Statistical and Computational Approaches in ICME with Applications in Fatigue and Additive Manufacturing

This thesis showcases a set of computational and statistical approaches with applications in integrated computational materials engineering. The first is the development of the microstructure based, statistically equivalent representative volume element (M-SERVE) for the Ni-based superalloy Ren'e 88DT. The incredible strength of Ni-based superalloys can be traced to the γ-γ’ microstructure, where the morphology of the microstructure playing a substantial role in the material properties. A robust collection of image processing tools, statistical characterization approaches, and microstructure reconstruction methods are developed, allowing for the computationally efficient generation of statistically equivalent microstructures. The second main thrust of this thesis is the development of a Bayesian classifier for crack nucleation events in the Ni-based superalloy Ren'e 88DT under fatigue loading. A large set of experimentally obtained crack nucleation sites are imaged, and subsequently simulated with a homogenized constitutive model. A crystal plasticity constitutive law is simulates the image based microstructure, and is embedded in a self-consistent rate-dependent elasto-plastic model to provide accurate boundary conditions. The results are input to a data-driven Bayesian classification methodology that automatically incorporates the most informative state variables. This is augmented by the addition of theoretically derived crack nucleation indicators and results in a human interpretable and effective model that predicts crack nucleation likelihood. The final component of this thesis is an effective crystal plasticity model for additively manufactured Ti-6Al-4V. The microstructure of additively manufactured Ti-6Al-4V is characterized by a complex Widmanstdätten morphology containing 12 unique α lath variants. Characterization of the microstructure necessitates a pipeline of image processing and sterological techniques. The material model explicitly represents parent β grains, with statistical representations of the α laths and variant volume fractions within them. The material model which directly incorporates the statistics of the α laths is then calibrated to the experimental data, while maintaining the vast majority of the material parameters which were previously calibrated for Ti-6242. This allows for an accurate representation of rate dependency and other important material parameters. Finally the material model is validated by matching the experimental mechanical responses of microstructures with substantively different α laths, that the model was not trained on

Two Dimensional Depletion Interactions with Attractive Depletants

The objective of this thesis is to be able to characterize two dimensional depletion forces at an interface and determine what, if any, effect attraction between depletants has on depletion interaction. We decided to investigate attractive depletants as we wanted to determine how colloids adsorbed to an interface would be depleted with nano-scale depletants undergoing Van der Walls attraction. To accomplish this goal we wrote simulations to test various conditions for depletion in a two dimensional system. In this system we were able to define parameters such as the area fraction of the depletants, size ratio between the colloids and the depletants, and interactions between depletants. We then developed a theory to predict the interactions between the colloids as a function of the system parameters and depletant-depletant interactions. This theory pieces together several other well-known depletion papers. We start with the A.O theory to ensure that our simulation is working properly. Then we build up to using an adsorption interaction theory used for polymer chain depletants developed by Lekkerkerker et al. Finally, to utilize this theory, we had to predict how the colloids would alter the depletant density profiles around them; which meant incorporating a theory from Glandt et.al to predict how depletants pack around an object. This allowed us to predict the density profiles of depletants around colloids. We can take these density profiles and use the adsorption theory to determine how depletant-depletant attraction effects the depletion interaction profile between colloids. We then were able to determine from the interaction potential the contact forces of the colloids as well as their second virial coefficients. This can help us determine if depletant-depletant attraction can be used to modify the depletion force to aid in single domain crystal formation