Stacking fault emission from grain boundaries: Material dependencies and grain size effects

Understanding dislocation mechanics at the mesoscale using phase field dislocation dynamics

“…Hence, the plastic strain can be expressed in terms of the order parameters and can be written as [1,3,4] bζ α (x, t)δ n (s α i m α j + s α j m α i ), (2.1) where N is the number of slip systems, b is the magnitude of the Burgers vector, s α is the slip direction, m α is the slip plane normal associated with slip system α, and δ n is a Dirac distribution supported on the slip plane, n.…”

“…This equation relates the change in the phase field variables in time to the variation in the total system energy with respect to the phase field variables [1,4,5] as follows:…”

“…In this section, extensions required to account for the motion and interactions of Shockley partial dislocations belonging to the {111} 112 systems are discussed. Because the phase field variables are defined in terms of perfect dislocation slip directions, linear combinations of these order parameters must be used in order to account for partials [1,6]. Hence, at a minimum, in order to model partial dislocations three phase field variables must be active on the same glide plane (for fcc metals).…”

“…For example, points G and G 2 represent the intrinsic and unstable SFEs, respectively. In the present calculations, these points will be taken directly from the γ -surface or GSFE curves generated via atomistic methods [1,2,9,13,14]. Figure 1a shows the GSFE curves for a wide range of fcc metals as calculated with DFT [2].…”

“…Hence, atomic motions and interactions are not explicitly calculated and much larger crystal sizes and longer time scales (of the order of seconds) can be assessed. In efforts to recover some atomic-scale physics, PFDD has been extended to permit incorporation of the energetics of atomic-scale dislocation cores from density functional theory (DFT) calculations [1,2], which is particularly important for partial dislocation motion and interactions. Most recent model advancements include additional energetics accounting for differences in moduli in two-phase materials and dislocation interactions with bi-phase interfaces [3].…”