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PAPERS: Multimaterial Design Methods for AM

A Multilevel Upscaling Method for Material Characterization of Additively Manufactured Part Under Uncertainties

[+] Author and Article Information
Recep M. Gorguluarslan

The George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
813 Ferst Drive N.W.,
Atlanta, GA 30332
e-mail: rmg@gatech.edu

Sang-In Park

The George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
813 Ferst Drive N.W.,
Atlanta, GA 30332
e-mail: spark339@gatech.edu

David W. Rosen

The George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
813 Ferst Drive N.W.,
Atlanta, GA 30332
e-mail: david.rosen@me.gatech.edu

Seung-Kyum Choi

The George W. Woodruff School of
Mechanical Engineering,
Georgia Institute of Technology,
813 Ferst Drive N.W.,
Atlanta, GA 30332
e-mail: schoi@me.gatech.edu

1Corresponding author.

Contributed by the Design for Manufacturing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 24, 2015; final manuscript received June 15, 2015; published online October 12, 2015. Assoc. Editor: Timothy W. Simpson.

J. Mech. Des 137(11), 111408 (Oct 12, 2015) (12 pages) Paper No: MD-15-1036; doi: 10.1115/1.4031012 History: Received January 24, 2015; Revised June 15, 2015

An integrated multiscale modeling framework that incorporates a simulation-based upscaling technique is developed and implemented for the material characterization of additively manufactured cellular structures in this paper. The proposed upscaling procedure enables the determination of homogenized parameters at multiple levels by matching the probabilistic performance between fine and coarse scale models. Polynomial chaos expansion (PCE) is employed in the upscaling procedure to handle the computational burden caused by the input uncertainties. Efficient uncertainty quantification is achieved at the mesoscale level by utilizing the developed upscaling technique. The homogenized parameters of mesostructures are utilized again at the macroscale level in the upscaling procedure to accurately obtain the overall material properties of the target cellular structure. Actual experimental results of additively manufactured parts are integrated into the developed procedure to demonstrate the efficacy of the method.

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References

Deshpande, V. S., Fleck, N. A., and Ashby, M. F., 2001, “Effective Properties of the Octet-Truss Lattice Material,” J. Mech. Phys. Solids, 49(8), pp. 1747–1769. [CrossRef]
Wadley, H. N. G., Fleck, N. A., and Evans, A., 2003, “Fabrication and Structural Performance of Periodic Cellular Metal Sandwich Structures,” Compos. Sci. Technol., 63(16), pp. 2331–2343. [CrossRef]
Gibson, I., Rosen, D. W., and Stucker, B., 2010, Additive Manufacturing Technologies, Springer, New York.
Cheimarios, N., Kokkoris, G., and Boudouvis, A. G., 2010, “Multiscale Modeling in Chemical Vapor Deposition Processes: Coupling Reactor Scale With Feature Scale Computations,” Chem. Eng. Sci., 65(17), pp. 5018–5028. [CrossRef]
Rohan, E., and Cimrman, R., 2010, “Two-Scale Modeling of Tissue Perfusion Problem Using Homogenization of Dual Porous Media,” Int. J. Multiscale Comput. Eng., 8(1), pp. 81–102. [CrossRef]
Juanes, R., 2005, “A Variational Multiscale Finite Element Method for Multiphase Flow in Porous Media,” Finite Elem. Anal. Des., 41(7–8), pp. 763–777. [CrossRef]
Allen, J. K., Seepersad, C., Choi, H.-J., and Mistree, F., 2006, “Robust Design for Multiscale and Multidisciplinary Applications,” ASME J. Mech. Des., 128(4), pp. 832–843. [CrossRef]
Chen, W., Yin, X., Lee, S., and Liu, W. K., 2010, “A Multiscale Design Methodology for Hierarchical Systems With Random Field Uncertainty,” ASME J. Mech. Des., 132(4), p. 041006. [CrossRef]
Ruderman, A., Choi, S.-K., Patel, J., Kumar, A., and Allen, J. K., 2010, “Simulation-Based Robust Design of Multiscale Products,” ASME J. Mech. Des., 132(10), p. 101003. [CrossRef]
Dos Reis, F., and Ganghoffer, J. F., 2012, “Equivalent Mechanical Properties of Auxetic Lattices from Discrete Homogenization,” Comput. Mater. Sci., 51(1), pp. 314–321. [CrossRef]
Tollenaere, H., and Caillerie, D., 1998, “Continuous Modeling of Lattice Structures by Homogenization,” Adv. Eng. Software, 29(7–9), pp. 699–705. [CrossRef]
Cansizoglu, O., Harrysson, O., Cormier, D., West, H., and Mahale, T., 2008, “Properties of Ti-6Al-4V Non-Stochastic Lattice Structures Fabricated Via Electron Beam Melting,” Mater. Sci. Eng. A, 492(1–2), pp. 468–474. [CrossRef]
Cahill, S., Lohfeld, S., and McHugh, P. E., 2009, “Finite Element Predictions Compared to Experimental Results for the Effective Modulus of Bone Tissue Engineering Scaffolds Fabricated by Selective Laser Sintering,” J. Mater. Sci.: Mater. Med., 20(6), pp. 1255–1262. [CrossRef] [PubMed]
Park, S.-I., Rosen, D. W., Choi, S.-K., and Duty, C. E., 2014, “Effective Mechanical Properties of Lattice Material Fabricated by Material Extrusion Additive Manufacturing,” Additive Manuf., 1–4, pp. 12–23. [CrossRef]
Gorguluarslan, R. M., and Choi, S.-K., 2014, “A Simulation-Based Upscaling Technique for Multiscale Modeling of Engineering Systems Under Uncertainty,” Int. J. Multiscale Comput. Eng., 12, pp. 549–566. [CrossRef]
Schwarz, G., 1978, “Estimating the Dimension of a Model,” Ann. Stat., 6(2), pp. 461–464. [CrossRef]
Koutsourelakis, P.-S., 2007, “Stochastic Upscaling in Solid Mechanics: An Exercise in Machine Learning,” J. Comput. Phys., 226(1), pp. 301–325. [CrossRef]
Shell, M. S., 2008, “The Relative Entropy is Fundamental to Multiscale and Inverse Thermodynamic Problems,” J. Chem. Phys., 129, p. 144108. [CrossRef] [PubMed]
Arnst, M., and Ghanem, R., 2008, “Proabilistic Equivalence and Stochastic Model Reduction in Multiscale Analysis,” Comput. Methods Appl. Mech. Eng., 197, pp. 3584–3592. [CrossRef]
Wiener, N., 1938, “The Homogenous Chaos,” Am. J. Math., 60(4), pp. 897–936. [CrossRef]
Choi, S.-K., Grandhi, R. V., and Canfield, R. A., 2006, Reliability-Based Structural Design, Springer, London.
Zhang, H., Dai, H., Beer, M., and Wang, W., 2013, “Structural Reliability Analysis on the Basis of Small Samples: An Interval Quasi-Monte Carlo Method,” Mech. Syst. Signal Process., 37(1–2), pp. 137–151. [CrossRef]
Posada, D., and Buckley, T. R., 2004, “Model Selection and Model Averaging in Phylogenetics: Advantages of Akaike Information Criterion and Bayesian Approaches Over Likelihood Tests,” Syst. Biol., 53(5), pp. 793–808. [CrossRef] [PubMed]
Myung, I. J., 2003, “Tutorial on Maximum Likelihood Estimation,” J. Math. Psychol., 47(1), pp. 90–100. [CrossRef]
McKay, M. D., Conover, W. J., and Beckman, R. J., 1979, “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code,” Technometrics, 21(2), pp. 239–245.
Agarwala, M. K., Jamalabad, V. R., Langrana, N. A., Safari, A., Whalen, P. J., and Danforth, S. C., 1996, “Structural Quality of Parts Processed by Fused Deposition,” Rapid Prototyping J., 2(4), pp. 4–19. [CrossRef]
Lee, B. H., Abdullah, J., and Khan, Z. A., 2005, “Optimization of Rapid Prototyping Parameters for Production of Flexible ABS Object,” J. Mater. Process. Technol., 169(1), pp. 54–61. [CrossRef]

Figures

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Fig. 1

Deviations on each layer of the geometry of the struts fabricated by FDM process

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Fig. 2

Simulation-based stochastic upscaling framework

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Fig. 3

Proposed multilevel stochastic upscaling modeling framework. (a) Flowchart of the stochastic upscaling process and (b) multilevel upscaling framework.

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Fig. 4

Proposed multilevel stochastic upscaling framework for cellular structures

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Fig. 5

Fabricated lattice structures for tensile test. (a) Dimensions of lattice structure and (b) four-lattice structure type with different rotation angles.

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Fig. 6

Geometric variables that possess uncertainty on struts due to the process parameters

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Fig. 7

Mesoscale level upscaling for homogenized diameter

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Fig. 8

Mean value (left) and standard deviation (right) of the response for various number of samples

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Fig. 9

PDF plots of fine scale and coarse scale responses for struts with various angles and corresponding error values

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Fig. 10

Comparison of homogenized diameter values with the measured diameter values

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Fig. 11

Fine scale model of lattice structures with various rotation angles: (a) lattice structure with 0 deg rotation, (b) lattice structure with 15 deg rotation, (c) lattice structure with 30 deg rotation, and (d) lattice structure with 40 deg rotation

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Fig. 12

Comparison of Young’s modulus results for each lattice structure. The standard deviations for experimental results are as follows: 0 deg structure: 2.31 MPa, 15 deg structure: 2.36 MPa, 30 deg structure: 0.62 MPa, and 45 deg structure: 0.03 MPa.

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