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Special Section Papers

Stochastic Elastic Property Evaluation With Stochastic Homogenization Analysis of a Resin Structure Made Using the Fused Deposition Modeling Method

[+] Author and Article Information
Sei-ichiro Sakata

Department of Mechanical Engineering,
Kindai University,
3-4-1, Kowakae,
Higashi-Osaka City, Osaka 577-8502, Japan
e-mail: sakata@mech.kindai.ac.jp

Yuki Yamauchi

Department of Mechanical Engineering,
Graduate School of Kindai University,
3-4-1, Kowakae,
Higashi-Osaka City, Osaka 577-8502, Japan
e-mail: 1833330337e@kindai.ac.jp

1Corresponding author.

Manuscript received April 11, 2018; final manuscript received August 22, 2018; published online June 5, 2019. Assoc. Editor: George Stefanou.

ASME J. Risk Uncertainty Part B 5(3), 030901 (Jun 05, 2019) (12 pages) Paper No: RISK-18-1018; doi: 10.1115/1.4043398 History: Received April 11, 2018; Revised August 22, 2018

This paper describes the stochastic elastic property evaluation of a resin structure, which is made using the fused deposition modeling (FDM) method, through experimental and numerical tests. The FDM method is an additive manufacturing method, and it enables the fabrication of complex shaped structures at a low cost. However, a resin structure that is made using the FDM method has a complex microstructure, and a multiscale problem must be considered for the evaluation of its mechanical properties. In addition, if the microstructure is not well controlled compared to the structure obtained using a conventional processing technique, a multiscale stochastic problem should be also considered. In this paper, first, the randomness in a resin specimen manufactured using the FDM method is experimentally investigated, and the necessity of considering the microscopic randomness for the mechanical property evaluation of the resin structure is discussed. Next, appropriate numerical modeling for evaluating the probabilistic property of an apparent elastic property of the specimen (as a mechanical property of the resin structure made using the FDM method) is discussed, along with a comparison between the experimental results and the numerical results obtained using the Monte Carlo simulation with several analysis models. Based on the results, the effectiveness of the evaluation using a detailed hierarchical modeling is discussed. In addition, the perturbation-based hierarchical stochastic homogenization analysis is performed, and the applicability of the method is discussed based on the numerical results.

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Figures

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Fig. 1

A sample resin specimen: (a) outline of the specimen and (b) thin specimen for zero porosity

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Fig. 2

Microstructures of the specimen: (a) high density, (b) middle density, and (c) low density

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Fig. 3

Average porosity of each specimen

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Fig. 4

Expectation and CV of the apparent elastic modulus for each specimen

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Fig. 5

Outline of the virtual tensile test with homogenization analysis

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Fig. 6

Outline of the specimen

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Fig. 7

Schematic view of the microstructure in the specimen

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Fig. 8

Finite element model of the unit cell: (a) bird view of the unit cell, (b) bird view of the resin structure, (c) cross-sectional view of the upper part, and (d) cross-sectional view of the lower part

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Fig. 9

Definition of the geometrical random variable (path width at cross point)

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Fig. 10

Sample view of the microstructure measurement

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Fig. 11

Histogram of the measured width at cross points

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Fig. 12

Cross section of the specimen

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Fig. 13

Schematic view of the path route in each layer in the low density specimen: (a) the first layer, (b) the second–fourth layer, and (c) the fifth–seventh layer

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Fig. 14

Schematic view of the numerical models for the stochastic tensile analysis: (a) equivalent homogeneous material, (b) skin-core model, and (c) detailed model

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Fig. 15

Assumed expectation and CV of the path width: (a) only core model, (b) skin-two core model, and (c) detailed model

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Fig. 16

Computed expectation of the apparent Young's modulus for each density specimen

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Fig. 17

Computed CVs of the apparent Young's modulus for each density specimen

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Fig. 18

Expected apparent Young's modulus of the specimen assuming perfect correlation between each adjacent layer

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Fig. 19

CV of apparent Young's modulus of the specimen assuming perfect correlation between each adjacent layer

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Fig. 20

Relationship between the assumed correlation and the estimated expectation of the apparent Young's modulus

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Fig. 21

Relationship between the assumed correlation and the estimated CV of the apparent Young's modulus

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Fig. 22

Dependency of the expectation of apparent Young's modulus of the specimen on the number of divisions along the loading direction

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Fig. 23

Dependency of the CV of apparent Young's modulus of the specimen on the number of divisions along the loading direction

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Fig. 24

CV estimated by MC and hierarchical stochastic homogenization based on the first-order perturbation for each fabrication density

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Fig. 25

Comparison between the estimated CVs for each equivalent elastic constant, obtained using MC and the first-order perturbation-based hierarchical stochastic homogenization analysis: (a) CV for LD, (b) CV for MD, and (c) CV for HD

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Fig. 26

Comparison between the path width variation and the equivalent elastic property of the cores along the loading direction, obtained using direct FEM and first-order approximation: (a) LD, (b) MD, and (c) HD

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