Abstract

Abstract A new method for combined finite-element and atomistic analysis of crystal defects has been developed. The coupling between the atomistic core and the surrounding continuum is described in terms of non-local elasticity theory. Static and dynamic tests demonstrate the satisfactory performance of this method. The model is applied to crack propagation on cleavage and non-cleavage planes in b.c.c. crystals, using potentials for iron and tungsten as examples. On the cleavage planes, pronounced directions of ‘easy’ crack propagation, besides less favourable directions, are found. On the preferred cleavage plane {100}, easy propagation is possible in any macroscopic direction by microscopic facetting of the crack front into easy directions, while on the secondary cleavage plane {110}, there is only one macroscopic direction in which cracks will propagate easily. On all other planes studied here, plastic processes at the crack tip (twinning and/or dislocation emission) intervene before brittle crack propagation; thereafter the cracks remain stationary to much higher stress intensities than on the cleavage planes. Thus the model gives a satisfactory explanation of the dependence of crack propagation on crystallographic orientation, and in particular of the difference between cleavage and non-cleavage planes, in b.c.c. crystals.