Barrier effect of grain boundaries on the avalanche propagation of polycrystalline plasticity

To investigate the barrier effect of grain boundaries on the propagation of avalanchelike plasticity at the atomic scale, we perform three-dimensional molecular dynamics simulations by using simplified polycrystal models including symmetric-tilt grain boundaries. The cutoffs of the stress-drop distributions following power-law distributions decrease as the size of the crystal grains decreases. We show that some deformation avalanches are confined by grain boundaries; on the other hand, unignorable avalanches penetrate all the grain boundaries included in the models. The blocking probability that one grain boundary hinders this system-spanning avalanche is evaluated by using an elemental probabilistic model.

Figure 1

(a) Typical stress-time curves, where the tensile stress ${\sigma }_z\left(t\right)$ of $N_{\text{GB}}=0$, 2, 4, and 6 models are depicted as dashed black, solid red, black, and blue lines, respectively. The schematic figure of the polycrystal models used in this study is imposed. (b) The probability distributions of stress drop $\mathrm{\Delta }{\sigma }_z$ in each model, where the empirical distributions in Eq. (2) fitted to each distribution are shown as thin black curves.

Figure 2

Snapshots of all atoms (top) and participant atoms representing slip areas during a plastic deformation event (bottom) in (a) the model with $N_{\text{GB}}=2$, (b) $N_{\text{GB}}=4$, and (c), (d) $N_{\text{GB}}=6$. The approximate positions of GBs are indicated by horizontal dashed lines. (d) The slip area percolates all the GBs in the model.

Figure 3

Distributions of the relative linear size of an avalanche $S_z$. The inset shows the probability of system-spanning events plotted against the number of GBs, $N_{\text{GB}}$. Open circles and the red dotted line indicate the probability estimated from the simulation results in Table 1 and the theoretical relationship depicted in Eq. (3), respectively.