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Research Papers

Viscoelastic–Viscoplastic Cyclic Deformation of Polycarbonate Polymer: Experiment and Constitutive Model

[+] Author and Article Information
Chao Yu

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

Guozheng Kang

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

Fucong Lu, Kaijuan Chen

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

Yilin Zhu

School of Architectural and Civil Engineering,
Chengdu University,
Chengdu, Sichuan 610106, China

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 25, 2015; final manuscript received December 21, 2015; published online January 18, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(4), 041002 (Jan 18, 2016) (14 pages) Paper No: JAM-15-1575; doi: 10.1115/1.4032374 History: Received October 25, 2015; Revised December 21, 2015

A series of uniaxial tests (including multilevel loading–unloading recovery, creep-recovery, and cyclic tension–compression/tension ones) were performed to investigate the monotonic and cyclic viscoelastic–viscoplastic deformations of polycarbonate (PC) polymer at room temperature. The results show that the PC exhibits strong nonlinearity and rate-dependence, and obvious ratchetting occurs during the stress-controlled cyclic tension–compression/tension tests with nonzero mean stress, which comes from both the viscoelasticity and viscoplasticity of the PC. Based on the experimental observation, a nonlinear viscoelastic–viscoplastic cyclic constitutive model is then constructed. The viscoelastic part of the proposed model is constructed by extending the Schapery's nonlinear viscoelastic model, and the viscoplastic one is established by adopting the Ohno–Abdel-Karim's nonlinear kinematic hardening rule to describe the accumulation of irrecoverable viscoplastic strain produced during cyclic loading. Furthermore, the dependence of elastic compliance of the PC on the accumulated viscoplastic strain is considered. Finally, the capability of the proposed model is verified by comparing the predicted results with the corresponding experimental ones of the PC. It is shown that the proposed model provides reasonable predictions to the various deformation characteristics of the PC presented in the multilevel loading–unloading recovery, creep-recovery, and cyclic tension–compression/tension tests.

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Figures

Grahic Jump Location
Fig. 1

Shape and size of specimen (unit: millimeter)

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Fig. 2

Multilevel loading–unloading recovery at a stress rate of 1.0 MPa/s (20 MPa → 40 MPa → 50 MPa → 55 MPa → 60 MPa → 65 MPa → 70 MPa → 71 MPa): (a) first cycle, (b) second cycle, (c) third cycle, (d) fourth cycle, (e) fifth cycle, (f) sixth cycle, (g) seventh cycle, and (h) eighth cycle

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Fig. 3

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

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Fig. 4

Multilevel loading–unloading recovery at a stress rate of 5.0 MPa/s (60 MPa → 65 MPa → 70 MPa → 71 MPa): (a) first cycle, (b) second cycle, (c) third cycle, and (d) fourth cycle

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Fig. 5

Viscoplastic strain–stress curves

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Fig. 6

Strain–time curves for creep

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Fig. 7

Ratchetting of the PC with a mean stress of 25 MPa and stress amplitude of 25 MPa at a stress rate of 1.2 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, and (c) evolution curves of peak and valley strains

Grahic Jump Location
Fig. 8

Ratchetting of the PC with a mean stress of 33 MPa and stress amplitude of 26.4 MPa at a stress rate of 1.0 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, (c) evolution curves of peak and valley strains, and (d) strain–time curves for strain recovery at zero-stress point after cyclic deformation

Grahic Jump Location
Fig. 9

Ratchetting of the PC with a mean stress of 26.4 MPa and stress amplitude of 33 MPa at a stress rate of 1.0 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, (c) evolution curves of peak and valley strains, and (d) strain–time curves for strain recovery at zero-stress point after cyclic deformation

Grahic Jump Location
Fig. 10

Ratchetting of the PC with a mean stress of 19.8 MPa and stress amplitude of 39.6 MPa at a stress rate of 1.0 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, (c) evolution curves of peak and valley strains, and (d) strain–time curves for strain recovery at zero-stress point after cyclic deformation

Grahic Jump Location
Fig. 11

Ratchetting of the PC with a mean stress of 13.2 MPa and stress amplitude of 46.2 MPa at a stress rate of 1.0 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, (c) evolution curves of peak and valley strains, and (d) strain–time curves for strain recovery at zero-stress point after cyclic deformation

Grahic Jump Location
Fig. 12

Evolution curves of the elastic–viscoelastic compliance versus number of cycles in the tension-unloading (25 ± 25 MPa) and tension–compression (13.2 ± 46.2 MPa) tests

Grahic Jump Location
Fig. 13

Ratchetting of the PC with a mean stress of 50 MPa and stress amplitude of 10 MPa at a stress rate of 1.0 MPa/s: (a) experimental stress–strain curve and (b) simulated stress–strain curve

Grahic Jump Location
Fig. 14

Ratchetting of the PC with a mean stress of 50 MPa and stress amplitude of 10 MPa at a stress rate of 5.0 MPa/s: (a) experimental stress–strain curve and (b) simulated stress–strain curve

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Fig. 15

Ratchetting of the PC with a mean stress of 50 MPa and stress amplitude of 10 MPa at a stress rate of 20.0 MPa/s: (a) experimental stress–strain curve and (b) simulated stress–strain curve

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Fig. 16

Evolution curves of the peak/valley strains versus number of cycles with the same mean stress (50 MPa) and stress amplitudes (10 MPa) but at various stress rates: (a) valley strains and (b) peak strains

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Fig. 17

Ratchetting of the PC with three stress levels (40 ± 10 MPa → 50 ± 10 MPa → 40 ± 10 MPa) at a stress rate of 1.2 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, and (c) evolution curves of peak and valley strains

Grahic Jump Location
Fig. 18

Ratchetting of the PC with three stress levels (40 ± 10 MPa → 40 ± 20 MPa → 40 ± 10 MPa) at a stress rate of 1.2 MPa/s: (a) experimental stress–strain curve, (b) simulated stress–strain curve, and (c) evolution curves of peak and valley strains

Grahic Jump Location
Fig. 19

Simulated cyclic stress–plastic strain curves at a stress rate of 1.2 MPa/s: (a) 33 ± 26.4 MPa, (b) 26.4 ± 33 MPa, (c) 19.8 ± 39.6 MPa, and (d) 13.2 ± 46.2 MPa

Grahic Jump Location
Fig. 20

Simulated results without considering the dependence of elastic compliance on the accumulated plastic strain at a stress rate of 1.0 MPa/s: (a) 33 ± 26.4 MPa and (b) 13.2 ± 46.2 MPa

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