Models for grain microstructure evolution and grain statistics

Kim, Jaekwang

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https://hdl.handle.net/2142/120089 Copy

Description

Title

Models for grain microstructure evolution and grain statistics

Author(s)

Kim, Jaekwang

Issue Date

2023-04-24

Director of Research (if dissertation) or Advisor (if thesis)

Admal, Nikhil C.

Doctoral Committee Chair(s)

Admal, Nikhil C.

Committee Member(s)

• Johnson, Harley T.
• Hilgenfeldt, Sascha
• Charpagne, Marie A.

Department of Study

Mechanical Sci & Engineering

Discipline

Theoretical & Applied Mechans

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Grain microstructure
• Polycrystalline
• Motion by curvature
• Stochastic method
• Phase field model
• threshold dynamics
• artificial neural network

Abstract

One of the important aims of grain boundary modeling is to predict the evolution of a large collection of grains under various thermo-mechanical loads to establish the relation between process parameters and the resulting microstructure. In this thesis, we focus on a microstructure phenomenon called grain growth, of which a defining characteristic is the motion of grain boundaries driven by surface tension to decrease the interfacial energy. Pronounced at high temperature, grain growth is responsible for creating final microstructure, and therefore influences macroscopic properties of polycrystalline material. While various scales of models have been developed for grain growth, models that describe a single microstructure are often computationally intensive, resulting in significantly limited size for tractable systems. However, since the dimensions of microstructure space of possible grain configuration are enormously large, a solution to the process-structure relationship problem is necessarily statistical. This motivates us to develop efficient models that describe the microstructure evolution of an ensemble of polycrystals. In this thesis, we approach grain growth at two scales. First, we focus on developing an efficient mesocale model and associated computational algorithm for its implementation to efficiently track full-field microstructure during grain growth. In particular, we improve the Kobayashi–Warren–Carter (KWC) model, a memory efficient dual-phase field grain boundary model. While the grain boundary energy of original KWC model is restricted to Read–Shockley-type, we generalize it to incorporate arbitrary misorientation- dependent grain boundary energies. The generalized KWC model inherits the memory efficiency of the original KWC model. Furthermore, we develop a new computational method that adapts the thresholding method of Merriman–Bence–Osher scheme for the dual-phase field model. The algorithm implements the curvature motion of grain boundaries represented by the generalized KWC model with a computational cost of O(N log N ), where N is the number of grid points. We use these tools to study the grain microstructure evolution in a two-dimensional face-centered cubic copper polycrystal to characterize grain growth under crystal symmetry-invariant grain boundary energies. In the second part of the thesis, we investigate grain growth from a statistical level and develop an ultrafast computational infrastructure in predicting microstructure. Restricting our attentions to two-dimensional isotropic grain growth, we conceive a new stochastic framework that evolves the joint distribution of two coarse grain descriptors, areas and the number of sides (topology) of grains. Under the assumption of spatial homogeneity, we track grain statistics of the entire system using the descriptors of a collection of representative grains, or rep grains. The von Neumann–Mullins law, which states the rate of change of grain area as an exclusive function of topology, is used to deterministically evolve the areas of rep grains. However, since grains change their topology as they evolve by interacting with neighbors, we construct a topology transformation model (TTM) that predicts the probability of topology transformation of a grain in terms of its current state and the states of its neighbors. The construction of the TTM relies on a data-driven approach using a fully connected deep neural network. Topology transformations recorded in phase field simulations are used as training data. Combined with the von Neumann–Mullins law, the resulting neural network model is used in a Monte Carlo simulation to evolve grain microstructures in a statistical sense. The stochastic framework is validated against the asymptotic and transient grain statistics predicted by large-scale phase field simulations.

Graduation Semester

2023-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2023 Jaekwang Kim

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