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.
The mode I plane strain crack tip field with strain gradient effects is presented in this paper based on a simplified strain gradient theory within the framework proposed by Acharya and Bassani.The theory retains the essential structure of the incremental version of the conventional J_2 deformation theory.No higher-order stress is introduced and no extra boundary value conditions beyond the conventional ones are required.The strain gradient effects are considered in the constitutive relation only through the instantaneous tangent modulus.The strain gradient measures are included into the tangent modulus as internal parameters.Therefore the boundary value problem is the same as that in the conventional theory.Two typical crack problems are studied:(a)the crack tip field under the small scale yielding condition induced by a linear elastic mode-I K-field and(b)the complete field for a compact tension specimen.The calculated results clearly show that the stress level near the crack tip with strain gradient effects is considerable higher than that in the classical theory.The singularity of the strain field near the crack tip is nearly equal to the square-root singularity and the singularity of the stress field is slightly greater than it.Consequently,the J-integral is no longer path independent and increases monotonically as the radius of the calculated circular contour decreases.
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.
