Introduction

The problem of understanding why some materials are intrinsically brittle, while others are intrinsically ductile has a long history [][][][][][]. A solid will be said to be ``intrinsically'' brittle when the atoms at the tip of a sharp crack can find a configuration in equilibrium between the bonding forces of the atoms at the tip which tend to close the crack, and the stress concentration caused by the external load on the solid, which tends to open the crack. If no sharp crack configuration is possible, but the cracked lattice breaks down in shear, with emission of a dislocation, then the material is intrinsically ductile. Thus, the intrinsic ductility of a material will depend on the kind of bonding forces in the solid, in addition to other factors such as the crystallography, crack plane, possible slip planes, the type of load, etc. In 1992, Rice [] opened a new chapter in the history of this problem by showing that the criterion for the emission of a dislocation from a crack tip in what we will call the ``Mode II configuration'' is associated with the theoretical shear strength of the solid expressed as an energy-a quantity Rice called the unstable stacking fault energy, . In the Mode II configuration, the dislocation is emitted on the plane directly ahead of the crack, and the emission event does not blunt the crack tip. Zhou Carlsson and Thomson (ZCT) [] showed that in a simple hexagonal lattice with simple force laws, for a crack in the more important ``Mode I'' blunting configuration (emission occurs at a nonzero angle to the crack plane), the criterion depends on a product of the unstable stacking fault energy and the intrinsic surface energy, . Thomson and Carlsson [] attempted to understand the results of ZCT by means of standard dislocation/crack models, and showed that for sufficiently small surface energy, the criterion for emission should shift from one dependent on the product, , to one dependent on , only.

Although the ductility criterion for bulk materials is important, fracture at various types of interfaces in materials is far more common, and this paper will address the Mode I emission criterion for cracks on interfaces. But interest in the interfacial cracking problem is high also because the elasticity analysis for that case is anomalous, and involves a singular mixing of tensile and shear modes at the tip of the crack[][]. Recently, Zhou and Thomson [] addressed the emission of such a crack in the Mode II configuration, and showed that the elastic anomalies can be understood in terms of a ``local core stress intensity factor''. Similar ideas about cutting off the elastic solution at a critical distance in the core of the crack had been suggested earlier by Rice, etal []. Zhou and Thomson also showed that the Rice criterion could be applied to the interface case for the Mode II emission. In this current paper, we extend our study to the blunting Mode I interfacial configuration, with the dislocation moving into the ``ductile'' side of the interface couple.

As an important byproduct of this study of interfacial fracture, we shall find that the introduction of the interface also opens up the force law parameter space which can be explored, so that we can explore force laws where the arguments of Thomson and Carlsson suggest there might be a transition to the Rice type of emission criterion. Thus, the results of this study will have implications for the wider problem of intrinsic ductility in general and are not limited simply to interfacial cracking.

In the most general terms, the central problem before us is whether one can find a criterion for intrinsic ductility which can be couched in terms of simple parameters of the undeformed material such as the surface energy and the unstable stacking fault energy. On its face, one is greatly surprised that the complex response of a material at a crack tip can be characterized by parameters which do not reflect, directly, the complicated processes acting at the crack tip. If it should turn out that such simple criteria can be found, valid for all materials and all interfaces, then one has in hand a very powerful tool for material design. It is this general question we shall address here, even though our modeling will be restricted to a simple lattice with simple force laws. If it is possible to find such criteria for our simple case, one has a powerful hint to explore for more general cases.

In the next section, we review the elastic analysis for the interface crack and present the basic equations to be used in analyzing the lattice results. In the third section, the lattice model is described, and the results are presented in the fourth section. Finally, in the fifth and sixth sections, we express our results in a form which can hopefully serve as predictive guidelines for exploring the ductility of interfaces in solids.