Jason Gruber

Sparse data structure and algorithm for the phase field method

The concepts of sparse data structures and related algorithms for phase field simulations are discussed. Simulations of polycrystalline grain growth with a conventional phase field method and with sparse data structures are compared. It is shown that memory usage and simulation time scale with the number of nodes but are independent of the number of order parameters when a sparse data structure is used.

Testing a curvature driven moving finite element grain growth model with the generalized three dimensional von Neumann relation

Abstract The von Neumann – Mullins relation has been extended to higher dimensions by MacPherson and Srolovitz. Their exact solution relates the rate of volume change of an individual grain in a 3-dimensional isotropic polycrystal to its mean width and total length of triple lines (assuming isotropic boundaries). The objective of this study is to verify that grains in a moving finite element grain growth model obey this law. Algorithms have been developed in order to calculate mean width of individual grains in digital microstructures for which the grain structure is discretized with both volumetric and surface meshes. Theoretical rate predictions were obtained from the measured mean widths and triple line lengths. Good agreement was found between growth rates measured in the simulations and the predictions of MacPherson – Srolovitz theory for the cases of an isolated shrinking sphere, individual grains in a digitally generated coarse polycrystal, and individual grains in a microstructure reconstructed from serial sectioning of stabilized cubic zirconia. Departures from this relationship appeared to be related to the grain shape.

Orientation Distribution of Σ3 Grain Boundary Planes in Ni before and after Grain Boundary Engineering

The distribution of grain boundary plane orientations in polycrystalline Ni has been measured before and after grain boundary engineering. The grain boundary engineered microstructure has a relatively higher concentration of Σ3 grain boundaries and, when compared to the initial structure, more of these boundaries have orientations that are inclined by more than 10° from the (111) orientation of the ideal coherent twin. Although the conventionally measured grain size is not affected by the grain boundary engineering process, the average size of the regions containing only Σ3n grain boundaries increases by nearly a factor of two. The observations indicate that the increase in the relative population of Σ3 grain boundaries results both from the preferential elimination of random grain boundaries and the generation of new Σ3 grain boundaries which do not have (111) grain boundary plane orientations.

Effect of anisotropic interfacial energy on grain boundary distributions during grain growth

Through simulations with the moving finite element program GRAIN3D, we have studied the effect of anisotropic grain boundary energy on the distribution of boundary types in a polycrystal during normal grain growth. An energy function similar to that hypothesized for magnesia was used, and the simulated grain boundary distributions were found to agree well with measured distributions. The simulated results suggest that initially random microstructures develop nearly steady state grain boundary distributions that have local maxima and minima corresponding to local minima and maxima, respectively, of the energy function.

Computer Simulations Combining Finite Difference and Finite Element Methods: Solute Drag on Migrating Grain Boundaries in Three-Dimension

The current study aims to improve our fundamental understanding of solute segregation and solute drag on migrating grain boundaries (GB) in three dimensions. Computer simulation combines finite difference and finite element methods. An exemplary case study is reported, in which a spherical grain is embedded inside a cubic grain and shrinks as a result of motion by curvature, as a preliminary to modeling grain growth in single phase materials. The results agree qualitatively with literature studies in 1-D.