ICF13B

13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Elasto-Dynamic Behaviour of Interacting Inhomogeneities and Cracks Shaker A. Meguid1,*, Xiaodong Wang2 1Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada M5S 3G8 2Department of Mechanical Engineering, University of Alberta, Edmonton, Canada T6G 2G8 * Corresponding author: meguid@mie.utoronto.ca Abstract The paper presents a theoretical treatment of the dynamic behavior of fibre reinforced composites containing matrix cracks and reinforcing inhomogeneities. A pseudo-incident wave method is used to treat the dynamic interaction between cracks and inhomogeneities. Using this method, the original interaction problem is reduced to the solution of coupled single crack/inhomogeneity subproblems, for which analytical solutions could be derived. The interaction effects are introduced via the superposition of the different subproblems. The steady state solution of the interacting crack problem is obtained using integral transform method and the solution of the inhomogeneity problem is determined using Fourier expansion. The dynamic stress intensity factors (SIFs) at the matrix crack are obtained and numerical examples are provided to show the effect of the frequency, geometry of microdefects and material properties upon the dynamic SIFs. Keywords Dynamic interaction, Crack, Inhomogeneity, Composite 1. Introduction A major issue in modeling the micromechanical behaviour of advanced composites is how to deal with the interaction between cracks and inhomogeneities, which governs the overall failure mechanism of the materials [1-4]. The quasi-static interaction problem in composite materials has received considerable attention but the dynamic interaction between cracks and inhomogeneities is still limited [5-9]. Compared with quasistatic problems, the formulation of dynamic problems is much more complicated and difficult to deal with and the experimental data are difficult to obtain. It should be mentioned that most advanced composite materials are currently being used or considered for use in situations involving dynamic loading. Numerical methods, such as finite element analysis or boundary element method, can be used for this type of dynamic analyses under certain conditions but has their own limitations when multiple defects are involved. Analytical study of interacting cracks under dynamic loads is still attracting researchers [10-12] because of its high reliability and accuracy in simulating the dynamic response of multiple defects in composite materials. It is the objective of the present paper to review and present the usage of the pseudo-incident wave method for the analysis of steady state dynamic interaction problems. Based on this method, the original interaction problem is reduced into single crack and single inhomogeneity subproblems, which are coupled through the scattered waves. The single crack and single inhomogeneity problems are solved analytically using integral transform method and Fourier expansion, respectively. Following this introduction, the paper is divided into three more sections: the formulations, results and discussions and conclusions. 2. Formulation of the Problem Consider now the dynamic interaction between arbitrary defects, which could be in forms of cracks or inhomogeneities, in an infinite elastic isotropic solid under steady state dynamic antiplane loading, as shown in Fig.1. The displacement field corresponding to a steady state dynamic loading can be generally expressed in terms of the frequency ω as (1)

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