Computation of conventional fracture mechanics parameters via molecular dynamics simulations

Abstract

The Williams series expansion is the fundamental solution of conventional continuum fracture mechanics for characterizing the stress fields around the crack tip in a homogeneous material in the linear elastic regime. Nowadays stress intensity factors, T-stresses and the higher-order coefficients of the Williams series expansion are proved to be important parameters describing the near crack-tip fields in isotropic linear elastic materials. The central aim of this study is to understand if one can obtain these fracture parameters of conventional fracture mechanics from atomistic simulations based on molecular dynamics simulations. The ability to describe fracture processes at atomic scale via stress intensity factors, T-stresses and higher-order coefficients will provide the opportunity to take into account many effects such as material microstructures, crystallographic orientation, chemical compositions and concentrations and others. In this research the values of stress intensity factors, T-stress and coefficients of the Williams series expansion are obtained using atomistic simulations based on molecular dynamics method with a classical molecular dynamics code Large-scale Atomic/Molecular Massively Parallel Simulator. The classical over-deterministic method is used to determine stress intensity factors, T-stresses and coefficients of higher-order terms of the Williams series expansion of the near crack-tip stress field from molecular dynamics modelling of a plate with a central crack. The accuracy of the proposed approach is tested for this rather simple cracked configuration. There is the theoretical analytical solution with all the coefficients of the higher-order terms in the Williams series expansion. The existing theoretical solution allows us to compare the angular distributions of the stress tensor components for a large plane with the central crack. It is shown that results obtained from molecular dynamics simulations and the theoretical analytical solutions are in good agreement.