Phase field dislocation dynamics formulation coupled with Fourier based micromechanics solver and its application to grain boundary-dislocation interactions

Abstract

A new phase field dislocation dynamics formulation is presented, which couples micromechanical solvers and the time-dependent Ginzburg-Landau equation. Grain boundary (GB)-dislocation interactions are studied by describing GBs as inclusions. Grain boundary properties are computed from Molecular Statics simulations and an additional contribution to the total energy that takes into account the GB energy is considered in the calculations. Interaction of a screw dislocation with minimum energy and metastable states of low and high angle $\langle$110$\rangle$ symmetric tilt grain boundaries are studied. We show good agreement between predictions from our phase field dislocation dynamics formulation and molecular dynamics simulations of grain boundary-dislocation interactions.

Figures (31)

• Figure 1: Pseudo-algorithm of the new PFDD formulation. $e_s=1\times 10^{-5}$ and $e_o=1\times 10^{-8}$ are stress and order parameter convergence tolerances.
• Figure 1: Disregistry $\Delta$ and stress component $\sigma_{yz}$ of a LAGB with GB energy $\gamma_{\mathsmaller{GB}}=751$ mJ/m$^2$ under an applied stress of $\sigma_{yz}^{app} = 750$ MPa at t=125, 250, 375, 500, 625 and 750. The inclusion representing the GB is represented in the middle of the domain using dashed lines and the detailed view is shown at (a) t=125.
• Figure 2: Grain boundary energy (GBE) as a function of misorientation angle for $<110>$ symmetric tilt grain boundary. The GBE of the LAGB and HAGB are colored in blue and orange, respectively. The same data points were used to study GB-dislocation interactions by dang2025dislocation.
• Figure 2: Disregistry $\Delta$ and stress component $\sigma_{yz}$ of a LAGB with GB energy $\gamma_{\mathsmaller{GB}}=751$ mJ/m$^2$ under an applied stress of $\sigma_{yz}^{app} = 750$ MPa at t=125, 250, 375, 500, 625 and 750. The inclusion representing the GB is represented in the middle of the domain using dashed lines and the detailed view is shown at (a) t=125.
• Figure 3: Grain boundary structure of $\langle 110 \rangle$ symmetric tilt. (a) Low-angle GB (LAGB) with the (1,1,6) GB plane and (b) a high-angle GB (HAGB) with the (5,5,2) GB plane in Cu. The minimum energy structures are shown in the top (751 and 847 mJ m$^{-2}$ for the LAGB and HAGB, respectively) and two metastable structures are shown in the middle (1003 and 938 mJ m$^{-2}$ for the LAGB and HAGB, respectively) and bottom (1228 and 998 mJ m$^{-2}$ for the LAGB and HAGB, respectively). The color bar corresponds to the centrosymmetry parameter computed using Ovito.