Coefficients of the williams power expansion of the near crack tip stress field in continuum linear elastic fracture mechanics at the nanoscale

Continuum mechanics and atomistic approaches for determination crack propagation direction angles under mixed mode (Mode I/ Mode II) loadings. [Display omitted] •The analysis of the near-crack-tip stress field obtained by MD method is presented.•SIFs, T-stresses and higher order coefficients of Williams expansions are evaluated.•The angular variations of continuum mechanics and atomistic stresses are compared.•A good match between MD simulations results and the LEFM results is established.•It’s shown that the continuum theory successfully describes the atomistic stresses. The paper presents the analysis of the stress field in the neighborhood of the crack tip by molecular dynamics method implemented in a classical molecular dynamics code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The molecular dynamics simulations are aimed at computing continuum linear elastic fracture mechanics parameters such as stress intensity factors, T-stresses and higher order coefficients of the Williams power series of the stress field in an isotropic linear elastic material. The overwhelming objective of the study is the comparison of continuum and atomistic approaches for the estimation of the near crack tip fields. Stress intensity factors, T-stresses and higher order coefficients of the Williams series expansion for a copper plate with a central crack under Mode I and Mixed Mode loadings are evaluated by atomistic modelling. The wide class of the computational experiments in LAMMPS is realized. The atomistic values of stress intensity factors and higher order terms of the Williams series expansion are compared with the values obtained from the classical solutions of continuum linear elastic fracture mechanics. It is shown that the continuum fracture theory successfully describes fracture and the near crack tip fields even at extremely confined singular stress field of only several nanometers. The circumferential distributions of the stress tensor components from atomistic modeling are retrieved and compared with the angular distributions of the stresses from linear elastic fracture mechanics. The comparison shows good agreement between two approaches.