Research Papers

An Experimental Study on Strain Hardening of Amorphous Thermosets: Effect of Temperature, Strain Rate, and Network Density

[+] Author and Article Information
Chuanshuai Tian

Department of Engineering Mechanics,
College of Mechanics and Materials,
Hohai University Nanjing,
Jiangsu 210098, China
e-mail: cstian@hhu.edu.cn

Rui Xiao

Department of Engineering Mechanics,
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, Jiangsu, China
e-mail: rxiao@hhu.edu.cn

Jun Guo

Department of Engineering Mechanics,
College of Mechanics and Materials,
Hohai University,
Nanjing 210098, Jiangsu, China
e-mail: jun2018@hhu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 20, 2018; final manuscript received June 24, 2018; published online July 17, 2018. Assoc. Editor: Junlan Wang.

J. Appl. Mech 85(10), 101012 (Jul 17, 2018) (8 pages) Paper No: JAM-18-1228; doi: 10.1115/1.4040692 History: Received April 20, 2018; Revised June 24, 2018

In this paper, we present an experimental study on strain hardening of amorphous thermosets. A series of amorphous polymers is synthesized with similar glass transition regions and different network densities. Uniaxial compression tests are then performed at two different strain rates spanning the glass transition region. The results show that a more pronounced hardening response can be observed as decreasing temperature and increasing strain rate and network density. We also use the Neo-Hookean model and Arruda–Boyce model to fit strain hardening responses. The Neo-Hookean model can only describe strain hardening of the lightly cross-linked polymers, while the Arruda–Boyce model can well describe hardening behaviors of all amorphous networks. The locking stretch of the Arruda–Boyce model decreases significantly with increasing network density. However, for each amorphous network, the locking stretch is the same regardless of the deformation temperature and rate. The hardening modulus exhibits a sharp transition with temperature. The transition behaviors of hardening modulus also vary with the network density. For lightly crosslinked networks, the hardening modulus changes 60 times with temperature. In contrast, for heavily crosslinked polymers, the hardening modulus in the glassy state is only 2 times of that in the rubbery state. Different from the results from molecular dynamic simulation in literatures, the hardening modulus of polymers in the glassy state does not necessarily increase with network density. Rather, the more significant hardening behaviors in more heavily crosslinked polymers are attributed to a lower value of the stretch limit.

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Zhang, R. , Bai, P. , Lei, D. , and Xiao, R. , 2018, “ Aging-Dependent Strain Localization in Amorphous Glassy Polymers: From Necking to Shear Banding,” Int. J. Solids Struct., 146, pp. 203–213. [CrossRef]
Van Melick, H. , Govaert, L. , and Meijer, H. , 2003, “ On the Origin of Strain Hardening in Glassy Polymers,” Polymer, 44(8), pp. 2493–2502. [CrossRef]
Li, H. X. , and Buckley, C. P. , 2010, “ Necking in Glassy Polymers: Effects of Intrinsic Anisotropy and Structural Evolution Kinetics in Their Viscoplastic Flow,” Int. J. Plast., 26(12), pp. 1726–1745. [CrossRef]
Govaert, L. E. , Engels, T. A. P., M. W. , Tervoort, T. A. , and Ulrich, W. S. , 2008, “ Does the Strain Hardening Modulus of Glassy Polymers Scale With the Flow Stress,” J. Polym. Sci. Part B, 46(22), pp. 2475–2481. [CrossRef]
Sarva, S. S. , Deschanel, S. , Boyce, M. C. , and Chen, W. , 2007, “ Stress–Strain Behavior of a Polyurea and a Polyurethane From Low to High Strain Rates,” Polymer, 48(8), pp. 2208–2213. [CrossRef]
Guo, H. , Guo, W. , Amirkhizi, A. V. , Zou, R. , and Yuan, K. , 2016, “ Experimental Investigation and Modeling of Mechanical Behaviors of Polyurea Over Wide Ranges of Strain Rates and Temperatures,” Polym. Test., 53, pp. 234–244. [CrossRef]
Zaroulis, J. S. , and Boyce, M. C. , 1997, “ Temperature, Strain Rate, and Strain State Dependence of the Evolution in Mechanical Behaviour and Structure of Poly(Ethylene Terephthalate) With Finite Strain Deformation,” Polymer, 38(6), pp. 1303–1315.
Dupaix, R. B. , and Boyce, M. C. , 2005, “ Finite Strain Behavior of Poly (Ethylene Terephthalate)(PET) and Poly (Ethylene Terephthalate)-Glycol (PETG),” Polymer, 46(13), pp. 4827–4838. [CrossRef]
Arruda, E. M. , Boyce, M. C. , and Quintus-Bosz, H. , 1993, “ Effects of Initial Anisotropy on the Finite Strain Deformation Behavior of Glassy Polymers,” Int. J. Plast., 9(7), pp. 783–811. [CrossRef]
Hine, P. J. , Duckett, A. , and Read, D. J. , 2007, “ Influence of Molecular Orientation and Melt Relaxation Processes on Glassy Stress-Strain Behavior in Polystyrene,” Macromolecules, 40(8), pp. 2782–2790. [CrossRef]
Senden, D. J. A. , van Dommelen, J. A. W. , and Govaert, L. E. , 2010, “ Strain Hardening and Its Relation to Bauschinger Effects in Oriented Polymers,” J. Polym. Sci. Part B, 48(13), pp. 1483–1494. [CrossRef]
Haward, R. N. , and Thackray, G. , 1968, “ The Use of Mathematical Models to Describe Isothermal Stress Strain Curves in Glassy Thermoplastics,” Proc. R. Soc. London Ser. A, 302(1471), p. 453. [CrossRef]
Tervoort, T. , and Govaert, L. , 2000, “ Strain-Hardening Behavior of Polycarbonate in the Glassy State,” J. Rheol., 44(6), pp. 1263–1277. [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]
Hoy, R. S. , and Robbins, M. O. , 2006, “ Strain Hardening of Polymer Glasses: Effect of Entanglement Density, Temperature, and Rate,” J. Polym. Sci. Part B, 44(24), pp. 3487–3500. [CrossRef]
Hoy, R. S. , and Robbins, M. O. , 2007, “ Strain Hardening in Polymer Glasses: Limitations of Network Models,” Phys. Rev. Lett., 99(11), p. 117801. [CrossRef] [PubMed]
Nayak, K. , Read, D. J. , McLeish, T. C. , Hine, P. J. , and Tassieri, M. , 2011, “ A Coarse-Grained Molecular Model of Strain-Hardening for Polymers in the Marginally Glassy State,” J. Polym. Sci. Part B, 49(13), pp. 920–938. [CrossRef]
Mahajan, D. K. , and Basu, S. , 2010, “ Investigations Into the Applicability of Rubber Elastic Analogy to Hardening in Glassy Polymers,” Modell. Simul. Mater. Sci. Eng., 18(2), p. 025001. [CrossRef]
Xu, W. , Wu, F. , Jiao, Y. , and Liu, M. , 2017, “ A General Micromechanical Framework of Effective Moduli for the Design of Nonspherical Nano- and Micro-Particle Reinforced Composites With Interface Properties,” Mater. Des., 127, pp. 162–172. [CrossRef]
Sudarkodi, V. , and Basu, S. , 2014, “ Investigations Into the Origins of Plastic Flow and Strain Hardening in Amorphous Glassy Polymers,” Int. J. Plast., 56, pp. 139–155. [CrossRef]
Chen, K. , and Schweizer, K. S. , 2009, “ Suppressed Segmental Relaxation as the Origin of Strain Hardening in Polymer Glasses,” Phys. Rev. Lett., 102(3), p. 038301. [CrossRef] [PubMed]
Chen, K. , Saltzman, E. , and Schweizer, K. , 2009, “ Segmental Dynamics in Polymers: From Cold Melts to Ageing and Stressed Glasses,” J. Phys.: Condens. Matter, 21(50), p. 503101. [CrossRef] [PubMed]
Voyiadjis, G. Z. , and Samadi-Dooki, A. , 2016, “ Constitutive Modeling of Large Inelastic Deformation of Amorphous Polymers: Free Volume and Shear Transformation Zone Dynamics,” J. Appl. Phys., 119(22), p. 225104. [CrossRef]
Nguyen, T. D. , Yakacki, C. M. , Brahmbhatt, P. D. , and Chambers, M. L. , 2010, “ Modeling the Relaxation Mechanisms of Amorphous Shape Memory Polymers,” Adv. Mater., 22(31), pp. 3411–3423. [CrossRef] [PubMed]
Xiao, R. , Choi, J. , Lakhera, N. , Yakacki, C. , Frick, C. , and Nguyen, T. , 2013, “ Modeling the Glass Transition of Amorphous Networks for Shape-Memory Behavior,” J. Mech. Phys. Solids, 61(7), pp. 1612–1635. [CrossRef]
Xiao, R. , and Nguyen, T. D. , 2015, “ An Effective Temperature Theory for the Nonequilibrium Behavior of Amorphous Polymers,” J. Mech. Phys. Solids, 82, pp. 62–81. [CrossRef]
Wang, M. C. , and Guth, E. , 1952, “ Statistical Theory of Networks of Non-Gaussian Flexible Chains,” J. Chem. Phys., 20(7), pp. 1144–1157. [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]
Holzapfel, G. A. , 2000, Nonlinear Solid Mechanics: A Continuum Approach for Engineers, Wiley, Chichester, UK.
Yakacki, C. M. , Shandas, R. , Lanning, C. , Rech, B. , Eckstein, A. , and Gall, K. , 2007, “ Unconstrained Recovery Characterization of Shape-Memory Polymer Networks for Cardiovascular Applications,” Biomaterials, 28(14), pp. 2255–2263. [CrossRef] [PubMed]
Safranski, D. L. , and Gall, K. , 2008, “ Effect of Chemical Structure and Crosslinking Density on the Thermo-Mechanical Properties and Toughness of (Meth)Acrylate Shape Memory Polymer Networks,” Polymer, 49(20), pp. 4446–4455. [CrossRef]
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]
Silberstein, M. N. , and Boyce, M. C. , 2010, “ Constitutive Modeling of the Rate, Temperature, and Hydration Dependent Deformation Response of Nafion to Monotonic and Cyclic Loading,” J. Power Sources, 195(17), pp. 5692–5706. [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]
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]
Bouvard, J.-L. , Francis, D. K. , Tschopp, M. A. , Marin, E. , Bammann, D. , and Horstemeyer, M. , 2013, “ An Internal State Variable Material Model for Predicting the Time, Thermomechanical, and Stress State Dependence of Amorphous Glassy Polymers Under Large Deformation,” Int. J. Plast., 42, pp. 168–193. [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]


Grahic Jump Location
Fig. 1

Storage modulus and tan δ of tBA-co-XLS networks with (a) 2 wt %, (b) 10 wt %, (c) 20 wt %, and (d) 40 wt % crosslinker as a function of temperature

Grahic Jump Location
Fig. 2

Comparison the experiments and model predictions of hyperelastic response of amorphous thermosets with (a) 2 wt %, (b) 10 wt %, (c) 20 wt %, and (d) 40 wt % crosslinker

Grahic Jump Location
Fig. 3

Stress response of tBA-co-XLS with 2 wt % crosslinker at strain rates of (a) 0.003/s and (b) 0.0003/s

Grahic Jump Location
Fig. 4

Stress response of tBA-co-XLS with 10 wt % crosslinker at strain rates of (a) 0.003/s and (b) 0.0003/s

Grahic Jump Location
Fig. 5

Stress response of tBA-co-XLS with 20 wt % crosslinker at strain rates of (a) 0.003/s and (b) 0.0003/s

Grahic Jump Location
Fig. 6

Stress response of tBA-co-XLS with 40 wt % crosslinker at strain rates of (a) 0.003/s and (b) 0.0003/s

Grahic Jump Location
Fig. 7

The strain rate-dependent stress response of tBA-co-XLS with 20 wt % crosslinker deformed at (a) 40 °C and (b) 30 °C

Grahic Jump Location
Fig. 8

The stress response as a function of normalized stretch a(λ1) of (a) tBA-co-XLS with 10 wt % crosslinker and (b) at tBA-co-XLS with 40 wt % crosslinker at a strain rate of 0.003/s

Grahic Jump Location
Fig. 9

The strain hardening modulus as a function of temperature for tBA-co-XLS with (a) 2 wt %, (b) 10 wt %, (c) 20 wt %, and (d) 40 wt % crosslinker



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