High temperature dislocation glide in the MoNbTi refractory multiprincipal element alloy

Numerous body-centered cubic refractory multiprincipal element alloys (RMPEAs) exhibit high temperature strengths that surpass those of Ni-based superalloys. The superior properties of RMPEAs have been shown to stem in part from the unique dislocation glide mechanisms in compositionally disordered systems. Here, using a three-dimensional phase field dislocation dynamics approach combined with Langevin dynamics, we simulate the glide mechanisms of screw and edge dislocations at elevated temperature and low stress levels in the RMPEA MoNbTi with a body-centered cubic, random solid solution structure. For $600-1200$ K, edge-dislocation glide is smooth, temperature sensitive, and faster than screw dislocation glide. Screw dislocations exhibit three distinct glide mechanisms over the same temperature range. Ultimately, the formation of nonplanar kink pairs that ensues above 900 K reduces screw mobility with respect to temperature and leads to athermal mobility from 1100 to 1200 K.

Figure 1

Setup for a screw dislocation dipole placed on the (110) plane in a nonorthogonal bcc computation grid.

Figure 2

One sample of the variable energetic computational cell of random solid solution MoNbTi used in PFDD simulations. The dislocation dipole is not included in the schematic. The central {110} plane is the maximum resolved shear stress plane (MRSSP).

Figure 3

Propagation distance as a function of time for a long initially edge-character dislocation on the (110) habit plane in MoNbTi under an applied stress of (a) $\sigma =0.01\mu$, (b) $\sigma =0.02\mu$, and (c) $\sigma =0.03\mu$. (d) Propagation distance plotted versus temperature for $\sigma =0.01\mu , \sigma =0.02\mu$, and $\sigma =0.03\mu$ at two different times, τ = 500 and τ = 1000.

Figure 4

Snapshots of the initially edge-character dislocation line at $\tau =1000$ at and insets of line position at $\tau =200$ and $\tau =500$. (a) 1200 K, $\sigma =0.01\mu ,$ (b) 900 K, $\sigma =0.02\mu ,$ and (c) 600 K, $\sigma =0.03\mu$. The colored surface indicates values of the USFE.

Figure 5

Propagation distance as a function of time for a long initially screw-character dislocation on the (110) habit plane in MoNbTi under an applied stress of (a) $\sigma =0.01\mu$, (b) $\sigma =0.02\mu$, and (c) $\sigma =0.03\mu$. (d) Propagation distance plotted versus temperature for $\sigma =0.01\mu , \sigma =0.02\mu$, and $\sigma =0.03\mu$ at two different times, $\tau =500$ and $\tau =1000$.

Figure 6

Snapshots of a screw dislocation line at the end of simulation time τ at temperatures of (a) 1200 K, (b) 900 K, and (c) 600 K. Insets at two previous time steps are shown for each condition. A snapshot of the dislocation in motion is shown in red and an instance of the dislocation in a dwell period is shown in white. The color bar indicates values of the USFE on the surface plots. Snapshot in (a) is taken under low stress $\sigma =0.01\mu$ and at $\tau =2000$, (b) medium stress $\sigma =0.02\mu$ and at $\tau =1000$, and (c) high stress $\sigma =0.03\mu$ and at $\tau =1000$.

Figure 7

Slipped regions of MoNbTi by a screw dislocation initially placed on the (110) habit plane under medium driving stress. (a) The initially straight screw dislocation at 0 K and $\tau =0$. For the left column, the boundary between ${\phi }_{\left(110\right)}=1$ (red) and ${\phi }_{\left(110\right)}=0$ (blue) is the initial position of the dislocation. For the right column, the snapshots track: (1) the unslipped regions (green) where the order parameter on the habit plane and two cross-slip planes are zero, (2) the slipped (110) plane (purple) where order parameter ${\phi }_{\left(110\right)}>0.8$ and order parameters of the two cross-slip planes are zero (i.e., ${\phi }_{\left(101\right)}={\phi }_{\left(01-1\right)}=0)$, and (3) regions of the crystal that undergo slip via nonplanar kps (orange) corresponding to the condition that ${\phi }_{\left(101\right)}\mathrm{and}{\phi }_{\left(01-1\right)}>0.8$ and ${\phi }_{\left(110\right)}=0$. (b)–(d) shown at the end of simulation. (e) Number of nonplanar kps as a function of temperature for low, medium, and high stress levels.

Figure 8

Screw mobility for three applied stresses plotted versus temperature. Mobility is taken as dislocation velocity normalized by applied stress and Burgers vector magnitude. Mobility is only plotted for temperature conditions at which a steady state velocity could be computed (i.e., waiting time<travel time). Screw dislocations display a temperature-insensitive mobility from $T=1100-1200\mathrm{K}$.

Figure 9

Summary of screw glide mechanism regimes: (a) multiple kp, (b) overlapping kp, and (c) overlapping kp and nonplanar kp regimes. (d) Screw glide mechanisms map across temperature and stress conditions. Quantitatively, the temperatures and stresses corresponding to the boundaries between regimes apply to MoNbTi, but the regimes are expected for screw dislocations in other RMPEAs.

Figure 10

Comparison of temperature-insensitive strengths from experimental data on MoNbTi and PFDD results on screw mobility.

Figure 11

Total number of thermal kps and propagation distance plotted as a function of temperature at zero stress.