A phase field dislocation dynamics model for a bicrystal interface system: An investigation into dislocation slip transmission across cube-on-cube interfaces

Abstract

In this work, we present a phase field dislocation dynamics formulation designed to treat a system comprised of two materials differing in moduli and lattice parameters that meet at a common interface. We apply the model to calculate the critical stress τ crit required to transmit a perfect dislocation across the bimaterial interface with a cubeon-cube orientation relationship. The calculation of τ crit accounts for the effects of: 1) the lattice mismatch (misfit or coherency stresses), 2) the elastic moduli mismatch (Koehler forces or image stresses), and 3) the formation of the residual dislocation in the interface. Our results show that the value of τ crit associated with the transmission of a dislocation from material 1 to 2 is not the same as that from material 2 to 1. Dislocation transmission from the material with the lower shear modulus and larger lattice parameter tends to be easier than the reverse and this apparent asymmetry in τ crit generally increases with increases in either lattice or moduli mismatch or both. In efforts to clarify the roles of lattice and moduli mismatch, we construct an analytical model for τ crit based on the formation energy of the residual dislocation. We show that path dependence in this energetic barrier can explain the asymmetry seen in the calculated τ crit values. Significantly, it reveals that τ crit scales with a (2) G (2) a (1) +a (2) a (1) a (2) − G (1) G (2) 2 , where G is the shear modulus, a is the lattice parameter, and the superscripts (1) and (2) indicate quantities for material 1 and material 2, respectively.

Understanding dislocation mechanics at the mesoscale using phase field dislocation dynamics

“…Transmission from the softer to the stiffer material and from the larger to smaller Burgers vector is favoured. Repeating the calculations for transmission of a screw dislocation shows the same trends [3].…”

“…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.…”

“…Green circles indicate edge transmission events, whereas red squares correspond to screw transmission events. Figure taken with permission from [3].…”

“…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].…”

On the competition between dislocation transmission and crack nucleation at phase boundaries

“…The most common approaches are the Peierls-Nabarro (PN) model [12][13][14], phase-field based models [15][16][17] and Field Dislocation Mechanics [18][19][20]. Using these models, dislocation transmission across simple grain and phase boundary structures was recently studied [21][22][23][24].Here we add a novel dimension to the problem beyond transmission, by extending the recently proposed 2D Peierls-Nabarro finite element (PN-FE) model [24] to incorporate decohesion. This extension enables us to study how the local stresses due to a dislocation or a pile-up of dislocations may result…”