In the present paper,the hardness and Young's modulus of film-substrate systems are determined by means of nanoindentation experiments and modified models.Aluminum film and two kinds of substrates,i.e.glass and silicon,are studied.Nanoindentation XP Ⅱ and continuous stiffness mode are used during the experiments.In order to avoid the influence of the Oliver and Pharr method used in the experiments,the experiment data are analyzed with the constant Young's modulus assumption and the equal hardness assumption.The volume fraction model(CZ model)proposed by Fabes et al.(1992)is used and modified to analyze the measured hardness.The method proposed by Doerner and Nix(DN formula)(1986)is modified to analyze the measured Young's modulus.Two kinds of modified empirical formula are used to predict the present experiment results and those in the literature,which include the results of two kinds of systems,i.e.,a soft film on a hard substrate and a hard film on a soft substrate.In the modified CZ model,the indentation influence angle,(?), is considered as a relevant physical parameter,which embodies the effects of the indenter tip radius, pile-up or sink-in phenomena and deformation of film and substrate.
In this paper, the problem of a crack perpendicular to and terminating at an interface in bimaterial structure with finite boundaries is investigated. The dislocation simulation method and boundary collocation approach are used to derive and solve the basic equations. Two kinds of loading form are considered when the crack lies in a softer or a stiffer material, one is an ideal loading and the other one fits to the practical experiment loading. Complete solutions of the stress field including the T stress are obtained as well as the stress intensity factors. Influences of T stress on the stress field ahead of the crack tip are studied. Finite boundary effects on the stress intensity factors are emphasized. Comparisons with the problem presented by Chen et al. (Int. J. Solids and Structure, 2003, 40, 2731–2755) are discussed also.
