Experience in modeling inclined cracks in materials with cubic crystal structure

In this work, a good coincidence of atomistic and continuum stress fields at the crack tip under mixed mode loading conditions in an anisotropic medium with cubic symmetry of elastic properties is revealed. The atomic stress distributions associated with the crack tip are obtained using the molecular dynamics method. Continuum distributions are obtained from the theoretical solution of the problem of determining the stress-strain state at the crack tip, based on the methods of the elasticity theory of anisotropic media and the subsequent decomposition of complex potentials by eigenfunctions. In the framework of a molecular dynamics computational experiment, a single-crystal face-centered copper at low temperature was considered in order to isolate the elastic mode of deformation of a single crystal, and the embedded atom potential was used. A distinctive feature of the conducted molecular dynamic modeling is the consideration of a crack that makes up various angles with planes of symmetry of the crystal. In the vicinity of the crack tip, points lying in annular regions at different distances from the crack tip and of different thickness were selected, and the dependences of the stress tensor components depending on the polar angle were plotted. A comparison of the angular dependencies obtained by atomistic calculation and using a theoretical solution showed their good consistency. It is found that the similarity of the angular dependences of the stress tensor components is observed for all the studied values of two angles: the angle between the axis of symmetry of the crystal lattice (in the plane of the plate) and the direction of the crack and the angle between the action of the tensile load and the crack line.
By virtue of this property of solutions, it can be concluded that solutions of continuous fracture mechanics can serve to describe stress fields at atomistic distances from the crack tip.