Fast crack propagation correlated with crack tip stress in 2D hexagonal atomic lattices

We construct strip finite element models of 2D hexagonal atomic lattices with initial cracks to simulate dynamic crack propagation under mode \(\mathrm{I}\) displacement loading, in which the atomic bonds of 2D lattices are represented by Timoshenko beam elements. Series of 2D lattices, including graphene, hexagonal boron nitride and virtual graphene-like materials, are modeled by varying the nonlinear constitutive relations of beam elements. Branching and oscillation phenomena inevitably occur in fast-propagating crack when the crack speed reaches a critical value, which is closely related to the stress field near the crack tip. Our results reveal that the size of nominal plastic zone \(r_{p}\) around crack front varies with different 2D lattices at both crack initiation and branching. The critical branching speeds \(V_{\mathrm {C}}\) change with material properties, and is correlated with the local stresses around the crack front. Further, we find that \(V_{\mathrm {C}}\) increases with the increment of conditional yield stresses of 2D lattices, but \(V_{\mathrm {C}}\) decreases with the increment of \(r_{p}\) monotonously and linearly at crack branching. Therefore, nonlinear zone, formed by redistributed singular stresses at crack tip, dominates crack kinking or branching during fast crack propagation.