Plasticity and Dislocation Dynamics in a Phase Field Crystal Model

The critical dynamics of dislocation avalanches in plastic flow is examined using a phase field crystal model. In the model, dislocations are naturally created, without any ad hoc creation rules, by applying a shearing force to the perfectly periodic ground state. These dislocations diffuse, interact and annihilate with one another, forming avalanche events. By data collapsing the event energy probability density function for different shearing rates, a connection to interface depinning dynamics is confirmed. The relevant critical exponents agree with mean field theory predictions.

Figure 1

The number of dislocations in a sheared PFC crystal. Intermittent events with sizes differing in orders of magnitude are observed. Parameters are $(\alpha {)}^2=255$, $\beta =0.9$, $v_0=1.581$, ${\rho }_0=0.3$, $ϵ=1.5$, $\lambda =40.0$, and $r=-0.5$.

Figure 2

The total speed of defect atoms in a sheared PFC crystal. Intermittent events with sizes differing in orders of magnitude are observed. Parameters are $(\alpha {)}^2=255$, $\beta =0.9$, $v_0=1.581$, ${\rho }_0=0.3$, $ϵ=1.5$, $\lambda =40.0$, and $r=-0.5$.

Figure 3

The probability distribution of the event energy during dislocation avalanches, for different values of the shearing rates.

Figure 4

Data collapse of the probability distribution of the event energy during dislocation avalanches, with $\tau =1.5$, $\mu =2$, and $v_c=1.5$.