Molecular Dynamics Simulations on Local Lattice Instability at Mode I Crack Tip in BCC Iron

Abstract

Molecular dynamics simulations are performed on the [001](010), [001] (110) and [11](111) through cracks in bcc Fe under mode I loading, in order to discuss about the local lattice stability at the crack tip within the framework of FS potential function. The crack width is set to $2c=0.1L_x, 0.2L_x$ and $0.5L_x$, respectively, against the periodic cell length of $L_x=20-30$ nm. The [001](010) crack shows ductile behavior of blunting by dislocation emission, resulting in the remarkable nonlinearity in the stress–strain curve. Both the [001](110) and [11](111) cracks propagates in a brittle manner, showing the abrupt stress drop by the rupture. Then the local stability is discussed by the positiveness of the determinant of $6\times 6$ matrix of elastic stiffness coefficients, $B_{ij}^\alpha$; that is, Wang’s B-criteria is applied to each atom. Negative atoms emerges at far smaller strain than the peak or rupture one, corresponding to the onset of local “plastic deformation”, i.e. dislocation emission or rearrangement at the crack surface. For the detail of the unstable mode, we have evaluated the eigenvalue of $B_{ij}^\alpha$ of each atom. Since the negative 1st eigenvalue leads the negative $\det B_{ij}^\alpha$, it is natural the tendencies of the former and the later are almost same. However, a few atoms at the [11](111) crack tip turn to negative in their 2nd eigenvalue just at or just after the stress–strain peak.