3D-2D transition in mode-I fracture microbranching in a perturbed hexagonal close-packed lattice

摘要

Mode-I fracture exhibits microbranching in the high velocity regime where thesimple straight crack is unstable. For velocities below the instability,classic modeling using linear elasticity is valid. However, showing theexistence of the instability and calculating the dynamics post-instabilitywithin the linear elastic framework is difficult and controversial. Theexperimental results give several indications that the microbranchingphenomenon is basically a three-dimensional phenomenon. Nevertheless, thetheoretical effort has been focused mostly in two-dimensional modeling. In thiswork we study the microbranching instability using three-dimensional atomisticsimulations, exploring the difference between the 2D and 3D models. We findthat the basic 3D fracture pattern shares similar behavior with the 2D case.Nevertheless, we exhibit a clear 3D-2D transition as the crack velocityincreases, while as long as the microbranches are sufficiently small, thebehavior is pure 3D-behavior, while at large driving, as the size of themicrobranches increases, more 2D-like behavior is exhibited. In addition, in 3Dsimulations, the quantitative features of the microbranches, separating theregimes of steady-state cracks (mirror) and post-instability (mist-hackle) arereproduced clearly, consistent with the experimental findings.