An atomistic study of brittle fracture: Toward explicit failure criteria from atomistic modeling
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Atomistic techniques are used to study brittle fracture under opening mode and mixed mode loading conditions. The influence of the discreteness of the lattice and of the lattice-trapping effect on crack propagation is studied using an embedded atom potential for nickel to describe the crack tip. The recently developed FEAt (Finite Element-Atomistic) coupling scheme provides the atomistic core region with realistic boundary conditions. Several crystallographically distinct crack-tip configurations are studied and commonly reveal that brittle cracks under general mixed mode loading situations follow an energy criterion (G-criterion) rather than an opening-stress criterion (^/-criterion). However, if there are two competing failure modes, they seem to unload each other, which leads to an increase in lattice trapping. Blunted crack tips are studied in the last part of the paper and are compared to the atomically sharp cracks. Depending on the shape of the blunted crack tip, the observed failure modes differ significantly and can drastically disagree with what one would anticipate from a continuum mechanical analysis.
I. INTRODUCTION The macroscopic properties of materials are often determined by events on the atomic scale. This is particularly clear in the case of brittle fracture, where the crack at its tip must be atomically sharp and break the bonds between atoms. It is therefore obvious that a detailed understanding of brittle fracture will ultimately require an understanding on the atomic scale. Atomistically modeling fracture processes is even more appealing if one acknowledges that it will naturally reproduce fracture by loading, whereas the widely used continuum models require explicit fracture criteria to predict crack propagation. Despite these advantages of atomistic techniques and despite the technological importance of brittle fracture, the atomic length scale is rarely adopted. This is partly due to the fact that atomistic studies of fracture are computationally rather demanding. After some early studies in the 1970s, which could, for example, show that the discreteness of the lattice manifests itself in the so-called lattice-trapping effect,1"3 advanced modeling techniques 4 " 6 and increasing computing power led to a growing interest over the past few years.5"12 Anisotropic linear elastic continuum analysis of a sharp crack13 shows that the relevant compounds of the stress and displacement fields of the crack can be expressed as: KK
(1) (2)
uv =
J. Mater. Res., Vol. 10, No. 11, Nov 1995 http://journals.cambridge.org
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where KM are the stress-intensity factors for mode M (I = opening, II = in-plane shear, and III = out-of-plane shear) loading, R is the distance from the crack tip, and a and f3 are functions of the angle & between R and the crack plane, and further include the crystallographic orientation of the crack system via the appropriate elastic constants. The crack system is specified by the crack plane and the crack front direction. Some of the difficulty in atomistica
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