Computational design of additively manufactured functionally graded materials by thermodynamic modeling with uncertainty quantification
Open Access
- Author:
- Bocklund, Brandon
- Graduate Program:
- Materials Science and Engineering (PHD)
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- September 29, 2021
- Committee Members:
- John Mauro, Program Head/Chair
Zi-Kui Liu, Chair & Dissertation Advisor
Allison Beese, Major Field Member
John Mauro, Major Field Member
Michael Janik, Outside Unit, Field & Minor Member
Richard Otis, Special Member - Keywords:
- thermodynamics
CALPHAD
alloys
additive manufacturing
uncertainty quantification
functionally graded materials - Abstract:
- Thermodynamics is language for describing the equilibrium and non-equilibrium states of the microscopic and macroscopic systems that make up our universe. In materials science, thermodynamic modeling is used to understand the energetic relationships between states and properties of matter and is a core pillar of the Integrated Computational Materials Engineering (ICME) approach for materials design. CALPHAD modeling, which describes the Gibbs energies of individual phases, is a key tool in ICME because of the technique's demonstrated ability to describe multicomponent thermodynamics through systematically constructing unary, binary, and ternary thermodynamic models that are extrapolated to multicomponent design spaces. The fundamental challenge in CALPHAD modeling is to build self-consistent, multicomponent thermodynamic databases that have an inverse pyramid dependence on constituent, low-order subsystems. The combinatoric explosion of binary and ternary subsystems that need to be assessed or re-assessed when adding or updating pure elements to a CALPHAD database makes it difficult to develop or update large multicomponent databases CALPHAD models are developed semi-empirically, meaning that both the models and data used to parameterize the models have underlying uncertainty. However, virtually all CALPHAD databases available today are point estimates of maximum likelihood parameterizations and can not describe any uncertainty in the predictions made using the underlying CALPHAD models. Quantifying the uncertainty in predictions made from CALPHAD models can improve how CALPHAD is used for ICME-driven materials design and also provide key insights into how our understanding, or lack of understanding, of materials thermodynamics can be leveraged to develop databases in more time- and cost-effective ways. This dissertation will discuss the development of ESPEI, an open-source user tool for semi-automated CALPHAD modeling and uncertainty quantification that uses the recently developed pycalphad software package as the thermodynamic engine. ESPEI uses a two-step approach that first parameterizes and selects CALPHAD models and second optimizes model parameters while quantifying their uncertainty using a Bayesian inference method implemented by an ensemble Markov chain Monte Carlo (MCMC) approach. The computational approach taken by ESPEI will be demonstrated by developing a Cu-Mg CALPHAD database with quantified and propagated uncertainty. Additively manufactured (AM) functionally graded materials (FGMs) are a recent development where the layer-by-layer deposition process of AM can be used to design materials that are graded in composition, phases, and properties. FGMs are an excellent platform for exploring regions of composition space that would be difficult or impossible explore using traditional processing methods, but the methods of using computational thermodynamics to predict the outcomes of the complex AM process are still maturing. ESPEI will be used to combine first-principles calculations and experimental data to assess and quantify the uncertainty in binary and ternary subsystems towards a Cr-Ti-Fe-Ni-V CALPHAD database that could be used to develop FGMs between Ti-, Fe-, and Ni-based alloys. Several case studies of different FGMs will be used to advance the understanding of how computational thermodynamics can be used to predict the phases that will form in FGMs produced by the complex AM process. Finally, the methods developed will be used to predict a viable composition path to join a 316 stainless steel alloy to Ti-6Al-4V using a series of graded interlayers along a thermodynamically stable composition path.