*4.2. Dislocation Nucleation*

Delamination and crack growth via dislocation nucleation have been observed by other researchers in the past [30,51]. Similar to the thermally activated lattice-trapped delamination mode discussed above, dislocation nucleation is thermally activated. Above some critical load, the activation barrier for dislocation nucleation goes to zero and spontaneous nucleation occurs [51]. Hence, we have a race between two thermally activated

processes—lattice-trapped delamination and dislocation nucleation—each characterized by their own activation enthalpy which varies with the stress intensity factor. This race gives rise to the crack volume trends exhibited in Figure 9. At lower stress, lattice-trapped delamination is slow so that the crack does not grow much before a dislocation is nucleated. As the stress is increased, the lattice-trapped delamination rate increases and there is a time lag before the dislocation nucleates, causing the crack volume at dislocation nucleation to increase. Finally, at very high stresses the athermal load is reached for dislocation nucleation so that a dislocation nucleates immediately during the simulations, causing the crack volume at dislocation nucleation to go to zero. This qualitatively explains the trends observed in Figure 9. A quantitative explanation would require a detailed understanding of the nucleation parameters for a dislocation at the crack tip, which are non-trivial to compute and beyond the scope of this work [51].

Unfortunately, the conditions of the simulations here were such that as soon as a dislocation nucleated, the particle delaminated almost instantaneously. This indicates that our systems were overdriven with the respect to dislocation-mediated delamination. It is possible that quantitatively useful delamination rates could be obtained under dislocationmediated delamination from simulations at lower stresses if a large enough pre-crack is manually inserted into the system. Here, if our applied stress was too low, the latticetrapped delamination rate was so small that a crack never became large enough to enable dislocation nucleation. Future work should focus on quantifying the dislocation-mediated delamination rate.
