Analysis of Indentation on Layered Elastic Medium with Surface Energy Effects

Abstract:

This paper presents the analysis of an axisymmetric frictionless rigid punch on a layered elastic medium with the consideration of surface energy effects by adopting Gurtin-Murdoch continuum theory of surface elasticity. The indentation problem is formulated as a mixed-boundary value problem with the displacement boundary condition being imposed at the contact area. The unknown contact pressure under the indenter is then determined by employing a discretization technique with use of the displacement Green’s functions. The required Green’s functions are expressed in the form of the Hankel integral transform. The accuracy of the proposed solution scheme is verified by comparing with existing solutions. Selected numerical results on displacement and stress profiles in a layered elastic half-space are presented to demonstrate the influence of various parameters on elastic fields. It is found that the layered medium becomes stiffer and shows size-dependent behavior due to the presence of surface stresses.

• Periodical: Key Engineering Materials (Volume 775)
• Pages: 524-530
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.775.524
• Online since: August 2018
• Authors: Supakorn Tirapat, Teerapong Senjuntichai*
• Keywords: Gurtin-Murdoch Model, Layered Medium, Nanoindentation, Size-Dependency, Surface Stresses, Thin Films

References

[1] E.W. Wong, P.E. Sheehan, C.M. Lieber, Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes, Science. 277 (1997) 1971-(1975).

DOI: 10.1126/science.277.5334.1971

[2] M.E. Gurtin, A.I. Murdoch, A continuum theory of elastic material surfaces, Arch. Ration. Mech. An. 57 (1975) 291-323.

DOI: 10.1007/bf00261375

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

DOI: 10.1016/0020-7683(78)90008-2

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

DOI: 10.1088/0957-4484/11/3/301

[5] R. Dingreville, J. Qu, M. Cherkaoui, Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films, J. Mech. Phys. Solids. 53 (2005) 1827-1854.

DOI: 10.1016/j.jmps.2005.02.012

[6] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7(6) (1992) 1564-1583.

DOI: 10.1557/jmr.1992.1564

[7] I.N. Sneddon, The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile, Int. J. Eng. Sci. 3 (1965) 47-57.

DOI: 10.1016/0020-7225(65)90019-4

[8] W. Chen, P. Engel, Impact and contact stress analysis in multilayer media. Int. J. Solids. Struct. 8 (1972) 1257-1281.

[9] J. Greenwood, J. Barber, Indentation of an elastic layer by a rigid cylinder, Int. J. Solids. Struct. 49 (2012) 2962-2977.

DOI: 10.1016/j.ijsolstr.2012.05.036

[10] X.J. Zhao, Surface loading and rigid indentation of an elastic layer with surface energy effects, Master thesis, The University of British Columbia, Canada, (2009).

[11] Y. Pinyochotiwong, J. Rungamornrat, T. Senjuntichai, Rigid frictionless indentation on elastic half space with influence of surface stresses, Int. J. Eng. Sci. 71 (2013) 15-35.

DOI: 10.1016/j.ijengsci.2013.04.005

[12] P. Intarit, T. Senjuntichai, J. Rungamornrat, Elastic layer under axisymmetric indentation and surface energy effects, Z. Angew. Math. Phys. 69 (2018) 29.

DOI: 10.1007/s00033-018-0925-x

[13] M.A. Attia, F.F. Mahmoud, Analysis of nanoindentation of functionally graded layered bodies with surface elasticity, Int. J. Mech. Sci. 94 (2015) 36-48.

DOI: 10.1016/j.ijmecsci.2015.02.016

[14] S. Tirapat, T. Senjuntichai, J. Rungamornrat, Influence of surface energy effects on elastic fields of a layered elastic medium under surface loading, Adv. Mater. Sci. Eng. 2017 (2017) 7530936.

DOI: 10.1155/2017/7530936

[15] Y.Z. Povstenko, Theoretical investigation of phenomena caused by heterogeneous surface tension in solids, J. Mech. Phys. Solids. 41 (1993) 1499-1514.

DOI: 10.1016/0022-5096(93)90037-g