Molecular dynamics calculations of asymptotic series coefficients for stress fields
K.A. Mushankova, L.V. Stepanova
Korolev Samara National Research University, Samara, Russia
Keywords: anisotropic medium, cubic symmetry of elastic properties, molecular dynamics method, atomistic stresses
Abstract
This paper presents an algorithm for the developed overdetermined method of constructing the asymptotics of the stress field near a nanocrack tip in an anisotropic linear elastic body with cubic symmetry. For the problem of combined loading (normal separation and transverse shear) of a nanoplate of monocrystalline copper and aluminum with a central cut, a molecular dynamics solution was obtained and used to derive an asymptotic representation for the stress tensor components. 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 appearance of a zone 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 macroscopic classical 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 (non-singular) terms were taken into account and the series coefficients of these terms were determined. It is shown that the developed algorithm can be used to effectively determine the coefficients of the higher-order terms of the series
|
