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