Simulation accuracy of crack-tip parameters with extended GP methods

The success in using the GP, short for the generalized particle dynamics method (Fan, 2009), with the cohesive zone method (CZM) to bridge crack propagation at the atomistic and mesoscopic scale (Xu et al., 2016) brings more attention to its central issue: simulation accuracy of crack-tip parameters. This issue is addressed in this work by an extension of the GP method in which finite element (FE) nodes are connected with the outermost particles, thus it can reduce artificial effects on the most interesting atomic regions to obtain accurate crack-tip parameters. The accuracy of the XGP, short for this extended GP method, is confirmed by comparisons of simulation results with classic analytical solutions of an edge-crack and a central cylindrical hole in a two dimensional plate. After developing a series of models from 60 nm to 5 μm, used in an asymptotic analysis for model size effect, it is applied to the atomistic crack-tip simulation of a Mode-I edge crack of iron under plane strain condition. Results show that there exists a problem-dependent critical model size, LCR, above which may not be necessary under a given error tolerance; below which the simulation result is inaccurate in underestimating crack-tip displacement, the range of the traction-separation (TS) curve and the critical energy release rate GIC and overestimating the initiation strain for the crack-tip BCC to FCC phase transformation.