Measurement of Nonlinear Poisson’s Ratio of Thermoplastic Polyurethanes under Cyclic Softening Using 2D Digital Image Correlation
Abstract
:1. Introduction
2. Materials and Methods
2.1. Specimens
2.2. Experimental Setup
2.3. Transformation from Green Strain to Biot Strain and Hencky Strain under Uniaxial Tension
2.4. Nonlinear Poisson’s Ratios
3. Results and Discussion
3.1. Transformation from the Green Strain to Biot Strain and Hencky Strain under Uniaxial Tension
3.2. Nonlinear Poisson’s Ratios Represented by Biot Strain and Hencky Strain
3.3. Verification of the Quasi-Static Condition of the Cyclic Test
3.4. Changes in Poisson’s Ratio during Cyclic Softening
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Song, E.; Li, J.; Won, S.M.; Bai, W.; Rogers, J.A. Materials for flexible bioelectronic systems as chronic neural interfaces. Nat. Mater. 2020, 19, 590–603. [Google Scholar] [CrossRef] [PubMed]
- Ghaffari, R.; Choi, J.; Raj, M.S.; Chen, S.; Lee, S.P.; Reeder, J.T.; Aranyosi, A.J.; Leech, A.; Li, W.; Schon, S.; et al. Soft Wearable Systems for Colorimetric and Electrochemical Analysis of Biofluids. Adv. Funct. Mater. 2019, 30, 1907269. [Google Scholar] [CrossRef]
- Ning, X.; Wang, X.; Zhang, Y.; Yu, X.; Choi, D.; Zheng, N.; Kim, D.S.; Huang, Y.; Zhang, Y.; Rogers, J.A. Assembly of Advanced Materials into 3D Functional Structures by Methods Inspired by Origami and Kirigami: A Review. Adv. Mater. Interfaces 2018, 5, 1–13. [Google Scholar] [CrossRef] [Green Version]
- Abdullah, A.M.; Li, X.; Braun, P.V.; Rogers, J.A.; Hsia, K.J. Kirigami-Inspired Self-Assembly of 3D Structures. Adv. Funct. Mater. 2020, 30, 1909888. [Google Scholar] [CrossRef]
- Aoki, M.; Juang, J.-Y. Forming three-dimensional closed shapes from two-dimensional soft ribbons by controlled buckling. R. Soc. Open Sci. 2018, 5, 171962. [Google Scholar] [CrossRef] [Green Version]
- Yu, C.; Duan, Z.; Yuan, P.; Li, Y.; Su, Y.; Zhang, X.; Pan, Y.; Dai, L.L.; Nuzzo, R.G.; Huang, Y.; et al. Electronically Programmable, Reversible Shape Change in Two- and Three-Dimensional Hydrogel Structures. Adv. Mater. 2013, 25, 1541–1546. [Google Scholar] [CrossRef]
- Rus, D.; Tolley, M.T. Design, fabrication and control of soft robots. Nature 2015, 521, 467–475. [Google Scholar] [CrossRef] [Green Version]
- Majidi, C. Soft Robotics: A Perspective—Current Trends and Prospects for the Future. Soft Robot. 2014, 1, 5–11. [Google Scholar] [CrossRef]
- Schmitt, F.; Piccin, O.; Barbé, L.; Bayle, B. Soft Robots Manufacturing: A Review. Front. Robot. AI 2018, 5. [Google Scholar] [CrossRef] [Green Version]
- Yeh, C.-Y.; Chen, C.-Y.; Juang, J.-Y. Soft hopping and crawling robot for in-pipe traveling. Extreme Mech. Lett. 2020, 39, 100854. [Google Scholar] [CrossRef]
- Yeh, C.-Y.; Chou, S.-C.; Huang, H.-W.; Yu, H.-C.; Juang, J.-Y. Tube-crawling soft robots driven by multistable buckling mechanics. Extrem. Mech. Lett. 2019, 26, 61–68. [Google Scholar] [CrossRef]
- Qi, H.J.; Boyce, M.C. Stress–strain behavior of thermoplastic polyurethanes. Mech. Mater. 2005, 37, 817–839. [Google Scholar] [CrossRef]
- Mullins, L. Softening of Rubber by Deformation. Rubber Chem. Technol. 1969, 42, 339–362. [Google Scholar] [CrossRef]
- Diani, J.; Fayolle, B.; Gilormini, P. A review on the Mullins effect. Eur. Polym. J. 2009, 45, 601–612. [Google Scholar] [CrossRef] [Green Version]
- Beatty, M.F.; Stalnaker, D.O. The Poisson Function of Finite Elasticity. J. Appl. Mech. 1986, 53, 807–813. [Google Scholar] [CrossRef]
- Greaves, G.N.; Greer, A.L.; Lakes, R.S.; Rouxel, T. Poisson’s ratio and modern materials. Nat. Mater. 2011, 10, 823–837. [Google Scholar] [CrossRef]
- Mihai, L.A.; Goriely, A. How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity. Proc. R. Soc. A 2017, 473, 20170607. [Google Scholar] [CrossRef] [Green Version]
- McClung, A.J.W.; Tandon, G.P.; Goecke, K.E.; Baur, J.W. Non-contact technique for characterizing full-field surface deformation of shape memory polymers at elevated and room temperatures. Polym. Test. 2011, 30, 140–149. [Google Scholar] [CrossRef]
- Pan, B. Digital image correlation for surface deformation measurement: Historical developments, recent advances and future goals. Meas. Sci. Technol. 2018, 29, 082001. [Google Scholar] [CrossRef]
- Peters, W.H.; Ranson, W.F. Digital Imaging Techniques in Experimental Stress-Analysis. Opt. Eng. 1982, 21, 427–431. [Google Scholar] [CrossRef]
- Lava, P.; Cooreman, S.; Debruyne, D. Study of systematic errors in strain fields obtained via DIC using heterogeneous deformation generated by plastic FEA. Opt. Lasers Eng. 2010, 48, 457–468. [Google Scholar] [CrossRef]
- Hoult, N.A.; Andy Take, W.; Lee, C.; Dutton, M. Experimental accuracy of two dimensional strain measurements using Digital Image Correlation. Eng. Struct. 2013, 46, 718–726. [Google Scholar] [CrossRef]
- Zhu, F.; Bai, P.; Shi, H.; Jiang, Z.; Lei, D.; He, X. Enhancement of strain measurement accuracy using optical extensometer by application of dual-reflector imaging. Meas. Sci. Technol. 2016, 27, 065007. [Google Scholar] [CrossRef]
- Pan, B.; Yu, L.; Wu, D. High-accuracy 2D digital image correlation measurements using low-cost imaging lenses: Implementation of a generalized compensation method. Meas. Sci. Technol. 2014, 25, 025001. [Google Scholar] [CrossRef]
- Pan, B.; Yu, L.; Yuan, J.; Shen, Z.; Tang, G. Determination of Viscoelastic Poisson’s Ratio of Solid Propellants using an Accuracy-enhanced 2D Digital Image Correlation Technique. Propellants Explos. Pyrotech. 2015, 40, 821–830. [Google Scholar] [CrossRef]
- Yu, L.; Pan, B. In-plane displacement and strain measurements using a camera phone and digital image correlation. Opt. Eng. 2014, 53. [Google Scholar] [CrossRef]
- Gooch, J.W. ASTM D638. In Encyclopedic Dictionary of Polymers; Gooch, J.W., Ed.; Springer New York: New York, NY, USA, 2011; p. 51. [Google Scholar]
- Blaber, J.; Adair, B.; Antoniou, A. Ncorr: Open-Source 2D Digital Image Correlation Matlab Software. Exp. Mech. 2015, 55, 1105–1122. [Google Scholar] [CrossRef]
- McGinty, B. Green & Almansi Strains. Available online: http://www.continuummechanics.org/greenstrain.html (accessed on 1 April 2021).
- Hill, R. Constitutive Inequalities for Isotropic Elastic Solids Under Finite Strain. Proc. R. Soc. Lond. Ser. Math. Phys. Sci. 1970, 314, 457–472. [Google Scholar]
- Hencky, H. Uber die Form des Elastizitatsgesetzes bei ideal elastischen Stoffen. Z. Phys. 1928, 9, 215–220. [Google Scholar]
- Pritchard, R.H.; Lava, P.; Debruyne, D.; Terentjev, E.M. Precise determination of the Poisson ratio in soft materials with 2D digital image correlation. Soft Matter 2013, 9, 6037–6045. [Google Scholar] [CrossRef]
- Avanzini, A.; Gallina, D. Effect of Cyclic Strain on the Mechanical Behavior of a Thermoplastic Polyurethane. J. Eng. Mater. Technol. 2011, 133, 021005. [Google Scholar] [CrossRef]
- Tschoegl, N.W.; Knauss, W.G.; Emri, I. Poisson’s Ratio in Linear Viscoelasticity—A Critical Review. Mech. Time-Depend. Mater. 2002, 6, 3–51. [Google Scholar] [CrossRef]
- Tscharnuter, D.; Jerabek, M.; Major, Z.; Lang, R.W. Time-dependent Poisson’s ratio of polypropylene compounds for various strain histories. Mech. Time-Depend. Mater. 2010, 15, 15–28. [Google Scholar] [CrossRef]
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Xu, Y.-X.; Juang, J.-Y. Measurement of Nonlinear Poisson’s Ratio of Thermoplastic Polyurethanes under Cyclic Softening Using 2D Digital Image Correlation. Polymers 2021, 13, 1498. https://doi.org/10.3390/polym13091498
Xu Y-X, Juang J-Y. Measurement of Nonlinear Poisson’s Ratio of Thermoplastic Polyurethanes under Cyclic Softening Using 2D Digital Image Correlation. Polymers. 2021; 13(9):1498. https://doi.org/10.3390/polym13091498
Chicago/Turabian StyleXu, Yi-Xian, and Jia-Yang Juang. 2021. "Measurement of Nonlinear Poisson’s Ratio of Thermoplastic Polyurethanes under Cyclic Softening Using 2D Digital Image Correlation" Polymers 13, no. 9: 1498. https://doi.org/10.3390/polym13091498