Study on crack propagation by eigenvalue/eigenvector of atomic elastic stiffness: Interaction with Ni/Co/Zr/Mo obstacles in Fe

Abstract

Molecular dynamics simulations are implemented on the interaction between mode I crack in Fe single crystal and cylindrical Ni/Co/Zr/Mo obstacles, substituting Fe atoms with those elements in a periodic slab cell. The crack penetrates the Ni and Co obstacles while it bypasses the Mo one by the slip and void nucleation at the Fe-Mo interface. The crack also cuts in the Zr obstacle; however, it is caught by the amorphized Zr atoms in Fe matrix, showing remarkable resistance against crack propagation. Then these behaviors are discussed with the eigenvalue/vector of the atomic elastic stiffness coefficient, Bαij=Δσiα/Δεj, where σiα and εj are the atomic stress and strain in the Voigt notation. Atoms in the Ni, Co, and Zr obstacles show lower eigenvalue, ηα(1), the solution of BαijΔεj=ηαΔεi, against Fe matrix while those in the Mo obstacle have higher one than Fe. That is, the crack cuts in the “soft” Ni, Co and Zr obstacles and bypasses the “hard” Mo one. The unstable modes of crack tip, slip in the obstacles and at the Fe-Mo interface are visualized from the maximum shear direction of the eigenvector of {Δε1,Δε2,･･･,Δγ6}T={Δεxx,Δεyy,･･･,Δγxy}T for unstable ηα(1)< 0 atoms.

Keywords

• local lattice instability
• atomic elastic stiffness
• crack
• embedded atom method
• obstacle