Predicting Dislocation Climb and Creep from Explicit Atomistic Details

Here we report kinetic Monte Carlo simulations of dislocation climb in heavily deformed, body-centered cubic iron comprising a supersaturation of vacancies. This approach explicitly incorporates the effect of nonlinear vacancy-dislocation interaction on vacancy migration barriers as determined from atomistic calculations, and enables observations of diffusivity and climb over time scales and temperatures relevant to power-law creep. By capturing the underlying microscopic physics, the calculated stress exponents for steady-state creep rates agree quantitatively with the experimentally measured range, and qualitatively with the stress dependence of creep activation energies.

Figure 1

(a) Simulation cell, in which a pair of edge dislocations ($\top$, $\perp$) of opposite sign (dislocation dipole) is created by removing a half plane of atoms (yellow). Vacancies (red) are distributed randomly; two are indicated with red arrows. (b) Various possible vacancy migration paths towards the dislocation core. (c) $E_{v-d}^{\mathrm{int}}$ and activation barrier for vacancy migration along various paths shown in (b).

Figure 2

Normalized diffusivity $D^{{\rho }_d,T}/D^{0,T}$ at different temperatures $T$ as a function of dislocation density ${\rho }_d$ for a constant vacancy concentration (${\varrho }_v={10}^{-4}$).

Figure 3

Dislocation climb velocity as a function of applied stress for (a) varied ${\rho }_d(\sigma )$ (via Taylor’s equation) and constant ${\varrho }_v={10}^{-4}$ for all ${\rho }_d$ at temperatures $T>0.4T_m$; and (b) varied ${\varrho }_{\mathrm{v}}(\sigma ,T)$ according to Eq. (1) for a set of constant ${\rho }_d$ and $T=800\mathrm{K}$, where ${\varrho }_v^{\mathrm{ref}}(729.9\mathrm{MPa},1100\mathrm{K})={10}^{-4}$. (c) Complete stress dependence of $v_{\mathrm{c}}$, where both ${\rho }_d$ and ${\varrho }_{\mathrm{v}}$ change simultaneously and correspond to $\sigma$. Statistical errors in $v_{\mathrm{c}}$ are smaller than the data points in log-scale. (d) Climb velocities in (a), (b), and (c) show power-law dependence on $\sigma$. Exponents of these power-laws $\beta$, $\gamma$, and $\mu$, respectively, vary weakly with $T$. Results for different levels of ${\varrho }_{\mathrm{v}}^{\mathrm{ref}}$ are shown in supplementary material 17.

Figure 4

(a) Creep over a range of stresses and temperatures $T>0.4T_m$ for reference supersaturation ${\varrho }_v^{\mathrm{ref}}(729.9\mathrm{MPa},1100\mathrm{K})={10}^{-4}$. (b) Stress exponents and effective activation energies at different temperatures and applied stresses, respectively. The solid horizontal line represents the activation barrier of self-diffusion (0.84 eV) in a dislocation-free lattice. The effective activation energy is a linear function of applied stress, $Q=Q_0-V_a\sigma$, where $Q_0=0.87\mathrm{eV}$. Calculated activation volume $V_a=(0.85\pm 0.03){\Omega }_0$, where ${\Omega }_0$ is the Fe atomic volume, is consistent with dislocation creep controlled by vacancy diffusion.