The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape

Vlassak, J.J., Ciavarella, M., Barber, J.R. and Wang, X. (2003) The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape Journal of the Mechanics and Physics of Solids, 51, (9), pp. 1701-1721. (doi:10.1016/S0022-5096(03)00066-8).


[img] PDF vlas_03.pdf - Accepted Manuscript
Download (3MB)


The contact of an indenter of arbitrary shape on an elastically anisotropic half space is considered. It is demonstrated in a theorem that the solution of the contact problem is the one that maximizes the load on the indenter for a given indentation depth. The theorem can be used to derive the best approximate solution in the Rayleigh–Ritz sense if the contact area is a priori assumed to have a certain shape. This approach is used to analyze the contact of a sphere and an axisymmetric cone on an anisotropic half space. The contact area is assumed to be elliptical, which is exact for the sphere and an approximation for the cone. It is further shown that the contact area is exactly elliptical even for conical indenters when a limited class of Green's functions is considered. If only the first term of the surface Green's function Fourier expansion is retained in the solution of the axisymmetric contact problem, a simpler solution is obtained, referred to as the equivalent isotropic solution. For most anisotropic materials, the contact stiffness determined using this approach is very close to the value obtained for both conical and spherical indenters by means of the theorem. Therefore, it is suggested that the equivalent isotropic solution provides a quick and efficient estimate for quantities such as the elastic compliance or stiffness of the contact. The "equivalent indentation modulus", which depends on material and orientation, is computed for sapphire and diamond single crystals.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/S0022-5096(03)00066-8
ISSNs: 0022-5096 (print)
Keywords: A: Indentation, B: Anisotropic material, Elastic material
ePrint ID: 23226
Date :
Date Event
Date Deposited: 21 Mar 2006
Last Modified: 16 Apr 2017 22:46
Further Information:Google Scholar

Actions (login required)

View Item View Item