Improved phase field model of dislocation intersections

Abstract

Revealing the long-range elastic interaction and short-range core reaction between intersecting dislocations is crucial to the understanding of dislocation-based strain hardening mechanisms in crystalline solids. Phase field model has shown great potential in modeling dislocation dynamics by both employing the continuum microelasticity theory to describe the elastic interactions and incorporating the γ-surface into the crystalline energy to enable the core reactions. Since the crystalline energy is approximately formulated by linear superposition of interplanar potential of each slip plane in the previous phase field model, it does not fully account for the reactions between dislocations gliding in intersecting slip planes. In this study, an improved phase field model of dislocation intersections is proposed through updating the crystalline energy by coupling the potential of two intersecting planes, and then applied to study the collinear interaction followed by comparison with the previous simulation result using discrete dislocation dynamics. Collinear annihilation captured only in the improved phase field model is found to strongly affect the junction formation and plastic flow in multislip systems. The results indicate that the improvement is essential for phase field model of dislocation intersections. INTRODUCTIONInteractions between dislocations gliding in intersecting slip planes play fundamental roles in the strain hardening during plastic deformation of crystalline materials.1-4 Dislocation intersections lead to the formation of dislocation junctions in minimum energy configurations. In face-centered cubic (FCC) crystals, the sessile junction known as Lomer-Cottrell lock 5,6 is assumed to be the most stable barrier to further dislocation motion in the traditional view.1,3 However, Madec and co-workers 7 reported that the interaction between two intersecting dislocations with collinear Burgers vectors is the strongest of all dislocation reactions. Previous modeling and simulations 7-24 on investigating the dislocation intersections emphasized the importance of the interaction details between individual dislocations, including not only the long-range elastic interactions but also the short-range core reactions. Most of these researches suggested that the dislocation interactions can be studied by multiscale approaches, where the discrete dislocation dynamics (DDD) based on continuum elasticity theory deals with the long-range elastic attraction or repulsion, and atomistic simulations the short-range reaction rules.9 Different from the DDD techniques that require priori rules as inputs, 10 another simulation method also based on continuum elastic theory called phase field model (PFM) 25-30 can straightforwardly account for the effects of short-range core reactions by incorporating the generalized stacking fault energy (γ-surface) 11 from atomistic or first principle calculations, such as dislocation dissociation. [31][32][33][34][35] With this advantage, the PFM model of dislocation shows great potent...

Discontinuous yielding of pristine micro-crystals

“…This method has evolved from the original Landau approach to the modeling of phase transitions [150][151][152][153][154][155]. In PFDD lattice slips are described by scalar order parameters and the energy wells represent quantized lattice invariant shears [147,156,157]; transition layers, separating regions with different amount of shear, represent the locations of dislocation lines. The Landau energy functional couples the tensorial linear elastic energy with the scalar lattice energy whose periodic structure is usually informed by atomic scale simulations based on the Cauchy-Born rule.…”

A comparison of different continuum approaches in modeling mixed-type dislocations in Al

“…In 2014, Shen et al [18] proposed the microscopic phase-field model in which all order parameter evolution is confined to the slip planes and the gradient energy is removed from the system energy. More recently, Zheng et al [19] modified the crystalline energy to fully account for the reactions between dislocations gliding in intersecting slip planes, while also neglecting the gradient energy.…”

Studying Grain Boundary Strengthening by Dislocation-Based Strain Gradient Crystal Plasticity Coupled with a Multi-Phase-Field Model

“…Some studies report how the phase field is coupled with isotropic plasticity [27] or CP [28] to analyze the finite or infinitesimal strains in larger material volumes. Recent studies also show an increasing trend towards discrete-dislocation-dynamics-based phase field models [29,30,31,32,33,34,35,36] to describe plastic deformation, but such models can only be applied to smaller systems due to the associated computational cost. The non-homogeneous deformation in the framework of phase field modeling has, however, been addressed by only a few researchers, who employed strain-gradient CP coupled with a phase field model like, for example, the work by Aldakheel on fracture analysis of metals [37].…”