13th International Conference on Fracture June 16-21, 2013, Beijing, China Cohesive Zone Analysis of Crack Propagation on a Hierarchical Structured Interface Xiaoru Wang1, Akihiro Nakatani1,∗ 1 Department of Adaptive Machine Systems, Osaka University, Suita, Osaka 565-0871, Japan ∗ Corresponding author: nakatani@ams.eng.osaka-u.ac.jp Abstract Hierarchical ramification structures are found of superior strength during fracture. Crack propagation along cohesive zone model binding with hierarchical ramification structures is simulated to analyze the fracture process. The feature of specified bonding surface results special pattern of crack propagation. Therefor, the potential that by changing the morphology of the bonding surface may control the toughness of the material is illustrated. Keywords Computational Mechanics, Cohesive Zone Model, Hierarchical Structure, Fracture Toughness, Criterion 1. Introduction Some biological materials have the internal structures that exhibit superior performances in mechanical properties[1]. There are quite a few studies to investigate the fundamental mechanism of the biological systems in order to develop the artificial bio inspired materials. In this study, we focus on the the hierarchical ramification structures that contribute to high fracture toughness. The hierarchical ramification structures are often observed in many biological system. The structures appear as fractal geometries which are generated naturally via quite simple rules and they contribute to redundancy for safety of their life. In this study, the cohesive zone model is adopted to a hierarchical structured interface and the crack propagation on the interface is studied. First, the problem of double cantilever beam problem is solved to estimate the fundamental effect of the microstructure of interface. According to the simple calculation, it is shown that the redundancy of ramification structure yields high fracture toughness. Secondly, the quasi-static crack propagation is studied in bulk materials. The small scale yielding condition is assumed and the linear elastic solution specifies the boundary displacement component. The boundary value problem in linear elasticity is solved for increasing remote stress intensity factor by using finite element method. The displacement field and stress distribution obtained by the simulation is discussed to study the mechanism of crack propagation. The relationships between the remote stress intensity factor and representative crack length are plotted for several cases of different microstructures. The effective interface area and the effective surface energy depends on the internal microstructure of interface. The effect of geometry cause the complex pattern of bonding-debonding domain. As the result, the representative length scale of fracture process zone depends on the heterogeneity and morphology of microscopic structure. The fracture toughness which is estimated as a remote stress intensity factor changes associated with the change of the fracture process zone due to the microstructure. -1-
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