The molecular dynamic technique is used to investigate static and dynamic aspects of crack extension. The material chosen for this study was the 2D triangular solid with atoms interacting via the Johnson potential. The 2D Johnson solid was chosen for this study since a sharp crack in this material remains stable against dislocation emission up to the critical Griffith load. This behavior allows for a meaningful comparison between the simulation results and continuum energy theorems for crack extension by appropriately defining an effective modulus which accounts for sample size effects and the non-linear elastic behavior of the Johnson solid. The simulation results for the energetics of quasi-static crack extension are in very good agreement with continuum predictions. During quasi-static crack extension under constant load boundary conditions the ratio of the work done by the external loads to the increase in elastic strain energy is ~ 1.94 which is close to the continuum prediction of 2.00 for a linear elastic solid. Good agreement was also obtained between the simulation results for the critical stress and the predictions of the Griffith criterion. Normalized crack velocity-crack length curves are presented for a variety of sample sizes and a variety of loading conditions. The measured terminal velocity was independent of sample size and loading condition and was 0.25 of the longitudinal sound velocity. The method of loading has some influence on acceleration of the crack to the terminal velocity. The details of the energy balance during dynamic crack extension are presented for various sample sizes. For the largest sample examined the crack reaches terminal velocity well before any elastic wave reflections occur at the sample boundary. Simulation results are presented for the stress fields of moving cracks and these dynamic results are discussed in terms of the dynamic crack propagation theories of Mott, Eshelby, and Freund.
ASJC Scopus subject areas
- General Engineering