELASTICITY;

EID: 84861810493     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2012.04.028     Document Type: Article

References (37)

1. S.P. Baker, and W.D. Nix Mechanical properties of compositionally modulated Au-Ni thin films: nanoindentation and microcantilever deflection experiments J. Mater. Res. 9 1994 3131 3144
2. W.K. Chan, J.R. Li, Y. Wang, S.Y. Zhang, and T.Y. Zhang Analysis of nanobridge tests Acta Mech. Solida Sin. 23 2010 283 296
3. A.C. Eringen Nonlocal polar elastic continua Int. J. Eng. Sci. 10 1972 1 16
4. A.C. Eringen On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves J. Appl. Phys. 54 1983 4703 4710 (Pubitemid 14450262)
5. A.C. Eringen, and D.G.B. Edelen On nonlocal elasticity Int. J. Eng. Sci. 10 1972 233 248
6. F. Essenburg Shear deformation in beams on elastic foundations J. Appl. Mech. 29 1960 313 317
7. B. Huang, and T.Y. Zhang Microbridge tests: II. On buckled thin gold films J. Micromech. Microeng. 16 2006 134 142 (Pubitemid 41818034)
8. M.J. Kobrinsky, E.R. Deutsch, and S.D. Senturia Effect of support compliance and residual stress on the shape of doubly supported surface-micromachined beams J. Microelectromech. S. 9 2000 361 369
9. S. Li, J. Wang, and M.D. Thouless The effects of shear on delamination in layered materials J. Mech. Solids Struct. 52 2004 193 214
10. C.Y. Nam, P. Jaroenapibal, D. Tham, D.E. Luzzi, S. Evoy, and J.E. Fischer Diameter-dependent electromechanical properties of GaN nanowires Nano. Lett. 6 2006 153 158 (Pubitemid 43382943)
11. J. Peddieson, G.R. Buchanan, and R.P. McNitt Application of nonlocal continuum models to nanotechnology Int. J. Eng. Sci. 41 2003 305 312
12. P. Poncharal, Z.L. Wang, D. Ugarte, and W.A. de Heer Electrostatic deflections and electromechanical resonances of carbon nanotubes Science 283 1999 1513 1516
13. S.Roy. Puri, A. Acharya, and D. Dimiduk Modeling dislocation sources and size effects at initial yield in continuum plasticity J. Mech. Mater. Struct. 4 2009 1603 1618
14. Y.J. Su, C.F. Qian, M.H. Zhao, and T.Y. Zhang Microbridge testing of silicon oxide/silicon nitride bilayer films deposited on silicon wafers Acta. Mater. 48 2000 4901 4915
15. L.J. Sudak Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics J. Appl. Phys. 94 2003 7281 7287
16. S.P. Timoshenko On the correction for shear of the differential equation for transverse vibration of prismatic bars Philos. Mag. 41 1921 744 746
17. S. Timoshenko Strength of materials: Part II. Advanced theory and problems third ed. 1957 New York
18. A.A. Volinsky, N.R. Moody, and W.W. Gerberich Interfacial toughness measurements for thin films on substrates Acta. Mater. 50 2002 441 466 (Pubitemid 34064992)
19. K.T. Wan, and K. Liao Measuring mechanical properties of thin flexible film by a shaft-loaded blister test Thin Solid Films 352 1999 167 172 (Pubitemid 129587829)
20. L.F. Wang, and H.Y. Hu Flexural wave propagation in single-walled carbon nanotubes Phys. Rev. B 71 2005 195412
21. X.S. Wang, and T.Y. Zhang Microbridge tests on bilayer thin films Metall. Mater. Trans. A 38 2007 2273 2282
22. X.S. Wang, J. Wang, M.H. Zhao, and T.Y. Zhang Microbridge testing on symmetrical trilayer films J. Microelectromech. Syst. 14 2005 634 645 (Pubitemid 41005084)
23. C.M. Wang, Y.Y. Zhang, S.S. Ramesh, and S. Kitipornchai Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory J. Phys. D: Appl. Phys. 39 2006 3904 3909 (Pubitemid 44261950)
24. X.S. Wang, J.R. Li, and T.Y. Zhang Microbridge tests: I. On asymmetrical trilayer films J. Micromech. Microeng. 16 2006 122 133
25. T.P. Weihs, S. Hong, J.C. Bravman, and W.D. Nix Mechanical deflection of cantilever microbeams: a new technique for testing the mechanical properties of thin films J. Mater. Res. 3 1988 931 942
26. E.W. Wong, P.E. Sheehan, and M.L. Charles Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes Science 277 1997 1971 1975 (Pubitemid 27449134)
27. W.H. Xu, and T.Y. Zhang Mechanical characterization of trilayer thin films by the microbridge testing method Appl. Phys. Lett. 83 2003 1731 1733
28. F.Q. Yang, and J.C.M. Li Micro and nano mechanical testing of materials and devices 2008 Springer New York
29. H.H. Yu, and J.W. Hutchinson Influence of substrate compliance on buckling delamination of thin films Int. J. Fracture 113 2002 39 55 (Pubitemid 34156128)
30. D.J. Zeng, and Q.S. Zheng Resonant frequency-based method for measuring the Young's moduli of nanowires Phys. Rev. B 76 2007 441 466
31. T.Y. Zhang, Y.J. Su, C.F. Qian, M.H. Zhao, and L.Q. Chen Microbridge testing of silicon nitride thin films deposited on silicon wafers Acta. Mater. 48 2000 2843 2857
32. T.Y. Zhang, M.H. Zhao, and C.F. Qian Effect of substrate deformation on the microcantilever beam-bending test J. Mater. Res. 15 2000 1868 1871
33. Y.Q. Zhang, G.R. Liu, and J.S. Wang Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression Phys. Rev. B 70 2004 205430 205436
34. T.Y. Zhang, X.S. Wang, and B. Huang Microbridge testing of thin films Mater. Sci. Eng. A. 409 2005 329 339 (Pubitemid 41742316)
35. Y.Q. Zhang, G.R. Liu, and X.Y. Xie Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal Phys. Rev. B 71 2005 195404 195407
36. Y.Y. Zhang, C.M. Wang, and V.B.C. Tan Buckling of multiwalled carbon nanotubes using Timoshenko beam theory J. Eng. Mech. ASCE 121 2006 952 958
37. T.Y. Zhang Microbridge tests F.Q. Yang, J.C.M. Li, Micro and nano mechanical testing of materials and devices 2008 Springer New York (Chapter 10)