UC Santa Barbara

Hexagonal close packed HCP materials are already being widely used as structural materials in several key industries, and there is currently great interest in expanding their employment in many next-generation engineering applications. The use of HCP materials necessitates understanding and modeling their deformation response, whether in processing or in service. The plastic deformation response of materials with an HCP crystal structure is governed by the glide of dislocations on both low index and high index planes. For an HCP crystal, whether it deforms in a brittle or ductile manner depends on the relative amounts of moving dislocations contributed on these low index and high index planes. The ease of dislocation motion is largely a consequence of the characteristics of the dislocation core structure, such as number of planes on which it extends, whether it dissociates into smaller partial dislocations, its splitting distance, and the width of the individual partials. Therefore, understanding individual dislocations (at the nanoscale level) on the unique slip planes of HCP metals, sheds important insight onto the deformation of HCP materials. Isolating individual dislocations is difficult to do experimentally and is limited by length and time scales in many quantum/atomistic models. As such, we employ a phase field formulation that incorporates periodic potentials, from first principle calculations, to model individual dislocations on the distinct HCP slip planes. This work explores individual dislocations using the phase field dislocation dynamics PFDD model which had to go through several code developments to account for the lower symmetry of HCP crystallography and its unique slip plane energetics, elastic anisotropy, and thermal fluctuations. This work explores dislocation dissociation, morphology, and mobility on the basal, prismatic and pyramidal II slip planes in HCP materials, taking a special focus on the relatively unstudied pyramidal-II plane. 10 different HCP materials are modeled over the course of this work, but special attention is given to understanding dislocations in Mg for its promises in lightweighting applications, as well as Ti and Zr which are also commonly studied HCP materials. The temperature dependencies of dislocation glide are studied by the additional consideration of thermal fluctuations into the energy minimization framework of the model. Since dislocation motion is largely a consequence of the characteristics of the dislocation core structure (number of planes on which is extends, whether it dissociates into smaller partial dislocations, its splitting distance, and the width of the individual partial cores) modeling dislocation dynamics in HCP requires a model that is capable of capturing these characteristics of dislocation core structure. Previously, the PFDD model was written for the symmetry of cubic crystal structures and had only been applied to face-centered cubic FCC materials. So for our work, the PFDD model is first extended to determine the static and dynamic properties of discrete dislocations belonging to all types of slip modes in the HCP crystal, such as the basal ⟨a⟩, prismatic ⟨a⟩, and pyramidal II ⟨c + a⟩ slip modes [1]. This is the first time a phase-field based dislocation dynamics model has been used to model HCP materials, so we look at equilibrium dislocation cores and dislocation dissociation under no stress so we can compare our results with results from other atomistic models and experiments for validation. The dissociation simulations using the HCP capable PFDD method incorporate directly density functional theory DFT-calculated generalized stacking fault energy GSFE surfaces and curves for the different HCP slip planes and employ isotropic elasticity. The results demonstrated good agreement with available results from molecular statics MS, DFT, or experimental observations of dislocations structures in Mg. We move forward into a deeper exploration of the pyramidal II plane, on which dislocation behavior remains elusive and the resulting material effects are unknown. We employ an elastically anisotropic version of the PFDD approach, to compute the equilibrium core structures of pyramidal-II ⟨c + a⟩ dislocations under zero externally applied stress conditions in ten HCP metals: Be, Co, Mg, Re, Ti, Zn, Cd, Hf, Y, and Zr. In all these metals, under zero applied stress, the initialized perfect ⟨c + a⟩ pyramidal dislocations dissociate into two partials that separate in plane, creating extended structures, with nanometer-sized splitting distances referred to as equilibrium stacking fault widths eSFW (that is the fully relaxed or equilibrated distance between partials under zero external applied stress). The eSFWs for these 10 metals scales inversely with their normalized intrinsic stacking fault energy I from their GSFE curves. In most cases, the dislocation partial core widths and Burgers vectors are not ideally equal. These asymmetries in the dislocation structures are explained by deviations in the pyramidal II GSFE landscape from that expected of a metal with an ideal c/a ratio and symmetric landscape. Metals with higher levels of elastic anisotropy have wider separation distances (20–35%) for both screw and edge character dislocations than what would be expected with effective isotropic constants. The discovery of the asymmetric dislocation cores on the pyramidal II plane prompted the following question: will the same energetics that result in asymmetric dislocation cores, also gives rise to asymmetric dislocation slip? We then applied an external shear stress that initiates dislocation glide along the slip plane of interest and note any changes in the splitting distances of the partial dislocations as they glide in tandem. If the partial dislocations and associated stacking fault glide while maintaining a consistent splitting distance between the two partial dislocations, we refer to this as the dynamic stacking fault width dSFW. We find glissile dislocations on the pyramidal II plane have dSFW that are directionally dependent. That is to say, if we apply a shear stress to initiate glide along one direction the measured dSFW differs from the dSFW measured when we apply a shear stress to induce glide in the opposite direction.The directional dependency of the dSFW is due to the asymmetries in GSFE curves and the decomposition of the Burgers vector for each partial dislocation. We explore this further by using a Frank-Read FR source to generate expanding dislocation loops. We calculate the critical shear stress σc for loop expansion for each FR source. We consider both screw and edge type initial dislocations in a FR source of different lengths on the basal and the pyramidal II plane and find the loop shape is dominated by screw type sections to minimize the line tension energy of the expanding loop. We also note large variations in the stacking faults throughout the FR loop expansion until the loop had expanded beyond its critical shape and a steady-state dSFW was reached. The evolution of the stacking faults during the FR dislocation loop expansion is due to the different energetic barriers to glide that governs each partial dislocation. Directional dependency is also noticed for the FR source simulations of the pyramidal II plane, as the energetic barriers (e.g. from the asymmetric GSFE profile) associated with the leading and the trailing partial are ”assigned” based on the directionality of the applied shear stress. All of the simulations up to now are deterministic and carried out under an assumed temperature of 0K. However, the pyramidal planes are suspected to be temperature dependent more so than the other slip planes and many material processes and applications occur at or above room temperature. So in order to truly understand pyramidal II dislocation behavior we need to explore the temperature dependency of pyramidal slip. This necessitates the extension of the PFDD formulation to account for thermal activation. In our final PFDD development we derive the Langevin force equations for the phase field framework to account for thermal fluctuations at variable temperatures. This produces a stochastic thermal noise term that we can add to the energy minimization equation in the PFDD model. This advanced PFDD model with thermal capabilities is then used to explore how temperature affects the time to dislocation loop formation from a Frank-Read FR source. We study Mg, Ti, and Zr over various temperatures T ranging from 0 ≤ T /Tm ≤ 0.5, where Tm is the melting temperature for each material. We also look at the velocity of infinitely long screw and edge type dislocations as they glide under the same shear stress we apply in the FR simulations. We find the leading partial for the screw dislocation ”breaks away” at a greater velocity than the trailing partial at higher temperatures T /Tm > 0.2 creating a continuously growing stacking fault. We find that when we decrease the applied shear stress the leading screw partial does not breakaway at higher temperatures. This breakaway is not observed for the temperatures and stresses applied to edge dislocations. In the FR source simulations this results in the screw portions ”smearing” out at higher temperatures. This breakaway phenomenon observed on the pyramidal II plane is both dislocation character type, stress and temperature dependent.