Ph.D Student | Kovel Guy |
---|---|

Subject | Crack Dynamics in Brittle crystals by 3D Molecular Dynamics Simulations |

Department | Department of Materials Science and Engineering |

Supervisors | Dr. Dov Sherman |

Professor Maytal Caspary-Toroker |

Recent fracture cleavage
experiments of silicon crystal specimens indicate that atomistic scale effects
influence macroscopic brittle cracks dynamics. These experiments emphasize the
importance of supplementing macroscopic experiments with calculations
describing the atomistic aspects at the crack tip. However, atomistic
simulations have yet to provide an accurate representation of brittle fracture
experiments as a boundary value problem (BVP) with appropriate boundary
conditions (BC). For example, atomistic simulations so far have shown the
existence of “lattice trapping”, where dynamic brittle crack propagation
requires energy far greater than the Griffith barrier of *2 _{s}*,
twice the free and relaxed surface energy of the cleavage plane of propagation.
In contrast, recent lab experiments show crack propagation occurring at energy
close to the Griffith barrier and at low velocities. We relate this effect to
the definition of the BVP of the atomistic models containing a crack: thin
model subjected to periodic BCs which subject the atomistic model to be under
plane strain conditions and enforces the crack front to be straight. In the
experiments, the crack front was shown to be curved, which presumably enforces
completely different nano-scale bond breaking mechanisms and sequence along the
crack front, which itself changes the macroscopic energy-speed relationship of
a dynamic crack. In this research, we attempt to address some of the issues
that contribute to this discrepancy.

Molecular Dynamic simulations of
static and dynamic crack in the cleavage
system (first bracket denotes crack plane, the second direction of propagation)
of a silicon-like brittle crystal were performed as a Psudo-2D and 3D BVP. We
used strip-like computational models, commonly used in calculations of crack
dynamics. In our models, *L*, *H*, and *W*, represent the length,
height, and width, respectively. Different computational model sizes from
150x25x1 nm^{3} (approximately 10^{5} atoms) up to 300x100x50
nm^{3} (approximately 10^{7} atoms), with and without periodic
BC were investigated. The 3D model without periodic BC was introduced here for
the first time.

We show that the commonly used
geometry of thin computational model with periodic BC, creates an artificially
straight crack-front and contribute to a ‘lattice trapping’ type computational
byproduct. We used displacement extrapolation method, in which the local stress
intensity factor is calculated based on the crack opening displacement, and
found that while displacement square-root behavior holds for any height *H*,
when the computational model is shorter than 70nm (which includes the vast
majority of atomic calculations done so far), it does not obey the
Griffith-Irwin K-G relationship between the stress intensity factor, *K*,
and the strain energy release rate, *G*. While not considered a
computational byproduct of the calculations, this limits the ability of current
atomistic simulations to accurately predict macroscopic fracture behavior, and
in particular, the dynamic energy-speed relationship.

We propose to use 3D multi-scale calculation like quasicontinuum, combining continuum finite element analysis and molecular dynamic analysis of micrometer thick models, and very large lateral computational model without periodic boundary conditions, to better capture crack dynamics and the kinks advance and formation along the curved crack front in particular.