Molecular Dynamics Calculations of Asymptotic Series Coefficients for Stress Fields

This paper presents an overdeterministic algorithm for constructing the asymptotics of the stress field near the tip of a nanocrack in an anisotropic linear elastic body with cubic symmetry. A molecular dynamics solution of the problem of mixed loading (mode I fracture and transverse shear) of single-crystal copper and aluminum nanoplates with a central cut is described. Based on this solution, an asymptotic representation for the stress tensor components was derived. The atomistic stresses in the vicinity of the crack tip were calculated, and the coefficients of the series representing the stress field were determined using the values of the atomistic stress tensor components. The molecular dynamics calculations were performed for a temperature of 10 K to exclude the occurrence of nonlinear elastic deformation near the crack tip. The stress fields in the atomistic and analytical solutions were compared. The stresses at different distances from the nanocrack tip are in good agreement with the solutions of problems of classical macroscopic theory of anisotropic elasticity and can be described using a series that extends the Williams series to anisotropic media. In the series extended to anisotropic materials, the regular (nonsingular) terms are taken into account and the series coefficients of these terms are determined. It is shown that the developed algorithm can be used to effectively determine the coefficients of the higher-order terms of the series.