Identification of stress intensity factors, T-stresses and higher-order coefficients of regular terms in the Williams series expansion through molecular dynamics simulations

Molecular dynamics (MD) approach and finite element analysis are enforced for the investigating the stress - strain fields in the proximity of the notch tip in a copper plate with single horizontal and inclined edge notches. The MD simulation embodied in a classical molecular dynamics program Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is aimed at evaluating conventional continuum linear elastic fracture mechanics key parameters, precisely stress intensity factors (SIF), T-stresses and generalized stress intensity factors (higher order factors) of the Max Williams power series expansion (WE) of the stress field adjacent with the notch tip for pure tensile (Mode I), pure shear (Mode II) and mixed mode (combinations of Mode I and Mode II) loadings of the notched specimen in linear elastic isotropic media. The paramount intent of the research is the comparability of continuum and atomistic procedures for the appraisement of the near notch tip fields exploiting the exemplification of one of the widespread cracked configurations. SIFs, T-stresses and higher order amplitude coefficients of the WE for the single-edge notched Cu plane under Mode I and Mixed Mode loadings are estimated by atomistic and finite element modelling. The wide class of the MD computations in LAMMPS is effectuated. The atomistic values of SIFs and amplitude factors of higher order terms of the WE are correlated with the quantities gained from the numeric solutions obtained by finite element method. It is elucidated that the continuum fracture theory properly characterizes failure and the near notch tip fields even at tremendously limited distances of only few nanometers. The angular stress distributions found from atomic modeling are restored and correlated with the angular behaviours of the stresses obtained from continuum linear elastic fracture theory. The juxtaposition is shown to be in reasonable agreement between two approaches.