Examining and calculation of non-classical in the solutions to the true elastic cable under concentrated loads in nanofilm

Document Type: Reasearch Paper

Authors

Department of Mechanical Engineering, East Azerbaijan Science and Research Branch, Islamic Azad University, Tabriz, Iran.

10.7508/ijnd.2015.05.003

Abstract

Due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. In this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on Gurtin-Murdoch continuum model to consider surface stress effects. Fourier integral transforms are used to solve the non-classical boundary-value problem related to inclined point load and an analytical solution is obtained for the corresponding boundary-value problem. Selected numerical results are presented for different values of loading angle and are compared with the classical ones to illustrate the influence of the surface stress effects on the stiffness of nano-coating and ultra-thin films. It is found that the surface stress effects have a quite large influence on the response of the nanofilm especially for more vertical loading (higher values of the angle of loading) and make the layer stiffer than the classical case.

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[1]  Vinci R. P., Vlassak J. J., (1996), Mechanical behavior of thin films. Annual Rev. Mater. Sci. 26: 431-462.

[2]  Zhao M., Xiang Y., Xu J., Ogasawara N., Chiba N., Chen X., (2008), Determining mechanical properties of thin films from the loading curve of nanoindentation testing. Thin Solid Films. 516: 7571-7580.

[3]  Pervan P., Valla T., Milun M., (1998), Structural and electronic properties of vanadium ultra-thin film on Cu(100). Surf. Sci. 397: 270-277.

[4]  Ngo D., Feng X., Huang Y., Rosakis A. J., (2008), Multilayer thin films/substrate system with variable film thickness subjected to non-uniform misfit strains. Acta Mater. 56: 5322-5328.

[5]  Chen S. H., Liu L., Wang T. C., (2007), Small scale, grain size and substrate effects in nano-indentation experiment of film-substrate systems. Int. J. Solids and Struc. 44: 4492-4504.

[6]  Li M., Chen W., Cheng Y., Cheng C., (2009), Influence of contact geometry on hardness behavior in nano-indentation.Vacuum. 84: 315-320.

[7]  Dhaliwal R. S., Rau I. S., (1970), The axisymmetric boussinesq problem for a thick elastic layer under a punch of arbitrary profile. Int. J. Eng. Sci. 8: 843-856.

[8]  Dhaliwal R. S., Rau I. S., (1972), Further consideration on the axisymmetric boussinesq problem. Int. J. Eng. Sci. 10: 659-663.

[9]  Yasumoto M., Tomimasu T., (2002), A proposed novel method for thin-film fabrication assisted by mid-infrared free electron laser, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers. Detec. Assoc. Equip. 480: 92-97.

[10] Itaka K., Yamashiro M., Yamaguchi J., Yaginuma S., Haemori M., Koinuma H., (2006), Combinatorial approach to the fabrication of organic thin films. App. Surf. Sci. 252: 2562-2567.

[11] Gurtin M. E., Murdoch A. I., (1975), A continuum theory of elastic material surface. Arch. Ratio. Mech. Anal. 57: 291-323.

[12] Gurtin M. E., Murdoch A. I., (1978), Surface stress in solids. Int. J. Solids and Struc. 14: 431-440.

[13] Mogilevskaya S. G., Crouch S. L., Stolarski H. K.,(2008), Multiple interacting circular nano-inhomogeneities with surface/interface effects. J. Mech. Phys. Solids. 56: 2298-2327.

[14] Li Z. R., Lim C. W., He L. H., (2006), Stress concentration around a nanoscale spherical cavity in elastic media: effects of surface stress. Europ. J. Mech. A.:Solids. 25: 260-270.

[15] He L. H., Lim C. W., (2006), Surface Green function for a soft elastic half-space: influence of surface stress. Int. J. Solids and Struc. 43: 132-143.

[16] Gordeliy E., Mogilevskaya S. F., Crouch S. L., (2009), Transient thermal stresses in a medium with a circular cavity with surface effects. Int. J. Solids and Struc. 46: 1834-1848.

[17] Koguchi H., (2008), Surface Green function with surface stresses and surface elasticity using Stroh.s formalism. J. Appl. Mech. Transact. ASME. 75: 061014.

[18] Bar On B., Altus E., Tadmor E. B., (2010), Surface effects in non-uniform nanobeams: continuum vs. atomistic modeling. Int. J. Solids and Struct. 47: 1243-1252.

[19] Shen S., Hu S., (2010), A theory of flexoelectricity with surface effect for elastic dielectrics. J. Mech. Phys. Solids.58: 665-677.

[20] Sneddon I. N., (1951), Fourier transforms, McGraw-Hill, New York, Springer.

[21] Selvadurai A. P. S., (2000), Partial differential equations in mechanics, New York, Springer.

[22] Miller R. E., Shenoy V. B., (2000), Size-dependent elastic properties of nanosized structural elements. Nanotech. 11: 139-147.

[23] Shenoy V. B., (2005), Atomistic calculations of elastic properties of metallic fcc crystal surfaces. Phys. Rev. B. 71: 094104.

[24] Meyers M. A., Chawla K. K., (1999), Mechanical behavior of materials, Prentice-Hall, NJ.