Date of Award

Fall 11-18-2023

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Materials and Infrastructure Systems

First Advisor

Xiang Chen

Abstract

This dissertation presents a comprehensive study that addresses two critical challenges in the field of computational materials science and engineering from nano- to mesoscale. First, to overcome the well-acknowledged length scale limitation associated with atomistic simulations, a novel two-step approach is introduced for a probabilistic prediction of stress-strain curves in terms of material volume. The method combines Molecular Dynamics (MD) simulations and a multioutput Gaussian process (MOGP) with Bayesian analysis to model stress-strain behavior and predict stress and strain values. The model effectively captures the intricate three-stage curve shape exhibited in stress-strain plots, discerning key points such as yielding, hardening, and failure. Through crucial pre-processing steps involving logarithmic transformation and standardization of input and output values, the MOGP model mitigates the impact of outliers, ensures model stability, and facilitates meaningful comparisons among different variables. The model’s accuracy and reliability are rigorously validated through Leave-One-Out Cross-Validation (LOOCV) and in-depth analysis of error metrics. The research findings demonstrate that the developed MOGP model provides highly accurate predictions of stress-strain behavior for various material sizes, thus contributing invaluable insights to materials science and engineering while offering a versatile tool for designing materials with superior mechanical properties. The integration of uncertainty estimates enables precise forecasting of stress-strain behavior beyond the typical size limitations of MD simulations, offering a versatile tool applicable to various materials. Second, to address the limited predictive capability of the existing Crystal Plasticity (CP) method in interface modeling, this work establishes a new sequential multiscale method that incorporates interfacial parameters generated from Molecular Dynamics (MD) simulations into the continuum level Crystal Plasticity Finite Element Analysis (CPFEA) model. The simulation results, as validated by experiments in the literature, acknowledge the significant influence of interface properties on material behaviors. Specifically, the flow parameter of the finite-thickness interface is first obtained by MD simulations; the Nucleation Theory with the nudged elastic band (NEB) technique is then employed to bridge the temporal domains of the atomistic and continuum models, which extrapolates the low-strain-rate yield stresses from the high-strain-rate MD results. To address length scale limitations, the above-mentioned MOGP-based machine learning model is harnessed as a robust tool for accurately forecasting stress-strain curves of materials at larger sizes, with the training data of MD simulations of materials of varying dimensions. The integrated flow parameters and extrapolated yield stresses are then incorporated into the CPFEA model, allowing for grain-level CP simulations over extended time scales. The validation of the CPFEA model against experimental results demonstrates its accuracy in describing material behavior. Additionally, the interfacial parameters obtained from MD simulations using the NEB method offer valuable insights into dislocation nucleation from interfaces. Determination of the athermal component of the yield stress and an intrinsic thermally activated portion through calculations based on Fisher plots enhances the understanding of material behavior, facilitating the development of advanced materials with improved mechanical properties. With the successful development and demonstration of these two novel methodologies, this dissertation contributes to the field of materials science and engineering by enabling precise probabilistic predictions of stress-strain behavior beyond the typical size of atomistic simulations and enhancing the capability of CP simulations for materials with interfaces. The research findings offer valuable insights and pave the way for designing materials with enhanced mechanical properties for various engineering applications.

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