An Over-deterministic Method Based on Atomistic Stress Fields: Higher Order Terms of the Williams power expansion

Abstract

The investigation of the atomistic near crack-tip stress fields under Mixed Mode loading via molecular dynamics method implemented in a flexible classical molecular dynamics method software LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) is presented. The molecular dynamics modelling is applied for evaluation of the coefficients of higher-order terms of the Williams’ expansion -based approximation for the near crack tip fields in isotropic linear elastic materials. Fracture mechanics parameters such as stress intensity factors, higher-order coefficients of the Williams power-series for a copper plate with a central crack under Mode I and Mixed Mode (Mode I+Mode II) loadings are obtained by atomistic simulations. All computational experiments are realized in LAMMPS with the Embedded Atom Method (EAM) potential. The atomistic values of higher-order coefficients of the Williams series expansion are computed by the over-deterministic method and liken to the values obtained from classical continuum fracture mechanics solutions. It is demonstrated that the conventional continuum fracture theory successfully describes fracture quantities at extremely limited singular stress field of only several nanometers.