### Abstract

The goal of this work is to predict the effect of part geometry and process parameters on the direction and magnitude of heat flow ‒ heat flux ‒ in parts made using metal additive manufacturing (AM) processes. As a step towards this goal, the objective of this paper is to develop and apply the mathematical concept of heat diffusion over graphs to approximate the heat flux in metal AM parts as a function of their geometry. This objective is consequential to overcome the poor process consistency and part quality in AM. Currently, part build failure rates in metal AM often exceed 20%, the causal reason for this poor part yield in metal AM processes is ascribed to the nature of the heat flux in the part. For instance, constrained heat flux causes defects such as warping, thermal stress-induced cracking, etc. Hence, to alleviate these challenges in metal AM processes, there is a need for computational thermal models to estimate the heat flux, and thereby guide part design and selection of process parameters. Compared to moving heat source finite element analysis techniques, the proposed graph theoretic approach facilitates layer-by-layer simulation of the heat flux within a few minutes on a desktop computer, instead of several hours on a supercomputer.

Original language | English (US) |
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Pages (from-to) | 375-382 |

Number of pages | 8 |

Journal | Procedia Manufacturing |

Volume | 33 |

DOIs | |

Publication status | Published - Jan 1 2019 |

Event | 16th Global Conference on Sustainable Manufacturing, GCSM 2018 - Lexington, United States Duration: Oct 2 2018 → Oct 4 2018 |

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### Keywords

- Additive Manufacturing
- Discrete Approximation
- Graph Theory
- Heat Equation
- Heat Flux
- Thermal Modeling

### ASJC Scopus subject areas

- Industrial and Manufacturing Engineering
- Artificial Intelligence

### Cite this

*Procedia Manufacturing*,

*33*, 375-382. https://doi.org/10.1016/j.promfg.2019.04.046