Size-Dependent Fracture Toughness of Nanoscale Structures: Crack-Tip Stress Approach in Molecular Dynamics

By adopting the local virial stress, the authors overcome the barrier of ambiguous crack-tip stress field in molecular dynamics (MD) simulations and perform direct calculations of fracture toughness. Both MD and corresponding continuum finite-element method (FEM) solutions indicate that fracture toughness measured in stress intensity factor (or energy release rate) decreases with the decreasing crack length. Accordingly, fracture toughness cannot be treated as a material constant when the crack length is several nanometers. The size-dependent behavior of fracture toughness is explained in terms of the size of the singular stress zone (the K-dominance zone). It is found that as the crack length decreases, the K-dominance zone also decreases, making the singular part of the crack-tip stress not capable of accounting for the full fracture driving force. As a result, the critical stress intensity factor at failure (the fracture toughness) is lowered whereas the remote failure stress is raised.