Local lattice instability analysis on mode I through cracks in single crystalline Fe (Effect of crack array under periodic boundary condition)

Abstract

As a series study which clarify the local stability at crack tip based on the positiveness of atomic elastic stiffness (AES), mode I type loading is applied on the periodic slab cell of bcc-Fe with single center crack and double cracks at the center and corner, by using molecular dynamics simulation. All the [001](010), [001](110) and [112](111) cracks shows propagation with cleavage cracking, under the condition of fixing the periodic cell length except in the loading direction. The [001](110) and [112](111) cracks show immediate fracture without remarkable plastic deformation, and it is found that the number of negative AES atoms at the stress-strain peak or the limit of crack propagation is almost constant despite of the different mechanical condition of crack array. The critical domain of negative AES for crack propagation is evaluated as about 40 and 25 atomic lines per crack tip, for the [001](110) and [112](111) cracks, respectively. The [001](010) cracks show dislocation emission and twin formation before cleavage cracking, and we can't distinguish the negative AES at the twin boundary and cleavage cracking, so that we can't define simple criteria as mentioned above. Finally we evaluate the eigenvalue of the AES as the further investigation of the unstable mode of the negative AES. It is natural that the emergence of negative 1st eigenvalue reflects the loss of positiveness of AES determinant; however, the [112](111) cracks show negative 2nd eigenvalue just after the stress-strain peak (single crack model) and just before it (double crack model). The atoms with negative 2nd eigenvalue are observed just at the tip of cleavage cracking as 1 or 2 atomic line in the first stage of unstable cracking; however, they are also observed in the various position, e.g. boundary of the local phase transformation, in the later stage toward the final fracture.