Atomic elastic stiffness analysis to predict twinning in Fe single crystal under shear

Abstract As a series study that discusses local instability by atomic elastic stiffness, B ij a = Δ σ i a / Δ e j , molecular dynamics simulations of simple shear on Fe perfect lattice are performed to discuss twin deformation. In the simulation of extremely low temperature of 0.1 K, many twin boundaries are nucleated in a periodic slab cell of stacked ( 1 ¯ 1 ¯ 2 ) planes just after the stress drop or elastic limit under shear. The 1st eigenvalue η a ( 1 ) of the 6 × 6 matrix B ij a shows fluctuation in each ( 1 ¯ 1 ¯ 2 ) planes just before the elastic limit. At the stress-strain peak, η a ( 1 ) 0 or unstable layers emerge and twin deformation occurs at these unstable “band” in the simulation cell. The period of the η a ( 1 ) fluctuation is almost constant even if the cell size is expanded in the [ 1 ¯ 1 ¯ 2 ] and [1  1 ¯  0] direction, while the unstable band arrays tilt normal to the diagonal line of the simulation cell, under the cell expansion in the [1 1 1] direction. At the elevated temperature of 300 K, the simultaneous periodic band never appears but a few unstable bands appear locally in time sequence and bring twinning there.