New theory for. Mode I crack-tip dislocation emission

P Andric and WA Curtin, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 106, 315-337 (2017).

DOI: 10.1016/j.jmps.2017.06.006

A material is intrinsically ductile under Mode I loading when the critical stress intensity K-Ie for dislocation emission is lower than the critical stress intensity K-Ic for cleavage. K-Ie is usually evaluated using the approximate Rice theory, which predicts a dependence on the elastic constants and the unstable stacking fault energy gamma(usf) for slip along the plane of dislocation emission. Here, atomistic simulations across a wide range of fcc metals show that K-Ie is systematically larger (10-30%) than predicted. However, the critical (crack tip) shear displacement is up to 40% smaller than predicted. The discrepancy arises because Mode I emission is accompanied by the formation of a surface step that is not considered in the Rice theory. A new theory for Mode I emission is presented based on the ideas that (i) the stress resisting step formation at the crack tip creates lattice trapping against dislocation emission such that (ii) emission is due to a mechanical instability at the crack tip. The new theory is formulated using a Peierls-type model, naturally includes the energy to form the step, and reduces to the Rice theory (no trapping) when the step energy is small. The new theory predicts a higher K-Ie at a smaller critical shear displacement, rationalizing deviations of simulations from the Rice theory. Specific predictions of K-Ie for the simulated materials, usually requiring use of the measured critical crack tip shear displacement due to complex material non-linearity, show very good agreement with simulations. An analytic model involving only gamma(usf), the surface energy gamma(s), and anisotropic elastic constants is shown to be quite accurate, serves as a replacement for the analytical Rice theory, and is used to understand differences between Rice theory and simulation in recent literature. The new theory highlights the role of surface steps created by dislocation emission in Mode I, which has implications not only for intrinsic ductility but also for crack tip twinning and fracture due to chemical interactions at the crack tip. (C) 2017 Elsevier Ltd. All rights reserved.

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