Fracture properties of nanoscale single-crystal silicon plates: Molecular dynamics simulations and finite element method

The thickness- and chirality-dependent mixed-mode I-II critical stress strength factors (SIFs) and crack growth angles of single-crystal silicon (SCS) [10 0] and [1 1 0] plates are investigated using molecular dynamics (MD) simulations and finite element (FE) method based on the boundary layer model, respectively. The silicon-silicon (SiSi) bond in the FE method is modeled as a nonlinear Timoshenko beam based on the Tersoff potential (T3) for the first time, where all the parameters of the nonlinear beam are completely determined based on the continuum modeling. The present MD and FE results show that both critical SIFs and crack growth angles obviously depend on chiral angles, thicknesses and loading angles of SCS plates. Our FE results agree well with those from present MD simulations using the modified Tersoff potential. Checking against the SIFs of available results shows that present MD and FE results are reasonable. This study should be of great help for understanding thickness- and chirality-dependent fracture properties of SCS and designing silicon-based nanodevices.