טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentKovel Guy
SubjectCrack Dybnamics in Brittle crystals by 3D Molecular
Dynamics Simulations
DepartmentDepartment of Materials Science and Engineering
Supervisors Dr. Sherman Dov
Assistant Professor Caspary-Toroker Maytal


Abstract

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 nm3 (approximately 105 atoms) up to 300x100x50 nm3 (approximately 107 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.