Boundary element numerical analysis of elastic indentation of a sphere into a bi-layer material

The initial part of load/penetration plot in depth sensing spherical indentation (nano-indentation) is analysed. The results of a numerical study using a specifically developed simulation tool based on the boundary element method are presented. They reveal that the usual linear relationship between the indentation depth and the square of the contact radius for homogeneous materials is also valid in the case of a bi-layer material. It is also shown that the elastic response of the bi-layer material is specific of the coating alone only if the indentation depth, h, is less than 2% of the coating thickness, t. For higher indentation depths (10% > h/t > 1%), the macro-elastic response of the composite is seen to saturate with an overall elastic response still containing a contribution of roughly 10% of the coating modulus. The hypothesis of indentation limit h/t < 10% of bi-layer material insuring coating-specific response for penetration hardness (Buckle's rule) is roughly two orders of magnitude high when applied by default to the corresponding coating-specific elastic response. (C) 2003 Published by Elsevier Science Ltd.