Research Papers

An Integrated Approach to Additive Manufacturing Simulations Using Physics Based, Coupled Multiscale Process Modeling

[+] Author and Article Information
Deepankar Pal

Assistant Professor
Department of Mechanical Engineering,
J.B. Speed School of Engineering,
University of Louisville,
Louisville, KY 40292
e-mail: d0pal001@louisville.edu

Nachiket Patil

Senior Research Engineer
201 E. Jefferson Street,
Louisville, KY 40202
e-mail: nachiket.patil@3dsim.com

Kai Zeng

Department of Industrial Engineering,
J.B. Speed School of Engineering,
University of Louisville,
Louisville, KY 40292
e-mail: k0zeng01@louisville.edu

Brent Stucker

Clark Chair Professor
J. B. Speed School of Engineering,
University of Louisville,
Louisville, KY 40292
e-mail: brent.stucker@louisville.edu

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received April 21, 2014; final manuscript received September 12, 2014; published online October 24, 2014. Assoc. Editor: Joseph Beaman.

J. Manuf. Sci. Eng 136(6), 061022 (Oct 24, 2014) (16 pages) Paper No: MANU-14-1242; doi: 10.1115/1.4028580 History: Received April 21, 2014; Revised September 12, 2014

The complexity of local and dynamic thermal transformations in additive manufacturing (AM) processes makes it difficult to track in situ thermomechanical changes at different length scales within a part using experimental process monitoring equipment. In addition, in situ process monitoring is limited to providing information only at the exposed surface of a layer being built. As a result, an understanding of the bulk microstructural transformations and the resulting behavior of a part requires rigorous postprocess microscopy and mechanical testing. In order to circumvent the limited feedback obtained from in situ experiments and to better understand material response, a novel 3D dislocation density based thermomechanical finite element framework has been developed. This framework solves for the in situ response much faster than currently used state-of-the-art modeling software since it has been specifically designed for AM platforms. This modeling infrastructure can predict the anisotropic performance of AM-produced components before they are built, can serve as a method to enable in situ closed-loop process control and as a method to predict residual stress and distortion in parts and thus enable support structure optimization. This manuscript provides an overview of these software modules which together form a robust and reliable AM software suite to address future needs for machine development, material development, and geometric optimization.

Copyright © 2014 by ASME
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Fig. 1

Meshing configuration for a point energy source located within the fine mesh region. The point source could be a Gaussian heat source such as a concentrated laser or electron beam and the fine mesh region moves as the point energy source moves.

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Fig. 2

Multiscale mesh for UC showing: (a) the full 3D mesh with selective adaptive refinement near the sonotrode and the interfacial mating surfaces and (b) a close-up showing how the hexahedral elements 2 are preserved throughout refinement. The vertical refined region moves with sonotrode motion while the horizontal fine mesh region is indexed up layer-by-layer as new foils are added.

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Fig. 3

1/8th view of a volumetric refined mesh of two secondary precipitates (at diagonally opposite corners with different curvatures) diagonally opposite to each other placed in an Inconel 718 matrix (in blue) with different curvatures [17]

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Fig. 4

(a) Optical micrograph of an EBM-made Ti 6/4 microstructure showing hexagonal prior β grain motifs and (b) microstructurally informed mesh, and (c) in-plane mesh complexity [18]

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Fig. 5

Match of thermal contours between nonlinear thermomechanical analysis (a) (temperature in K) using the mesh provided in Fig. 1 and experiments (b) obtained using a forward looking infrared (FLIR) camera (temperature in Celsius)

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Fig. 6

Indirect validation of the melt pool showing the melt pool asymmetry due to the existence of solid (conductor on one side) and powder (insulator on the other side) of the melt pool

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Fig. 7

Force and moment balance scenarios to be considered for residual stress and distortion predictions

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Fig. 8

In situ single bead (a) thermal contours, (b) longitudinal residual stress contours, (c) longitudinal distortion, and (d) distortion angle w.r.t horizontal plane as a function of dynamic melt pool on the top layer of the build

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Fig. 9

Variation of GND with surface roughness. The simulated average grain size at the mating interface for the rough sample was ∼1.3 μm whereas the experimentally obtained and weight averaged value was found to be ∼1.33 μm. The simulated average grain size at the mating interface for the smooth sample was ∼2.43 μm which is in good agreement with Dr. K. Johnson's Ph.D. work [36].

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Fig. 10

Volume averaged true stress–strain plot for a vertically built EBM Ti6/4 sample computed by ANSYS and DDCPFEM. These average stress–strain evolutions have been compared against experiments [18].

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Fig. 11

Plastic strain distribution at 10% total average strain for the stress/strain curves from Fig. 10: (a) DDCPFEM simulations and (b) Ansys anisotropic multilinear continuum plasticity model

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Fig. 12

Schematic diagram illustrating the concept of an eigensolver

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Fig. 13

Nodal point by point match of a finite element solution for a thermal field with a modal reconstructed (eigensolver) solution for a Gaussian point energy source. The error is negligibly small (0.01%), and the results lie right on top of each other.

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Fig. 14

Nodal point by point comparison of a finite element solution with a modal reconstructed solution for a constant line energy source. The match is good (∼1% error) but not excellent when compared to Fig. 13.

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Fig. 15

Nodal point by point comparison of a finite element solution with a modal reconstructed solution for a constant area energy source. The modally reconstructed solution matches the trend (∼7% error) but not the magnitude of the solution due to unrefined orthogonal modes. This result is irrelevant for moving point energy problems associated with SLM or EBM, but should be taken into account when seeking the correct solution for area energy sources.

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Fig. 16

First four cross-sectional eigenmodes of the prismatic thermal problem

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Fig. 17

First fifth and sixth cross-sectional eigenmodes of the prismatic thermal problem

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Fig. 18

Cross-sectional eigenvalues of the thermal prismatic problem

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Fig. 19

Cross-sectional eigenvalues of the structural prismatic problem

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Fig. 20

Eigenvalues as a function of cross-sectional degrees of freedom

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Fig. 21

(a)–(d) Eigenvalue fitting as a function of a seven parameter Fourier expansion

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Fig. 22

Different cases (1–6) with solidified portion (in black) and powder portion (in white) in a given cross section of the powder bed

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Fig. 23

Eigenvalue evolution in cross sections for cases shown in Fig. 22. The trend is exactly the same as the completely solidified bed and has been observed to be fit individually with a 10 parameter Fourier expansion. The evolution using a 10 parameter Fourier expansion can be used to solve large eigenvalue problems.

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Fig. 24

Matlab generated lower triangular matrix for a sample thermal problem with periodic boundary conditions

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Fig. 25

Preserved solution optimized lower triangular matrix by modified CHOL (Cholesky factorization) method. Only 6.7% of the values were required to efficiently solve the problem with solution quality preservation.

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Fig. 26

Efficiency and speed statistics for modified CHOL method

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Fig. 27

Shear resistance as a function of macroscopic slip

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Fig. 28

Reference and deformed configurations during macroscopic slip

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Fig. 29

3D model with support structure

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Fig. 30

Schematic of incorporating support structure and scan pattern generation modules to the current FFDAMRD model

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Fig. 31

Meshing in the z-direction

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Fig. 32

Comparison of the original CAD model of a semi sphere with the stacked model. (a) Solid CAD model and (b) stacked model from layers of cross sections with stair-step-effect errors. The magnitude of the error increases from top to bottom.




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