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Research Papers

Numerical Modeling of Thermo-Mechanically Induced Stress in Substrates for Droplet-Based Additive Manufacturing Processes

[+] Author and Article Information
Chang Yoon Park

Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720
e-mail: changyoonpark@berkeley.edu

Tarek I. Zohdi

Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720
e-mail: zohdi@berkeley.edu

Manuscript received February 7, 2018; final manuscript received March 15, 2019; published online April 12, 2019. Assoc. Editor: Sam Anand.

J. Manuf. Sci. Eng 141(6), 061001 (Apr 12, 2019) (8 pages) Paper No: MANU-18-1074; doi: 10.1115/1.4043254 History: Received February 07, 2018; Accepted March 15, 2019

Within the scope of additive manufacturing (AM) methods, a large number of popular fabrication techniques involve high-temperature droplets being targeted to a substrate for deposition. In such methods, an “ink” to be deposited is tailor-made to fit the desired application. Concentrated stresses are induced on the substrate in such procedures. A numerical simulation framework that can return quantitative and qualitative insights regarding the mechanical response of the substrate is proposed in this paper. A combined smoothed particle hydrodynamics (SPH)-finite element (FE) model is developed to solve the governing coupled thermo-mechanical equations, for the case of Newtonian inks. We also highlight the usage of consistent SPH formulations in order to recover first-order accuracy for the gradient and Laplacian operators. This allows one to solve the heat-equation more accurately in the presence of free-surfaces. The proposed framework is then utilized to simulate a hot droplet impacting a flat substrate.

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Figures

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Fig. 1

Droplet impacting a surface

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Fig. 2

Algorithmic procedures of the code

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Fig. 3

Left: particle configuration. Right: Laplacian @ y = 0.5, h = 3Δx. (a) ∇2⟨½(x2+y2)⟩ uncorrected Laplacian and (b) ∇21⟨½(x2+y2)⟩ corrected Laplacian (our method).

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Fig. 4

SPH particles placed on top of finite element nodes

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Fig. 5

1D transient heat transfer problem schematic

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Fig. 6

1D transient heat transfer problem @ t = 0.03: (a) T(t = 0.03, x) and (b) error analysis

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Fig. 7

Poiseuille flow shear transfer test

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Fig. 8

Average shear stress error

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Fig. 9

Evolution of a fluid droplet impacting the substrate

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Fig. 10

Temperature distribution on the substrate surface at t/tc = 1.75

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Fig. 11

Stress (Von-Mises) distribution on the substrate surface

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Fig. 12

Stress on the substrate with respect to depth (t/tc = 1.75, x = 0)

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Fig. 13

Temperature evolution on substrate surface, with respect to time

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Fig. 14

Stress components, t/tc = 1.75

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