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Research Papers

Numerical Studies on Size Effect Behaviors of Glassy Polymers Based on Strain Gradient Elastoviscoplastic Model

[+] Author and Article Information
Yujun Deng, Jin Wang, Peiyun Yi, Linfa Peng, Xinmin Lai, Zhongqin Lin

State Key Laboratory of Mechanical System
and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China;
Shanghai Key Laboratory of Digital Manufacture
for Thin-walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 19, 2018; final manuscript received October 15, 2018; published online November 14, 2018. Assoc. Editor: Yong Zhu.

J. Appl. Mech 86(2), 021001 (Nov 14, 2018) (11 pages) Paper No: JAM-18-1482; doi: 10.1115/1.4041765 History: Received August 19, 2018; Revised October 15, 2018

The improvement of the accuracy and efficiency of microforming process of polymers is of great significance to meet the miniaturization of polymeric components. When the nonuniform deformation is reduced to the microscopic scale, however, the mechanics of polymers shows a strong reinforcement behavior. Traditional theoretical models of polymers which have not considered material feature lengths are difficult to describe the size effect in micron scale, and the process simulation models based on the traditional theory could not provide effective and precise guidance for polymer microfabrication techniques. The work reported here proposed strategies to simulate size effect behaviors of glassy polymers in microforming process. First, the strain gradient elastoviscoplastic model was derived to describe the size affected behaviors of glassy polymers. Based on the proposed constitutive model, an eight-node finite element with the consideration of nodes' rotation was developed. Then, the proposed finite element method was verified by comparisons between experiments and simulations for both uniaxial compression and microbending. Finally, based on the FE model, under the consideration of the effect of rotation gradient, the strain distribution, the deformation energy, and the processing load were discussed. These strategies are immediately applicable to other wide-ranging classes of microforming process of glassy polymers, thereby foreshadowing their use in process optimizations of microfabrication of polymer components.

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Figures

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Fig. 1

Flow chart for finite element method based on elastoviscoplastic couple stress model

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Fig. 2

(a) Cylindrical samples of PMMA and (b) FE model for uniaxial compression

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Fig. 3

Experiments and simulations of uniaxial compression under the strain rates of (a) 0.1 s−1, (b) 0.001 s−1, and (c) 0.0003 s−1

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Fig. 4

(a) Experimental setup and (b) FE model of microbending

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Fig. 5

Experimental and FE data for microbending with different film thicknesses: (a) 1.013 mm, (b) 0.669 mm, (c) 0.470 mm, (d) 0.356 mm, (e) 0.238 mm, and (f) 0.197 mm

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Fig. 6

Feature parameters in scaled microbending simulations

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Fig. 7

(a) Distribution of strain components on the film and (b) surface strain versus film thickness

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Fig. 8

(a) Distribution of rotational gradient on the film and (b) rotational gradient on the middle film versus film thickness

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Fig. 9

Contour plots of strain energy density and strain gradient energy density

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Fig. 10

The distribution of the deformation energy density on the middle line of the film: (a) strain energy density and (b) strain gradient energy density

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Fig. 11

(a) Normalized deformation energy versus film thickness and (b) normalized reaction force versus film thickness

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Fig. 12

Effect of (a) intrinsic material length and (b) second modulus in microbending

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