Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32578
Stress Distribution in Axisymmetric Indentation of an Elastic Layer-Substrate Body

Authors: Kotaro Miura, Makoto Sakamoto, Yuji Tanabe


We focus on internal stress and displacement of an elastic axisymmetric contact problem for indentation of a layer-substrate body. An elastic layer is assumed to be perfectly bonded to an elastic semi-infinite substrate. The elastic layer is smoothly indented with a flat-ended cylindrical indenter. The analytical and exact solutions were obtained by solving an infinite system of simultaneous equations using the method to express a normal contact stress at the upper surface of the elastic layer as an appropriate series. This paper presented the numerical results of internal stress and displacement distributions for hard-coating system with constant values of Poisson’s ratio and the thickness of elastic layer.

Keywords: Indentation, contact problem, stress distribution, coating materials, layer-substrate body.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 705


[1] R. S. Dhaliwal, “Punch problem for an elastic layer overlying an elastic foundation”, Int. J. Eng. Sci. vol. 8, pp. 273–288, 1970.
[2] H. Y. Yu, S. C. Sanday, B. B. Rath, “The effect of substrate on the elastic properties of films determined by the indentation test — axisymmetric boussinesq problem”, J. Mech. Phys. Solids, vol. 38, pp.745–764, 1990.
[3] J. Li, T. W. Chou, “Elastic Field of a Thin-Film/Substrate System under an Axisymmetric Loading,” Int. J. Solids Struct., vol. 34, pp. 4463–4478, 1997.
[4] A. M. Korsunsky, A. Constantinescu, “The Influence of Indenter Bluntness on the Apparent Contact Stiffness of Thin Coatings,” Thin Solid Films, vol. 517, pp. 4835–4844, 2009.
[5] R. Kulchytsky-Zhyhailo, G. Rogowski, “Stresses in Hard Coating Due to a Rigid Spherical Indenter on a Layered Elastic Half-Space,” Tribol. Int., vol. 43, pp. 1592–1601, 2010.
[6] M. Sakamoto, G. Li, T. Hara, E. Y. S. Chao, “A new method for theoretical analysis of static indentation test”, J. Biomech. vol. 29, pp. 679–685, 1996.
[7] K. Miura, M. Sakamoto, K. Kobayashi, J. A. Pramudita, Y. Tanabe, “Analytical Solution of Axisymmetric Indentation of an Elastic Layer-Substrate Body”, Theor. Appl. Mech. Japan, Vol. 64, pp. 81-101, 2018.
[8] A. E. H. Love, The Mathematical Theory of Elasticity, 4th ed., Cambridge University Press, 1927, pp. 274 –276.