Phase-field Models of Microstructure Evolution in a System with Elastic Inhomogeneity and Defects
Open Access
- Author:
- Hu, Shenyang
- Graduate Program:
- Materials Science and Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- March 05, 2004
- Committee Members:
- Long Qing Chen, Committee Chair/Co-Chair
David John Green, Committee Chair/Co-Chair
Qiang Du, Committee Member
Zi Kui Lui, Committee Member - Keywords:
- Phase-field model
microstructure evolution
precipitation in alloys
interfacial energy anisotropy
interface mobility anisotropy
dislocations
thin film and elastic inhomogeneity. - Abstract:
- Abstract Solid state phase transformations are often utilized to control materials microstructures and thus properties. Quantitative understanding of the thermodynamics and kinetics of phase transformations and the accompanying microstructure evolution can provide a scientific basis for designing advanced materials. In this thesis, the phase-field approach is employed to study the effect of elastic inhomogeneity and structural defects on phase separation kinetics and morphological evolution in bulk and film systems, the precipitation of theta prime phase (Al2Cu) in Al-Cu alloys, and solute strengthening of alloys. An accurate and efficient iteration method is proposed to solve the mechanical equilibrium equations in a solid with elastic inhomogeneity. By combining the iteration method for calculating the elastic energy and a semi-implicit spectral method for solving the Cahn–Hilliard equation an extremely efficient phase-field model is developed for studying morphological evolution in coherent systems with large elastic inhomogeneity. The morphological dependence of isolated particles as well as a phase separated multi-particle system on the degree of elastic inhomogeneity is systematically studied. The iteration method is further extended to a thin film system with the simultaneous presence of dislocations, compositional strains and a substrate constraint. Spinodal decomposition in a thin film with periodically distributed arrays of interfacial dislocations is simulated. The results show that the periodic stress field associated with the array of interfacial dislocations leads to a directional phase separation and the formation of ordered microstructures. It is demonstrated that when the period of the dislocation array becomes small, the wave length of the ordered microstructure tends to be the same as that of the dislocation array. The results have important implications that an ordered nanostructure could be designed by controlling the interfacial dislocation distribution. The metastable theta prime (Al2Cu) precipitates are one of the primary strengthening precipitates in Al-Cu alloys. They are of a plate-like shape with strong interfacial energy and mobility anisotropies. A phase-field model which can automatically incorporate the thermodynamic and kinetic information from databases is developed. The relationships between phase-field model parameters and material thermodynamic and kinetic properties are established. Systematic simulations of growth in 1D, 2D and 3D are carried out. The growth of a single precipitate in 1D exactly reproduces the results from analytical solutions. The equilibrium shape simulated in two dimensions is in good agreement with that predicted by the Wulff construction based on the interfacial energy anisotropy. 2D and 3D simulations produce typical precipitate morphologies and precipitate configurations that are observed in prior experiments. The simulation results on the growth of an isolated precipitate in 2D show that the lengthening is diffusion-controlled, and follows the growth law whereas the thickening follows the growth law. The elastic energy associated with the lattice mismatch between the precipitate and the matrix was shown to speed up the lengthening while decrease the thickening and coarsening process. The phase-field model can serve as a basis for quantitative understanding of the influence of elastic energy, interface energy anisotropy and interface mobility anisotropy on the precipitation of theta prime in Al-Cu alloys. Precipitates and solutes are commonly used to strengthen alloys. A phase field model of dislocation dynamics, which employs 12 order parameter fields to describe the dislocation distribution in a single fcc crystal, and one composition field to describe the solute distribution, is developed for a binary alloy. This model is able to simulate phase transformation, solute diffusion, dislocation motion as well as their interaction under applied stresses. A new functional form for describing the eigenstrains of dislocations is constructed, which eliminates the dependence of the magnitude of the dislocation Burgers vector on applied stresses and provides a correct dislocation stress field. A relationship between dislocation velocity and applied stresses is obtained by theoretical analysis, which can be used to determine phase-field model parameters with kinetic data of dislocation mobility. The effect of dislocation velocities on Cottrell atmosphere, and the dynamic dragging force of Cottrell atmosphere on the dislocation motion are simulated. The results demonstrate that the phase-field model correctly describes the long-range elastic interactions and short-range interaction that determines dislocation reactions.