Nonlinear Methods for Modelling Atomistic Brittle Fracture

P. Patel


Fracture is a fundamental process through which materials fail. Our understanding of fracture mechanics determines our ability to predict the process. Griffith first conceptualised a continuum description of fracture in the 1920s, and today, simulations are also performed at the atomistic scale. Hierarchical, and simultaneous, multiscale approaches are used; where DFT provides accurate electronic interactions at the crack tip coupled with classical mechanics to reach the large length scale required to capture the long range stress fields found in fractured systems. Here, tools are developed with hierarchical modelling in mind and to reduce computational cost. The accuracy of DFT is demonstrated via a comparison to experimental fracture propagation of the SiC 6H polytype on the (0001) plane. The slow stable crack growth of the experiment allowed comparison of the experimentally measured fracture energy with the computational surface energy from DFT calculations, which showed relatively good agreement. The discretised nature of an atomistic lattice leads to a feature called lattice trapping. To explore this, methods to compute energy barriers for breaking a single bond along the crack advancement direction were developed. The methods were tested on a fractured diamond-structured carbon system, which was open along the (111) plane, and a fractured 2D hexagonal lattice. The continuum description for fracture is not sufficient for an atomistic lattice. A method which attempts to improve the discrepancy between the descriptions by computing a correction term on a larger atomistic domain was developed. It showed improved convergence of the strain and total energy with respect to the uncorrected case.