Research Papers

Self-Folding of Thick Polymer Sheets Using Gradients of Heat

[+] Author and Article Information
Duncan Davis, Bin Chen

Department of Chemical and
Biomolecular Engineering,
NC State University,
Raleigh, NC 27695-7905

Michael D. Dickey

Department of Chemical and
Biomolecular Engineering,
NC State University,
Raleigh, NC 27695-7905
e-mail: mddickey@ncsu.edu

Jan Genzer

Department of Chemical and
Biomolecular Engineering,
NC State University,
Raleigh, NC 27695-7905
e-mail: jgenzer@ncsu.edu

1Corresponding authors.

Manuscript received July 18, 2015; final manuscript received November 2, 2015; published online March 7, 2016. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(3), 031014 (Mar 07, 2016) (8 pages) Paper No: JMR-15-1203; doi: 10.1115/1.4032209 History: Received July 18, 2015; Revised November 02, 2015

Self-folding converts two-dimensional (2D) sheets into three-dimensional (3D) objects in a hands-free manner. This paper demonstrates a simple approach to self-fold commercially available, millimeter-thick thermoplastic polymer sheets. The process begins by first stretching poly(methyl methacrylate) (PMMA), polystyrene (PS), or polycarbonate (PC) sheets using an extensometer at elevated temperatures close to the glass transition temperature (Tg) of each sheet. Localizing the strain to a small strip creates a “hinge,” which folds in response to asymmetric heating of the sheet. Although there are a number of ways to supply heat, here a heat gun delivers heat to one side of the hinge to create the necessary temperature gradient through the polymer sheet. When the local temperature exceeds the Tg of the polymer, the strain in the hinged region relaxes. Because strain relaxation occurs gradually across the sheet thickness, the polymer sheet folds in the direction toward the heating source. A simple geometric model predicts the dihedral angle of the sheet based on the thickness of the sheet and width of the hinge. This paper reports for the first time that this approach to folding works for a variety of thermoplastics using sheets that are significantly thicker (∼10 times) than those reported previously.

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Grahic Jump Location
Fig. 1

Process for self-folding. (a) Locally prestraining a polymer sheet creates a hinge. Selective heating of one side of the hinge causes asymmetric strain relaxation that induces folding. When applied uniformly, heat causes unfolding and the sample reverts to the original shape. The full cycle causes some permanent deformation, but the focus here is on the folding step. (b) Schematic of the preparation steps using an extensometer. A picture of the setup is shown in Fig. 7 in the Appendix. (c) A heat gun asymmetrically heats one side of the prestrained polymer sheet to induce self-folding.

Grahic Jump Location
Fig. 5

(a) Temperature (red-solid line, left ordinate) and dihedral angle (blue-dashed line, right ordinate) as a function of heating time overlaid with the surface temperature profile of the same sample. The PMMA starts folding after the surface exceeds Tg (∼105 °C) for 1.5 mm (b), 2.0 mm (c), and 3.0 mm (d) thick samples. A 3.0 mm thick PMMA sheet starts folding after the surface reaches Tg.

Grahic Jump Location
Fig. 4

(a) Experimental data (symbols) and geometric model predictions (lines) of αD versus λ for varying thicknesses of PMMA. (b) Experimental data (symbols) and geometric model predictions (line) of αD versus λ for 2.0 mm thick PMMA, PS, and PC. (c) Data from Figs. 4(a) and 4(b) plotted as a function of the arctan function from the geometric model. The black line denotes prediction from Eq. (3).

Grahic Jump Location
Fig. 6

The top of each pair shows the model's prediction of temperature profiles inside the sheets: PMMA 1.5 mm (left), PMMA 2.0 mm (middle), and PMMA 3.0 mm (right). The bottom of each pair denotes the temporal evolution of the temperature on the front side (solid red line) and the backside (dashed blue line) of the sample.

Grahic Jump Location
Fig. 3

Photographs of self-folding samples. (a) PMMA samples with thickness ranging from 1.5 to 12 mm. (b) PS samples with λ ranging from 1.33 to 2.67. (c) PC samples exposed to the heat gun for 30–45 s. (d) A PMMA sample folded to αD ∼ 180 deg that is supporting a 9 kg weight demonstrates the strength of the folded samples.

Grahic Jump Location
Fig. 2

A geometric model predicts the folding angle αF of the commercial prestrained sheets [49]. Grips from an extensometer start at a distance Wi apart and strain the sample a distance Ws. The straining causes the sample to shrink in the hinged region. Heat delivered to the top of the sample causes the top of the sample to shrink and therefore the sample folds. In our system, W = (Wi + Ws).

Grahic Jump Location
Fig. 9

Dihedral angles calculated using the Almansi (solid blue lines) and Swainger (dashed green lines) strains as a function of extension ratio (λ) using the model given by Eq. (1). The symbols represent the experimental data collected from PMMA sheets with thicknesses 1.5 mm (a), 2.0 mm (b), and 3.0 mm (c).

Grahic Jump Location
Fig. 10

Temperature (red-solid line, left ordinate) and the dihedral angle (blue-dashed line, right ordinate) as a function of time of PS (upper—thickness 2.0 mm) and PC (bottom—thickness 2.0 mm). The material starts folding at around the time the surface of the sheet reaches Tg (∼103 °C for PS and ∼147 °C for PC).

Grahic Jump Location
Fig. 11

The top of each pair shows the model's prediction of temperature profiles inside the sheets: PS 2.0 mm (left) and PC 2.0 mm (right). The bottom of each pair denotes the temporal evolution of the temperature on the front side (solid red line) and the backside (dashed blue line) of the sample.

Grahic Jump Location
Fig. 7

Experimental setup for programing strain in polymer sheets in an extensometer. There are two metal grips in the center of the oven that pull the sample vertically while the four IR lamps control the temperature with an error of ±1 °C. Each of the two metal grips has two screws that secure the sample.

Grahic Jump Location
Fig. 8

Temperature profiles of the hinge region of PS, PC, and PMMA (all thicknesses) as a function of time. We use an IR camera to measure the temperature of the hinge while the material folds. The heat gun starts heating the sample at ∼2 s.



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