Cleavage Planes of Icosahedral Quasicrystals: A Molecular Dynamics Study
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Cleavage Planes of Icosahedral Quasicrystals: A Molecular Dynamics Study Frohmut Rösch 1, Christoph Rudhart 1, Peter Gumbsch 2,3, and Hans-Rainer Trebin 1 Universität Stuttgart, Institut für Theoretische und Angewandte Physik, 70550 Stuttgart, Germany 2 Universität Karlsruhe, Institut für Zuverlässigkeit von Bauteilen und Systemen, 76131 Karlsruhe, Germany 3 Fraunhofer Institut für Werkstoffmechanik, 79194 Freiburg, Germany 1
ABSTRACT The propagation of mode I cracks in a three-dimensional icosahedral model quasicrystal has been studied by molecular dynamics techniques. In particular, the dependence on the plane structure and the influence of clusters have been investigated. Crack propagation was simulated in planes perpendicular to five-, two- and pseudo-twofold axes of the binary icosahedral model. Brittle fracture without any crack tip plasticity is observed. The fracture surfaces turn out to be rough on the scale of the clusters. These are not strictly circumvented, but to some extent cut by the dynamic crack. However, compared to the flat seed cracks the clusters are intersected less frequently. Thus the roughness of the crack surfaces can be attributed to the clusters, whereas the constant average heights of the fracture surfaces reflect the plane structure of the quasicrystal. Furthermore a distinct anisotropy with respect to the in-plane propagation direction is found. INTRODUCTION Fracture of materials is ultimately caused by bond breaking processes on the atomic scale. However, the macroscopic geometry and the dimensions of the sample determine the stress concentration and therefore the strength of the loading at the crack tip. Thus, fracture is a multiscale phenomenon. To understand the breaking of the bonds on an atomic scale one has to perform numerical experiments, since experimental information on this length scale can hardly be obtained. In pure metals and simple intermetallic alloys, molecular dynamics studies have provided useful insight into crack propagation, whereas in complex metallic alloys the mechanisms are not yet so clear. The behaviour of quasicrystals is of special interest because they exhibit a plane structure on the one hand and clusters as building units on the other hand. These clusters are assumed to cause the experimentally observed roughness of fracture surfaces in icosahedral AlPdMn [1]. The main intention of this paper is to check by molecular dynamics simulations whether this assumption is reasonable. For this purpose the influence of the plane structure and the clusters on fracture surfaces has been investigated for different orientations and applied loads. The load of the sample can be expressed by the stress intensity factor. In linear elastic continuum mechanics, a sharp mode I (opening mode) crack is characterised by a singular stress field and a corresponding displacement field, which both are proportional to the stress intensity factor K. This factor is proportional to the applied external load and contains the geometry of the sample. A simple energy based con
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