0
Research Papers

Time-Dependent Uniaxial Ratchetting of Ultrahigh Molecular Weight Polyethylene Polymer: Viscoelastic–Viscoplastic Constitutive Model

[+] Author and Article Information
Kaijuan Chen

State Key Laboratory of Traction Power,
Southwest Jiaotong University,
Chengdu 610031, Sichuan, China;
Applied Mechanics and Structure Safety Key
Laboratory of Sichuan Province,
School of Mechanics and Engineering,
Southwest Jiaotong University,
Chengdu 610031, Sichuan, China

Guozheng Kang

State Key Laboratory of Traction Power,
Southwest Jiaotong University,
Chengdu 610031, Sichuan, China;
Applied Mechanics and Structure Safety Key
Laboratory of Sichuan Province,
School of Mechanics and Engineering,
Southwest Jiaotong University,
Chengdu 610031, Sichuan, China
e-mails: guozhengkang@home.swjtu.edu.cn;
guozhengkang@126.com

Chao Yu, Fucong Lu, Han Jiang

Applied Mechanics and Structure Safety Key
Laboratory of Sichuan Province,
School of Mechanics and Engineering,
Southwest Jiaotong University,
Chengdu 610031, Sichuan, China

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 14, 2016; final manuscript received July 11, 2016; published online August 1, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(10), 101003 (Aug 01, 2016) (11 pages) Paper No: JAM-16-1187; doi: 10.1115/1.4034120 History: Received April 14, 2016; Revised July 11, 2016

Uniaxial tension–unloading recovery, creep-recovery, and stress-controlled cyclic tests are first performed to investigate the recoverable viscoelasticity and irrecoverable viscoplasticity (including the uniaxial ratchetting) of ultrahigh molecular weight polyethylene (UHMWPE) polymer at room temperature. The results show that obvious time-dependent ratchetting occurs in the asymmetrical stress-controlled cyclic tension–compression and tension–tension tests of the UHMWPE, and total ratchetting strain consists of both recoverable viscoelastic and irrecoverable viscoplastic parts. Based on the experimental observation, a new viscoelastic–viscoplastic constitutive model is proposed to describe the time-dependent ratchetting of the UHMWPE. In the proposed model, the viscoplastic strain is set to be contributed simultaneously by the unified viscoplastic and creep ones. Meanwhile, a memory surface is introduced into the viscoelastic model to improve the description to the shapes of stress–strain hysteresis loops. Finally, the proposed model is verified by comparing the predictions with the corresponding experimental results of the UHMWPE. It is clearly demonstrated that the proposed model predicts the creep, viscoelastic recovery, and uniaxial time-dependent ratchetting of the UHMWPE well.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Lewis, G. , 2001, “ Properties of Crosslinked Ultra-High Molecular Weight Polyethylene,” Biomaterials, 22(4), pp. 371–401. [CrossRef] [PubMed]
Pruitt, L. A. , 2005, “ Deformation, Yielding, Fracture and Fatigue Behavior of Conventional and Highly Cross-Linked Ultra-High Molecular Weight Polyethylene,” Biomaterials, 26(8), pp. 905–915. [CrossRef] [PubMed]
Hua, X. , Wroblewski, B. M. , Jin, Z. , and Wang, L. , 2012, “ The Effect of Cup Inclination and Wear on the Contact Mechanics and Cement Fixation for Ultra-High Molecular Weight Polyethylene Total Hip Replacements,” Med. Eng. Phys., 34(3), pp. 318–325. [CrossRef] [PubMed]
Pan, D. , Kang, G. , Zhu, Z. , and Liu, Y. , 2010, “ Experimental Study on Uniaxial Time-Dependent Ratcheting of a Polyetherimide Polymer,” J. Zhejiang Univ. Sci. A, 11(10), pp. 804–810. [CrossRef]
Chen, K. , Kang, G. , Lu, F. , and Jiang, H. , 2015, “ Uniaxial Cyclic Deformation and Internal Heat Production of Ultra-High Molecular Weight Polyethylene,” J. Polym. Res., 22(11), pp. 1–9.
Benaarbia, A. , Chrysochoos, A. , and Robert, G. , 2014, “ Influence of Relative Humidity and Loading Frequency on the PA6. 6 Cyclic Thermomechanical Behavior—Part I: Mechanical and Thermal Aspects,” Polym. Test., 40, pp. 290–298. [CrossRef]
Benaarbia, A. , Chrysochoos, A. , and Robert, G. , 2015, “ Influence of Relative Humidity and Loading Frequency on the PA6. 6 Thermomechanical Cyclic Behavior—Part II: Energy Aspects,” Polym. Test., 41, pp. 92–98. [CrossRef]
Jiang, H. , Zhang, J. , Kang, G. , Xi, C. , Jiang, C. , and Liu, Y. , 2013, “ A Test Procedure for Separating Viscous Recovery and Accumulated Unrecoverable Deformation of Polymer Under Cyclic Loading,” Polym. Test., 32(8), pp. 1445–1451. [CrossRef]
Lu, F. , Kang, G. , Zhu, Y. , Xi, C. , and Jiang, H. , 2016, “ Experimental Observation on Multiaxial Ratchetting of Polycarbonate Polymer at Room Temperature,” Polym. Test., 50, pp. 135–144. [CrossRef]
Averett, R. D. , Realff, M. L. , Michielsen, S. , and Neu, R. W. , 2006, “ Mechanical Behavior of Nylon 66 Fibers Under Monotonic and Cyclic Loading,” Compos. Sci. Technol., 66(11), pp. 1671–1681. [CrossRef]
Kang, G. , Liu, Y. , Wang, Y. , Chen, Z. , and Xu, W. , 2009, “ Uniaxial Ratchetting of Polymer and Polymer Matrix Composites: Time-Dependent Experimental Observations,” Mater. Sci. Eng. A, 523(1), pp. 13–20. [CrossRef]
Liu, W. , Gao, Z. , and Yue, Z. , 2008, “ Steady Ratcheting Strains Accumulation in Varying Temperature Fatigue Tests of PMMA,” Mater. Sci. Eng. A, 492(1), pp. 102–109. [CrossRef]
Lu, F. , Kang, G. , Jiang, H. , Zhang, J. , and Liu, Y. , 2014, “ Experimental Studies on the Uniaxial Ratchetting of Polycarbonate Polymer at Different Temperatures,” Polym. Test., 39, pp. 92–100. [CrossRef]
Shen, X. , Xia, Z. , and Ellyin, F. , 2004, “ Cyclic Deformation Behavior of an Epoxy Polymer—Part I: Experimental Investigation,” Polym. Eng. Sci., 44(12), pp. 2240–2246. [CrossRef]
Zhang, Z. , and Chen, X. , 2009, “ Multiaxial Ratcheting Behavior of PTFE at Room Temperature,” Polym. Test., 28(3), pp. 288–295. [CrossRef]
Zhang, Z. , Chen, X. , and Wang, Y. , 2010, “ Uniaxial Ratcheting Behavior of Polytetrafluoroethylene at Elevated Temperature,” Polym. Test., 29(3), pp. 352–357. [CrossRef]
Hassan, T. , Çolak, O. U. , and Clayton, P. M. , 2011, “ Uniaxial Strain and Stress-Controlled Cyclic Responses of Ultrahigh Molecular Weight Polyethylene: Experiments and Model Simulations,” ASME J. Eng. Mater. Technol., 133(2), p. 021010. [CrossRef]
Asmaz, K. , Colak, O. U. , and Hassan, T. , 2014, “ Biaxial Ratcheting of Ultra High Molecular Weight Polyethylene: Experiments and Constitutive Modeling,” J. Test. Eval., 42(6), pp. 1–7.
Reeves, E. A. , Barton, D. C. , FitzPatrick, D. P. , and Fisher, J. , 1998, “ A Two-Dimensional Model of Cyclic Strain Accumulation in Ultra-High Molecular Weight Polyethylene Knee Replacements,” Proc. Inst. Mech. Eng. Part H, 212(3), pp. 189–198. [CrossRef]
Chen, K. , Kang, G. , Lu, F. , Xu, J. , and Jiang, H. , 2016, “ Temperature-Dependent Uniaxial Ratchetting of Ultra-High Molecular Weight Polyethylene,” Fatigue Fract. Eng. Mater. Struct., 39(7), pp. 839–849. [CrossRef]
Beake, B. , 2006, “ Modelling Indentation Creep of Polymers: A Phenomenological Approach,” J. Phys. D: Appl. Phys., 39(20), pp. 4478–4485. [CrossRef]
Schapery, R. A. , 1969, “ On the Characterization of Nonlinear Viscoelastic Materials,” Polym. Eng. Sci., 9(4), pp. 295–310. [CrossRef]
Lai, J. , and Bakker, A. , 1996, “ 3-D Schapery Representation for Non-Linear Viscoelasticity and Finite Element Implementation,” Comput. Mech., 18(3), pp. 182–191. [CrossRef]
Pan, D. , Kang, G. , and Jiang, H. , 2012, “ Viscoelastic Constitutive Model for Uniaxial Time-Dependent Ratcheting of Polyetherimide Polymer,” Polym. Eng. Sci., 52(9), pp. 1874–1881. [CrossRef]
Xia, Z. , Shen, X. , and Ellyin, F. , 2005, “ An Assessment of Nonlinearly Viscoelastic Constitutive Models for Cyclic Loading: The Effect of a General Loading/Unloading Rule,” Mech. Time-Depend. Mater., 9(4), pp. 79–98. [CrossRef]
Xia, Z. , Shen, X. , and Ellyin, F. , 2005, “ Cyclic Deformation Behavior of an Epoxy Polymer—Part II: Predictions of Viscoelastic Constitutive Models,” Polym. Eng. Sci., 45(1), pp. 103–113. [CrossRef]
Lai, D. , Yakimets, I. , and Guigon, M. , 2005, “ A Non-Linear Viscoelastic Model Developed for Semi-Crystalline Polymer Deformed at Small Strains With Loading and Unloading Paths,” Mater. Sci. Eng. A, 405(1), pp. 266–271. [CrossRef]
Nguyen, S. T. T. , Castagnet, S. , and Grandidier, J. C. , 2013, “ Nonlinear Viscoelastic Contribution to the Cyclic Accommodation of High Density Polyethylene in Tension: Experiments and Modeling,” Int. J. Fatigue, 55, pp. 166–177. [CrossRef]
Bergström, J. , Kurtz, S. , Rimnac, C. , and Edidin, A. , 2002, “ Constitutive Modeling of Ultra-High Molecular Weight Polyethylene Under Large-Deformation and Cyclic Loading Conditions,” Biomaterials, 23(11), pp. 2329–2343. [CrossRef] [PubMed]
Schapery, R. A. , 1997, “ Nonlinear Viscoelastic and Viscoplastic Constitutive Equations Based on Thermodynamics,” Mech. Time-Depend. Mater., 1(2), pp. 209–240. [CrossRef]
Levenberg, E. , and Uzan, J. , 2004, “ Triaxial Small-Strain Viscoelastic-Viscoplastic Modeling of Asphalt Aggregate Mixes,” Mech. Time-Depend. Mater., 8(4), pp. 365–384. [CrossRef]
Kim, J. S. , and Muliana, A. H. , 2010, “ A Combined Viscoelastic-Viscoplastic Behavior of Particle Reinforced Composites,” Int. J. Solids Struct., 47(5), pp. 580–594. [CrossRef]
Khan, A. , and Zhang, H. , 2001, “ Finite Deformation of a Polymer: Experiments and Modeling,” Int. J. Plast., 17(9), pp. 1167–1188. [CrossRef]
Frank, G. J. , and Brockman, R. A. , 2001, “ A Viscoelastic-Viscoplastic Constitutive Model for Glassy Polymers,” Int. J. Solids Struct., 38(30), pp. 5149–5164. [CrossRef]
Drozdov, A. , 2007, “ Viscoelasticity and Viscoplasticity of Semicrystalline Polymers: Structure Property Relations for High-Density Polyethylene,” Comput. Mater. Sci., 39(4), pp. 729–751. [CrossRef]
Ayoub, G. , Zaïri, F. , Naït-Abdelaziz, M. , and Gloaguen, J. M. , 2010, “ Modelling Large Deformation Behaviour Under Loading-Unloading of Semicrystalline Polymers: Application to a High Density Polyethylene,” Int. J. Plast., 26(3), pp. 329–347. [CrossRef]
Yu, C. , Kang, G. , Lu, F. , Zhu, Y. , and Chen, K. , 2016, “ Viscoelastic-Viscoplastic Cyclic Deformation of Polycarbonate Polymer: Experiment and Constitutive Model,” ASME J. Appl. Mech., 83(4), p. 041002. [CrossRef]
Abdel-Karim, M. , and Ohno, N. , 2000, “ Kinematic Hardening Model Suitable for Ratchetting With Steady-State,” Int. J. Plast., 16(3), pp. 225–240. [CrossRef]
Kang, G. , Kan, Q. , Zhang, J. , and Sun, Y. , 2006, “ Time-Dependent Ratchetting Experiments of SS304 Stainless Steel,” Int. J. Plast., 22(5), pp. 858–894. [CrossRef]
Kang, G. , and Kan, Q. , 2007, “ Constitutive Modeling for Uniaxial Time-Dependent Ratcheting of SS304 Stainless Steel,” Mech. Mater., 39(5), pp. 488–499. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Results of the UHMWPE in multilevel loading–unloading recovery test (i.e., 9 MPa → 11 MPa → 13 MPa → 15 MPa → 17 MPa → 19 MPa → 21 MPa): (a) first cycle, (b) second cycle, (c) third cycle, (d) fourth cycle, (e) fifth cycle, (f) sixth cycle, and (g) seventh cycle

Grahic Jump Location
Fig. 2

Strain–time curves of the UHMWPE for the strain recovery at zero stress point and with various peak stresses

Grahic Jump Location
Fig. 3

Irrecoverable viscoplastic strain–stress curve

Grahic Jump Location
Fig. 4

Results of the UHMWPE obtained in the loading–unloading recovery tests at a stress of rate 1 MPa/s and with various peak stresses: (a) stress–strain curves and (b) strain–time curves

Grahic Jump Location
Fig. 5

Strain–time curves of the UHMWPE in the creep-recovery tests with different creep stresses (i.e., 6, 10, and 14 MPa)

Grahic Jump Location
Fig. 6

Ratchetting of the UHMWPE with a stress level of 6 ± 10 MPa and at a stress rate of 5 MPa/s: (a) experimental stress–strain curve [5], (b) simulated stress–strain curve by the model with a memory surface, and (c) simulated stress–strain curve by the model without memory surface

Grahic Jump Location
Fig. 7

Ratchetting of the UHMWPE with a stress level of 10 ± 2 MPa and at a stress rate of 5 MPa/s: (a) experimental stress–strain curve and (b) predicted stress–strain curve

Grahic Jump Location
Fig. 8

Experimental [5] and predicted results of the UHMWPE in the cyclic tests at same stress rate of 5 MPa/s and with same stress amplitude of 10 MPa, but with various mean stresses: (a) evolution curves of ratchetting strains and (b) strain–time curves during the zero stress holding after the cyclic tests

Grahic Jump Location
Fig. 9

Experimental [5] and predicted results of the UHMWPE in the cyclic tests at same stress rate of 5 MPa/s and with same mean stress of 10 MPa, but with various stress amplitudes: (a) evolution curves of ratchetting strains and (b) strain–time curves during the zero stress holding after the cyclic tests

Grahic Jump Location
Fig. 10

Experimental [5] and predicted results of the UHMWPE in the cyclic tests with same stress level of 6 ± 10 MPa but at various stress rates: (a) evolution curves of ratchetting strains and (b) strain–time curves during the zero stress holding after the cyclic tests

Grahic Jump Location
Fig. 11

Experimental and predicted results of the UHMWPE in the cyclic test with same stress level of 6 ± 10 MPa and with peak stress hold for 10 s and at a stress rate of 5 MPa/s: (a) experimental stress–strain curve, (b) predicted stress–strain curve with creep model and memory surface, (c) predicted stress–strain curve with creep model and without memory surface, and (d) predicted stress–strain curve with memory surface and without creep model

Grahic Jump Location
Fig. 12

Experimental and predicted results of the UHMWPE in the cyclic tests with same stress level of 6 ± 10 MPa and at a stress rate of 5 MPa/s, but with certain peak/valley stress holds: (a) evolution curves of ratchetting strains and (b) strain–time curves during the zero stress holding after the cyclic tests

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In