Mechanical & Materials Engineering, Department of


First Advisor

Prahalada K. Rao

Second Advisor

Kevin D. Cole

Third Advisor

Jeffrey E. Shield

Date of this Version

Spring 4-17-2020


J. A. Severson, "Thermal Modeling of Additive Manufacturing Using Graph Theory: Validation with Directed Energy Deposition," Master of Science, Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, 2020.


Publication of this work in ASME transactions is pending.

A THESIS Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Master of Science, Major: Mechanical Engineering and Applied Mechanics, Under the Supervision of Professors Prahalada Rao and Kevin Cole. Lincoln, Nebraska: May 2020

Copyright 2020 Jordan A. Severson


Metal additive manufacturing (AM/3D printing) offers unparalleled advantages over conventional manufacturing, including greater design freedom and a lower lead time. However, the use of AM parts in safety-critical industries, such as aerospace and biomedical, is limited by the tendency of the process to create flaws that can lead to sudden failure during use. The root cause of flaw formation in metal AM parts, such as porosity and deformation, is linked to the temperature inside the part during the process, called the thermal history. The thermal history is a function of the process parameters and part design.

Consequently, the first step towards ensuring consistent part quality in metal AM is to understand how and why the process parameters and part geometry influence the thermal history. Given the current lack of scientific insight into the causal design-process-thermal physics link that governs part quality, AM practitioners resort to expensive and time-consuming trial-and-error tests to optimize part geometry and process parameters.

An approach to reduce extensive empirical testing is to identify the viable process parameters and part geometry combinations through rapid thermal simulations. However, a major barrier that deters physics-based design and process optimization efforts in AM is the prohibitive computational burden of existing finite element-based thermal modeling.

The objective of this thesis is to understand the causal effect of process parameters on the temperature distribution in AM parts using the theory of heat dissipation on graphs (graph theory). We develop and apply a novel graph theory-based computational thermal modeling approach for predicting the thermal history of titanium alloy parts made using the directed energy deposition metal AM process. As an example of the results obtained for one of the three test parts studied in this work, the temperature trends predicted by the graph theory approach had error ~11% compared to experimental trends. Moreover, the graph theory simulation was obtained within 9 minutes, which is less than the 25 minutes required to print the part.

Advisors: Prahalada K. Rao and Kevin D. Cole