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Research Papers

Uncertainty Propagation Analysis of Computational Models in Laser Powder Bed Fusion Additive Manufacturing Using Polynomial Chaos Expansions

[+] Author and Article Information
Gustavo Tapia

Industrial and Systems Engineering Department,
Texas A&M University,
College Station, TX 77843
e-mail: gtapia@tamu.edu

Wayne King

Physical and Life Sciences Directorate,
Lawrence Livermore National Laboratory,
Livermore, CA 94550
e-mail: weking@llnl.gov

Luke Johnson, Raymundo Arroyave, Ibrahim Karaman

Materials Science and Engineering Department,
Texas A&M University,
College Station, TX 77843

Alaa Elwany

Industrial and Systems Engineering Department,
Texas A&M University,
College Station 77843, TX
e-mail: elwany@tamu.edu

1Corresponding author.

Manuscript received November 8, 2017; final manuscript received July 30, 2018; published online October 5, 2018. Assoc. Editor: Sam Anand.

J. Manuf. Sci. Eng 140(12), 121006 (Oct 05, 2018) (12 pages) Paper No: MANU-17-1695; doi: 10.1115/1.4041179 History: Received November 08, 2017; Revised July 30, 2018

Computational models for simulating physical phenomena during laser-based powder bed fusion additive manufacturing (L-PBF AM) processes are essential for enhancing our understanding of these phenomena, enable process optimization, and accelerate qualification and certification of AM materials and parts. It is a well-known fact that such models typically involve multiple sources of uncertainty that originate from different sources such as model parameters uncertainty, or model/code inadequacy, among many others. Uncertainty quantification (UQ) is a broad field that focuses on characterizing such uncertainties in order to maximize the benefit of these models. Although UQ has been a center theme in computational models associated with diverse fields such as computational fluid dynamics and macro-economics, it has not yet been fully exploited with computational models for advanced manufacturing. The current study presents one among the first efforts to conduct uncertainty propagation (UP) analysis in the context of L-PBF AM. More specifically, we present a generalized polynomial chaos expansions (gPCE) framework to assess the distributions of melt pool dimensions due to uncertainty in input model parameters. We develop the methodology and then employ it to validate model predictions, both through benchmarking them against Monte Carlo (MC) methods and against experimental data acquired from an experimental testbed.

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Figures

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Fig. 1

Computational complexity of the gPCE model based on values for t and q

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Fig. 2

Example of the thermal field solution after simulation of the ET model, with a black contour line added at melting temperature. Plane xy shown at level z = 0, and plane xz shown at level y = 0.

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Fig. 3

Sparse gPCE with adaptive sampling flow chart

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Fig. 4

Performance of the sparse gPCE adaptive sampling algorithm: (a) CV error history after seven iterations showing convergence and (b) performance of the gPCE model over a test set

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Fig. 5

Generalized polynomial chaos expansions-based global SA: (a) normalized single effect and two-way interaction indices and (b) normalized total sensitivity indices

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Fig. 6

Histogram with a kernel density estimate (solid line) after 15,000 ET simulations from MC random sampling

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Fig. 7

Experimental measurements of single tracks on a 430F stainless steel bare plate: (a) optical microscopy image and (b) dataset distribution

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Fig. 8

Experimental validation of the ET model via UP

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Fig. 9

Application of the sparse and adaptive gPCE framework to the FEM model: (a) CV error path after 8 iterations (b) gPCE-based SA showing normalized single effect and two-way interactions Sobol indices

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Fig. 10

Experimental measurements of Ti–6Al–4V single tracks: (a) optical microscopy image and (b) dataset distribution

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Fig. 11

Experimental validation of the FEM model via UP

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