Phase-Field Modeling of Precipitation in Metallic Alloys: Morphology, Kinetics and Hardening Effects

Restricted (Penn State Only)
Ji, Yanzhou
Graduate Program:
Materials Science and Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
October 04, 2018
Committee Members:
  • Long-Qing Chen, Dissertation Advisor
  • Long-Qing Chen, Committee Chair
  • Zi-Kui Liu, Committee Member
  • Tarasankar Debroy, Committee Member
  • Sulin Zhang, Outside Member
  • Phase-Field Modeling
  • Precipitation
  • Precipitation hardening
  • Metallic alloys
Precipitation hardening is an important strengthening mechanism in metallic alloys, which is realized by impeding the dislocation motions in the matrix via stress field due to the precipitate/matrix lattice mismatch. The precipitation hardening effect is largely determined by a series of inter-correlated factors including the feature and evolution of precipitate morphologies, e.g., the size, shape, volume fraction and spatial distribution of the precipitate and their evolution; the coherency state of the precipitate; and the detailed precipitate-dislocation interaction mechanisms. Therefore, understanding and quantifying the morphology and kinetics of precipitation is an important step towards the estimation of precipitation hardening effects, as well as the proper design of alloys and the optimization of thermo-mechanical processing routes. The phase-field approach, as a powerful meso-scale simulation method, has been successfully applied to understand the precipitation phenomena. However, there are still several remaining challenges for precipitation phase-field models. In this thesis work, the precipitation phase-field models have been further extended and applied to deal with precipitate phases with different thermodynamic descriptions, to predict the morphology evolution and kinetics of fully coherent and semi-coherent precipitates with the help of first-principles calculations, to predict the possible dislocation evolution pathway and morphology evolution during the sequential coherency loss of an initially coherent or semi-coherent precipitate, to understand the competitions between the diffusional and diffusionless transformation mechanisms, and to provide necessary information for theoretical precipitation hardening models. The precipitate phase, depending on the specific materials systems, can be treated using solid solution model, sublattice model, or stoichiometric compounds (line compounds). To deal with these different treatments, we use the Kim-Kim-Suzuki model for the solid solution and sublattice cases, where the equal diffusion chemical potential of alloying elements is assumed to remove the extra potential at the interface. An internal equilibrium is assumed for the sublattice model within different sublattices which converts the sublattice site fractions to alloy compositions. To deal with the precipitation of line compounds, we develop a phase-field model for chemical reactions, which can capture both the solute diffusion in the matrix phase and the linear chemical reaction kinetics. The phase-field model is then applied to investigate the precipitate morphology, kinetics and hardening effect of the fully coherent β’-Mg7Nd in Mg-Nd alloys. The necessary input parameters, including the formation energies, lattice constants and elastic constants of both the Mg matrix and the β’ phase, as well as the anisotropic interfacial energies, are all obtained from first-principles calculations. Especially, the formation energies of the slightly off-stoichiometric Mg7Nd compound are also calculated, which are used to fit the formation energies of β’ into a parabolic function of solute composition. The interplay between the anisotropies in misfit strain energy and interfacial energy is discussed in detail, showing their dominance in determining the precipitate morphology at different aging stages. The simulated β’ morphology, with both anisotropies considered, is consistent with experimental observations. Theoretical models based on Orowan’s equation is used to predict the hardening effect of β’-Mg7Nd. The phase-field model, with similar thermodynamic treatment of the precipitate phase to that of β’-Mg7Nd, is further applied to the semi-coherent θ’-Al2Cu in Al-Cu-based alloys. To more accurately simulate the precipitation kinetics, a temperature-dependent nucleation model, with necessary input from experimental observations, and a more accurate parameterization of interface kinetic coefficient, are considered in the model. The phase-field simulations, with materials parameters from validated sources, are performed for isothermal aging at 463 K, 503 K and 533 K. The simulated θ’ is of disk shape under the anisotropies of misfit strain energy, interfacial energy and interface mobility. The predicted θ’ precipitation kinetics, including the evolution of mean diameters, mean thicknesses and volume fractions, show acceptable agreement with experimental measurements. Possible model improvements and extensions to minimize the discrepancies are discussed. Coherency loss of the initially coherent or semi-coherent precipitate during continued precipitate growth is a manifestation of energy minimization, which relaxes the misfit strain energy at the expense of increasing the interfacial energy by creating line defects at the matrix/precipitate interface. To understand the kinetics of coherency loss, as well as its effect on precipitate morphology, kinetics and hardening effects, we equivalently consider the effect of line defects, as well as the evolution of their average spacings, on the formulation of misfit strain energies and interfacial energies in the phase-field model. We apply this model to γ”-Ni3Nb in IN718, where γ” is treated using the sublattice model, to predict the critical γ” size to trigger the coherency loss under different criteria and a known dislocation configuration at interfaces. We further apply the model to predict the sequential loss of coherency in θ’-Al2Cu, which predicts a coherency loss pathway with the minimum energy cost. Diffusional precipitation transformation can change its transformation mechanism with the change of alloy composition, temperature and cooling rates. For example, in Ti-6Al-4V, start from β phase, the α phase can be a diffusional product during isothermal aging or slow cooling, while becomes diffusionless product during fast cooling. To understand this competition, we combine the graphical thermodynamic approach to predict the possible transformation pathways, and the phase-field simulation to predict the microstructure evolution during continuous cooling of Ti-6Al-4V. The simulated (α+β) morphologies are attributed to the interplay between the diffusional and diffusionless mechanisms, as well as that between the nucleation and growth of α phase.