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, B α i j =∆σ α i /∆ε j , where σ α i and ε j are the atomic stress and strain in the Voigt notation. Atoms in the Ni, Co, and Zr obstacles show lower eigenvalue, η α(1) , the solution of B α i j ∆ε j =η α ∆ε i , 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 {∆ε 1 , ∆ε 2 ,・ ・ ・,∆γ 6 } T ={∆ε xx , ∆ε yy ,・ ・ ・,∆γ xy } T for unstable η α(1) < 0 atoms.