Dynamics of a dislocation bypassing an impenetrable precipitate: The Hirsch mechanism revisited

The dynamical process where an edge dislocation in fcc copper bypasses an impenetrable precipitate is investigated by means of molecular dynamics simulation. A mechanism that is quite different from the Orowan mechanism is observed, where a dislocation leaves two prismatic loops near a precipitate, i.e., the Hirsch mechanism. It is found that the critical stress for the Hirsch mechanism is almost the same as the Orowan stress, while spatial inhomogeneity of the shear stress is essential to the Hirsch mechanism. We also find that repetition of the Hirsch mechanism does not increase the critical stress.

Figure 1

(Color online) Successive snapshots of an edge dislocation bypassing an impenetrable precipitate. The radius of the precipitate [dark gray (blue) atoms] is $1.5\mathrm{nm}$. A dislocation [light gray (red) atoms] is visualized by omitting atoms that have 12 nearest neighbors. (a) A dislocation bows out to form a screw dipole. (b) The screw dipole cross slips. (c) The screw dipoles undergo double cross slip to annihilate each other at the top of the precipitate. (d) The dislocation has bypassed the precipitate with a superjog. A prismatic loop is left behind.

Figure 2

(Color online) Geometry of the primary cross slip from $\left(111\right)$ to $\left(11\overline{1}\right)$. (a) A $\left[1\overline{1}1\right]$ projection. (b) A $\left[111\right]$ projection.

Figure 3

(Color online) (a) Configuration just after a single bypass process. A dislocation leaves two prismatic loops: an interstitial loop and a vacancy loop. The secondary loop is formed relatively far from the precipitate, since it has been dragged by the dislocation as a superjog. (b) A row of prismatic loops after the passage of three dislocations. Note that the loops on the right side of the precipitate do not form an apparent row.

Figure 4

(Color online) The critical resolved shear stresses for the Hirsch mechanism (denoted by the $\mathrm{red}\times \mathrm{symbols}$). Note that the Orowan stress is almost the same as the Hirsch stress. The green dashed lines represent Eq. (1) with $A=6.5\mathrm{N}∕\mathrm{m}$ and $B=0.5\mathrm{nm}$. (a) Dependence of the critical stress on the precipitate radius, where $L_x$ is $20.4\mathrm{nm}$. (b) Dependence of the critical stress on the spacing of the precipitates, where $r$ is $1.5\mathrm{nm}$.

Figure 5

(Color online) Spatial profiles of the average atomistic displacement in the $y$ direction when the bypass mechanisms begin. The red solid line represents the profile for the Hirsch mechanism, while the green dashed line denotes that for the Orowan mechanism. The gradient, which corresponds to the elastic shear strain, is asymmetric with respect to the glide plane $(z=95\mathrm{\AA })$ for the Hirsch mechanism. System parameters are $r=1.5\mathrm{nm}$ and $L=20.4\mathrm{nm}$.