Transitions in the morphology and critical stresses of gliding dislocations in multiprincipal element alloys

Refractory multiprincipal element alloys (MPEAs) are promising material candidates for high-temperature, high-strength applications. However, their deformation mechanisms, particularly at the dislocation scale, are unusual compared to those of conventional alloys, making it challenging to understand the origin of their high strength. Here, using an atomistically informed phase-field dislocation dynamics model, we study transitions in the morphology and critical stresses of long gliding screw dislocations over extended distances in a refractory MPEA. The model MPEA crystal accounts for the atomic-scale fluctuations in chemical composition across the glide planes via spatially correlated lattice energies and for the differences in glide resistances between screw and edge dislocations of unit length. We show that the dislocation moves in a stop-start motion, alternating between wavy morphology in free flight and nearly recovered straight screw orientation in full arrest. The periods of wavy glide are due to variable kink-pair formation and migration rates along the length, where portions with higher rates glide more quickly. The critical stress to initiate motion corresponds to the stress required to form and migrate a kink pair at the weakest region along the length of the dislocation. Heterogeneity in lattice energy leads to variability in the local stress-strain response and to a strain hardening-like response, in which the critical stress to reactivate glide increases with glide distance. Statistical assessment of hundreds of realizations of dislocations indicates that the amount of hardening directly scales with the dispersion in underlying lattice energy.

Figure 1

The USFE values calculated with DFT for each slip plane type and the normal distributions incorporated into the PFDD calculations. The mean and standard deviation for each plane are shown by the white point and error bars, respectively. The lighter colored points represent the bottom 20% of each distribution, where athermal kink pairs are likely to be nucleated.

Figure 2

Representative examples of screw-oriented FR source operation on each of the four planes studied. All surfaces have correlation length $l$ equal to $5w_0$. Dislocation lines are colored with respect to time. Lighter loops indicate a later time step than darker loops.

Figure 3

The critical stresses to activate a screw-oriented FR source on each plane. Each colored box is a separate simulation, and darker colors indicate where multiple simulations give the same critical stress value. The mean for each correlation length is also plotted with error bars corresponding to the standard deviation of the distribution.

Figure 4

The critical stages of FR source activation for both a plane with a low screw-edge ratio, {112} type, and a plane with a high screw-edge ratio, {134} type. Both screw- and edge-oriented sources show kink-pair nucleation as the limiting step. Before these kink pairs form, the dislocation will fall back to its original position if the stress is unloaded. The correlation lengths used in these examples range from $1w_0$ to $10w_0$.

Figure 5

Representative examples of edge-oriented FR source operation on each of the four planes studied. All surfaces have correlation length $l$ equal to $5w_0$. Dislocation lines are colored with respect to time. Lighter loops indicate a later time step than darker loops.

Figure 6

The critical stresses to activate an edge-oriented FR source on each plane. Each colored box is a separate simulation, and darker colors indicate where multiple simulations give the same critical stress value. The mean for each correlation length is also plotted with error bars corresponding to the standard deviation of the distribution.

Figure 7

[(a)–(d) Several stress-strain curves from screw dislocation propagation simulations on each slip plane type. The curves show a characteristic “staircase” as dislocations are pinned and unpinned several times before finally annihilating with periodic images. The definitions of ${\sigma }_i$ and ${\sigma }_f$ are illustrated in panel (a).

Figure 8

(a) The distribution of ${\sigma }_i$, the critical stress to initiate glide, grouped by plane type and correlation length. Darker symbols correspond to critical stresses shared by multiple iterations. The black dots show the mean stress for that correlation length and plane, with error bars equal to standard deviation across the 30 iterations. (b) The ratio ${\sigma }_f/{\sigma }_i$ for each plane as a function of correlation length. This value corresponds to the amount of hardening that occurs during dislocation glide. (c) The quantity $({\sigma }_f-{\sigma }_i)/{\sigma }_i$ for each correlation length plotted against the coefficient of variation of the underlying USFE surface. Higher variance in USFE leads to more hardening as the dislocation glides.

Figure 9

Representative examples of screw dislocation propagation on each of the four planes studied. The dashed lines indicate stable dislocations under stress, which require an increase in applied stress to advance. All four planes shown have a correlation length of $3w_0$, and dislocation lines are colored with respect to time, where lighter colors indicate a later time step.

Figure 10

Representative examples of the progression of screw dislocation glide in MoNbTi. The initially straight screw dislocation (shown in black) appears wavy during glide (shown in white) but become arrested under stress and returns to a straight screw morphology (shown in red). These examples are from a {110}-type plane and {123}-type plane, but dislocation glide proceeds in a similar fashion for all planes studied. The correlation length $l$ is $3w_0$ for both cases.

Figure 11

(Left) Examples of dislocations that were unloaded during glide in PFDD. The black line is the initial dislocation and the pink line is the unloaded dislocation. Just as the dislocations are wavy during glide, they remain wavy under zero stress if the stress is removed. The correlation length $l$ is $1w_0$ for all four cases pictured. (Right) Experimental observations of wavy dislocations in MoNbTi. Taken with permission from Ref. [27].

Figure 12

Examples of kink-pair nucleation on all four slip planes. The kink pairs in the top row are nucleated on the weakest screw dislocation for their slip plane, while the bottom row shows kink pairs on the strongest screw dislocation studied. The black line shows the initial placement of the dislocation at zero stress. Regardless of the slip plane, correlation length $l$, or critical stress, kink-pair nucleation controls the glide behavior of the dislocations.