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Research Papers

Experimental Characterization and Finite Element Prediction of Large Strain Spring-Back Behavior of Poly(Methyl Methacrylate)

[+] Author and Article Information
D. Mathiesen

Department of Mechanical and Aerospace Engineering,
The Ohio State University,
W185 Scott Laboratory,
201 West 19th Avenue,
Columbus, OH 43210
e-mail: mathiesen.2@osu.edu

A. Kakumani

Department of Mechanical and Aerospace Engineering,
The Ohio State University,
W185 Scott Laboratory,
201 West 19th Avenue,
Columbus, OH 43210
e-mail: kakumani.1@osu.edu

R. B. Dupaix

Department of Mechanical and Aerospace Engineering,
The Ohio State University,
E310 Scott Laboratory,
201 West 19th Avenue,
Columbus, OH 43210
e-mail: dupaix.1@osu.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the Journal of Engineering Materials and Technology. Manuscript received April 23, 2018; final manuscript received January 29, 2019; published online March 11, 2019. Assoc. Editor: Antonios Kontsos.

J. Eng. Mater. Technol 141(3), 031005 (Mar 11, 2019) (13 pages) Paper No: MATS-18-1117; doi: 10.1115/1.4042744 History: Received April 23, 2018; Accepted January 31, 2019

Spring-back of poly(methyl methacrylate) (PMMA) at large strains, various embossing temperatures, and release temperatures below glass transition is quantified through modified unconfined recovery tests. Cooling, as well as large strains, is shown to reduce the amount of spring-back. Despite reducing the amount of spring-back, these experiments show that there is still a substantial amount present that needs to be accounted for in hot embossing processes. Spring-back is predicted using finite element simulations utilizing a constitutive model for the large strain stress relaxation behavior of PMMA. The model's temperature dependence is modified to account for cooling and focuses on the glass transition temperature region. Spring-back is predicted with this model, capturing the temperature and held strain dependence. Temperature assignment of the sample is found to have the largest effect on simulation accuracy. Interestingly, despite large thermal gradients in the PMMA, a uniform temperature approximation still yields reasonably accurate spring-back predictions. These experiments and simulations fill a substantial gap in knowledge of large strain recovery of PMMA under conditions normally found in hot embossing.

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References

Hollick, E. J., Spalton, D. J., Ursell, P. G., Pande, M. V., Barman, S. A., Boyce, J. F., and Tilling, K., 1999, “The Effect of Polymethylmethacrylate, Silicone, and Polyacrylic Intraocular Lenses on Posterior Capsular Opacification 3 Years After Cataract Surgery,” Ophthalmology, 106(1), pp. 49–54. [CrossRef] [PubMed]
Chien, R. D., 2006, “Micromolding of Biochip Devices Designed With Microchannels,” Sens. Actuators A Phys., 128(2), pp. 238–247. [CrossRef]
Lu, C., Cheng, M. M., Benatar, A., and Lee, L. J., 2007, “Embossing of High-Aspect-Ratio-Microstructures Using Sacrificial Templates and Fast Surface Heating,” Polym. Eng. Sci., 47(6), pp. 830–840. [CrossRef]
Schneider, P., Steitz, C., Schafer, K. H., and Ziegler, C., 2009, “Hot Embossing of Pyramidal Micro-Structures in PMMA for Cell Culture,” Phys. Status Solidi A, 206(3), pp. 501–507. [CrossRef]
Palm, G., Dupaix, R. B., and Castro, J., 2006, “Large Strain Mechanical Behavior of Poly(Methyl Methacrylate) (PMMA) Near the Glass Transition Temperature,” ASME J. Eng. Mater. Technol., 128(4), pp. 559–563. [CrossRef]
Ghatak, A., and Dupaix, R. B., 2010, “Material Characterization and Continuum Modeling of Poly(Methyl Methacrylate) (PMMA) Above the Glass Transition,” Int. J. Struct. Changes Solids, 2(1), pp. 53–63.
Arruda, E. M., Boyce, M. C., and Jayachandran, R., 1995, “Effects of Strain Rate, Temperature and Thermomechanical Coupling on the Finite Strain Deformation of Glassy Polymers,” Mech. Mater., 19(2/3), pp. 193–212. [CrossRef]
Ames, N. M., Srivastava, V., Chester, S. A., and Anand, L., 2009, “A Thermo-Mechanically Coupled Theory for Large Deformations of Amorphous Polymers. Part II: Applications,” Int. J. Plast., 25(8), pp. 1495–1539. [CrossRef]
Hasan, O. A., and Boyce, M. C., 1995, “A Constitutive Model for the Nonlinear Viscoelastic Viscoplastic Behavior of Glassy Polymers,” Polym. Eng. Sci., 35(4), pp. 331–344. [CrossRef]
Dooling, P. J., Buckley, C. P., Rostami, S., and Zahlan, N., 2002, “Hot-Drawing of Poly(Methyl Methacrylate) and Simulation Using a Glass-Rubber Constitutive Model,” Polymer, 43(8), pp. 2451–2465. [CrossRef]
Mathiesen, D., Vogtmann, D., and Dupaix, R. B., 2014, “Characterization and Constitutive Modeling of Stress-Relaxation Behavior of Poly(Methyl Methacrylate) (PMMA) Across the Glass Transition Temperature,” Mech. Mater., 71(0), pp. 74–84. [CrossRef]
Greiner, R., and Schwarzl, F. R., 1984, “Thermal Contraction and Volume Relaxation of Amorphous Polymers,” Rheol. Acta, 23(4), pp. 378–395. [CrossRef]
Hasan, O. A., and Boyce, M. C., 1993, “Energy Storage During Inelastic Deformation of Glassy Polymers,” Polymer, 34(24), pp. 5085–5092. [CrossRef]
Quinson, R., Perez, J., Rink, M., and Pavan, A., 1996, “Components of Non-Elastic Deformation in Amorphous Glassy Polymers,” J. Mater. Sci., 31(16), pp. 4387–4394. [CrossRef]
Arzhakov, M. S., and Arzhakov, S. A., 1995, “A New Approach to the Description of Mechanical Behavior of Polymer Glasses,” Int. J. Polym. Mater., 29(3–4), pp. 249–259. [CrossRef]
Nguyen, T. D., Qi, J. H., Castro, F., and Long, K. N., 2008, “A Thermoviscoelastic Model for Amorphous Shape Memory Polymers: Incorporating Structural and Stress Relaxation,” J. Mech. Phys. Solids, 56(9), pp. 2792–2814. [CrossRef]
Srivastava, V., Chester, S. A., Ames, N. M., and Anand, L., 2010, “A Thermo-Mechanically-Coupled Large-Deformation Theory for Amorphous Polymers in a Temperature Range Which Spans Their Glass Transition,” Int. J. Plast., 26(8), pp. 1138–1182. [CrossRef]
Dupaix, R. B., and Boyce, M. C., 2007, “Constitutive Modeling of the Finite Strain Behavior of Amorphous Polymers in and Above the Glass Transition,” Mech. Mater., 39(1), pp. 39–52. [CrossRef]
Dooling, P. J., Buckley, C. P., and Hinduja, S., 1998, “The Onset of Nonlinear Viscoelasticity in Multiaxial Creep of Glassy Polymers: A Constitutive Model and Its Application to PMMA,” Polym. Eng. Sci., 38(6), pp. 892–904. [CrossRef]
Anand, L., and Ames, N. M., 2006, “On Modeling the Micro-Indentation Response of an Amorphous Polymer,” Int. J. Plast., 22(6), pp. 1123–1170. [CrossRef]
Boyce, M. C., Parks, D. M., and Argon, A. S., 1988, “Large Inelastic Deformation of Glassy Polymers. Part I: Rate Dependent Constitutive Model,” Mech. Mater., 7(1), pp. 15–33. [CrossRef]
Arruda, E. M., and Boyce, M. C., 1993, “A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials,” J. Mech. Phys. Solids, 41(2), pp. 389–412. [CrossRef]
Arruda, E. M., and Boyce, M. C., 1993, “Evolution of Plastic Anisotropy in Amorphous Polymers During Finite Straining,” Int. J. Plast., 9(6), pp. 697–720. [CrossRef]
Graham, R. S., Likhtman, A. E., McLeish, T. C. B., and Milner, S. T., 2003, “Microscopic Theory of Linear, Entangled Polymer Chains Under Rapid Deformation Including Chain Stretch and Convective Constraint Release,” J. Rheol., 47(5), pp. 1171–1200. [CrossRef]
Likhtman, A. E., and Graham, R. S., 2003, “Simple Constitutive Equation for Linear Polymer Melts Derived From Molecular Theory: Rolie-Poly Equation,” J. Nonnewton Fluid Mech., 114(1), pp. 1–12. [CrossRef]
De Focatiis, D. S. A., Buckley, C. P., and Embery, J., 2010, “Large Deformations in Oriented Polymer Glasses: Experimental Study and a New Glass-Melt Constitutive Model,” J. Polym. Sci. Part B Polym. Phys., 48(13), pp. 1449–1463. [CrossRef]
Dupaix, R. B., and Cash, W., 2009, “Finite Element Modeling of Polymer Hot Embossing Using a Glass-Rubber Finite Strain Constitutive Model,” Polym. Eng. Sci., 49(3), pp. 531–543. [CrossRef]

Figures

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Fig. 1

A one-dimensional representation of the constitutive model. Intermolecular interactions are represented by resistance A and network interactions by resistances B and C.

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Fig. 2

Strain and temperature profiles versus time used in experiments. Temperature axes are on the right and strain axes on the left. The dotted line at the end of the strain profile shows the height of the sample and the solid line the loading scheme of the platen.

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Fig. 3

Stress versus time for PMMA samples deformed at a strain rate of −1.0 min−1 to a held strain of −1.5. Solid lines are samples that are cooled beginning at 270 s. Dashed lines are samples that are not cooled, and line thickness indicates the initial temperature (Temb) of the sample. The onset of cooling is indicated by the vertical line at 270 s.

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Fig. 4

Temperature versus time for samples deformed at a strain rate of −1.0 min−1 and held at a strain of −1.5. (a) Temperature recorded from platen in experiment. (b) Solid line indicates temperature fit to platen temperature as given by Eq. (3). Dashed line indicates temperature found from thermal simulations given by Eq. (11).

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Fig. 5

Percent stress relaxed as a funcion of held strain and temperature for PMMA samples deformed at a strain rate of −1.0 min−1 with cooling

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Fig. 6

Effect of temperature and held strain on spring-back for PMMA samples deformed at a strain rate of (a) −1.0 min−1 and (b) −0.5 min−1

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Fig. 7

Effect of temperature and held strain of PMMA samples deformed at a strain rate of −1.0 min−1 on (a) cooling time and (b) release temperature of the platen

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Fig. 8

(a) Spring-back of samples deformed at a strain rate of −1.0 min−1 to different held strains with an initial temperature of 115 °C. Each sample was cooled for the same amount of time, tcool = 420 s. (b) Spring-back of samples at different Temb deformed at a strain rate of −1.0 min−1 to a held strain of −1.0. Each sample was cooled to a temperature of 100 °C prior to release.

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Fig. 9

Number of rigid links between entanglements (N) versus temperature. As temperature increases past Tg (∼102 °C), the number of links increases dramatically.

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Fig. 10

True stress versus time at 135 °C for a sample deformed at a strain rate of −1.0 min−1 to a held strain of −1.5. Model(Temp) calculates the number of rigid links between entanglements (N) as a function of current temperature. Model (Maxtemp) calculates N as a function of maximum temperature.

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Fig. 11

Stress as a function of strain for samples deformed at a strain rate of −1.0 min−1 to a final strain of −1.5. The solid line is for continuous deformation at 135 °C without holding. The dashed line represents holding the sample at a strain of −0.5 for 1000 s at 135 °C without cooling then continuing to deform the sample to a strain of −1.5. The dotted line represents holding the sample at a strain of −0.5 while cooling the sample to 105 °C over 1000 s then continuing to deform the sample to a strain of −1.5. On the right is the original 105 °C curve for samples strained to −1.5 without cooling; note the change in scale.

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Fig. 12

Stress versus time for PMMA samples deformed at a strain rate of −1.0 min−1 to a held strain of −1.5, −1.0, and −0.5 from top to bottom. Cooling of the sample begins 180 s after the hold period begins. Solid lines are experimentally obtained data and dashed lines are model predictions. Line thickness indicates the initial temperature of the sample when it is deformed.

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Fig. 13

Finite element mesh that was used in the finite element simulations of spring-back

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Fig. 14

Effect of embossing temperature and held strain on spring-back predicted by the FEM simulation for a strain rate of −1.0 min−1

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Fig. 15

FEM prediction of spring-back (a) when the PMMA samples are embossed at T = 115 °C at a held strains of −0.5, −1.0, −1.5 at a rate of −1.0 min−1 and cooled for 7 min. (b) for PMMA samples at various embossing temperatures strained to −1.0 at a rate of −1.0 min−1 and cooled to 100 °C.

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Fig. 19

Temperature of PMMA in °C for a sample compressed to a strain of −0.5 at Temb = 135 °C after cooling for (a) 31 s and (b) 600 s

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Fig. 18

Comparison of experimental spring-back with simulation predictions using different cooling profiles for a held strain of −1.0 and a strain rate of −1.0 min−1

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Fig. 17

Difference between PMMA temperature as determined from heat transfer analysis and curve-fit platen temperature. The curve-fit platen temperature under predicts the PMMA temperature for the majority of the simulations.

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Fig. 16

Heat transfer boundary conditions. The solid lines indicate the outline of the steel (no fill) and PMMA (cross-hatch fill). The dashed line indicates surfaces with convection and the dotted line indicates the symmetry axis.

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