Estimation of crack propagation direction angles under mixed mode loading in linear elastic isotropic materials by generalized fracture mechanics criteria and by molecular dynamics method

Abstract

The crack growth directional angles in the isotropic linear elastic plane with the central crack under mixed-mode loading conditions for the full range of the mixity parameter are found. The traditional strain energy density, maximum tangential stress and maximum tangential strain criteria are introduced and analyzed. The accuracy of each model is investigated and discussed by comparing its results to the molecular dynamics modelling. Three fracture criteria of traditional linear fracture mechanics (maximum tangential stress, and minimum strain energy density criteria) are generalized by mean the multi-parameter stress expansion in the vicinity of the crack tip. Atomistic simulations of the central crack growth process in an infinite plane medium under mixed-mode loading using Large-scale Molecular Massively Parallel Simulator (LAMMPS), a classical molecular dynamics code, are performed. The inter-atomic potential used in this investigation is Embedded Atom Method (EAM) potential. The plane specimens with initial central crack were subjected to Mixed-Mode loadings. The simulation cell contains 400000 atoms. The crack propagation direction angles under different values of the mixity parameter in a wide range of values from pure tensile loading to pure shear loading in a wide diapason of temperatures (from 0.1 К to 800 К) are obtained and analyzed. It is shown that the crack propagation direction angles obtained by molecular dynamics method coincide with the crack propagation direction angles given by the multi-parameter fracture criteria based on the strain energy density and the multi-parameter description of the crack-tip fields.