Elastic field of a thin-film/substrate system under an axisymmetric loading

paper presents the elastic solution of a layered half space with perfect interfacial bonding under an axisymmetrical compressive loading on the plane surface. The analysis is intended to model the nano-indentation of thin-film coating/substrate systems. Unlike most of the existing work of which the substrate is assumed as rigid and the numerical results are obtained by finite element analysis, the present paper presents theoretical solutions for the elastic coating/substrate systems. The surface displacement profiles and the stress fields are shown to be sensitive to the thickness of the coating layer and the ratio of the elastic modulus of the coating material to that of the substrate. When the film thickness is comparable to the loading contact radius, the film elastic property cannot be accurately determined by using Sneddon’s half-space indentation solution. Furthermore, there are pronounced differences in the stress fields of the hard-coating and the softcoating systems. When an indentation load is applied to a soft-thin-film/hard-substrate system, most the stress components are compressive. But for a hard-thin-film/soft-substrate system, the radial and hoop stresses in the film near the film/substrate interface change from tension to compression as the film thickness decreases. The normal and shear stress results are compared with those obtained from finite element analysis (Jayachandran, R., Boyce, M. C. and Argon, A. S. (1995) Mechanics of the indentation test and its use to assess the adhesion of polymeric coatings. In Adhesion Measurement of Films and Coatings, ed. K. L. Mittal. VSP, pp. 189-215) for the rigid substrate system. Also, the load-indentation depth results are compared with the experimental data of Oliver and Pharr (Oliver, W. C. and Pharr, G. M. (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of Material Research 7(6), 15641583) for tungsten subjected to elastic indentation. The agreement is quite satisfactory. Implications of the elastic field on the failure mechanisms of coating/substrate systems are also discussed. 0 1997 Elsevier Science Ltd