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Research Papers

# Uniaxial Strain and Stress-Controlled Cyclic Responses of Ultrahigh Molecular Weight Polyethylene: Experiments and Model Simulations

[+] Author and Article Information
Tasnim Hassan

Department of Civil, Construction and Environmental Engineering, North Carolina State University, Raleigh, NC 27695thassan@ncsu.edu

Ozgen U. Çolak

Department of Mechanical Engineering, Yildiz Technical University, 34349 Yildiz-Istanbul, Turkeyozgen@yildiz.edu.tr

Patricia M. Clayton

Department of Civil, Construction and Environmental Engineering, North Carolina State University, Raleigh, NCpmclayton@gmail.com

J. Eng. Mater. Technol 133(2), 021010 (Mar 07, 2011) (9 pages) doi:10.1115/1.4003109 History: Received April 15, 2010; Revised September 23, 2010; Published March 07, 2011; Online March 07, 2011

## Abstract

Thermoplastics such as ultrahigh molecular weight polyethylene (UHMWPE) are used for a wide variety of applications, such as bearing material in total replacement of knee and hip components, seals, gears, and unlubricated bearing. Accurate prediction of stresses and deformations of UHMWPE components under service conditions is essential for the design and analysis of these components. This, in turn, requires a cyclic, viscoplastic constitutive model that can simulate cyclic responses of UHMWPE under a wide variety of uniaxial and multiaxial, strain, and stress-controlled cyclic loading. Such a constitutive model validated against a broad set of experimental responses is not available mainly because of the lack of experimental data of UHMWPE. Toward achieving such a model, this study conducted a systematic set of uniaxial experiments on UHMWPE thin-walled, tubular specimens by prescribing strain and stress-controlled cyclic loading. The tubular specimen was designed so that both uniaxial and biaxial experiments can be conducted using one type of specimen. The experimental responses developed are presented for demonstrating the cyclic and ratcheting responses of UHMWPE under uniaxial loading. The responses also are scrutinized for determining the applicability of the thin-walled, tubular specimen in conducting large strain cyclic experiments. A unified state variable theory, the viscoplasticity theory based on overstress for polymers (VBOP) is implemented to simulate the recorded uniaxial responses of UHMWPE. The state of the VBOP model simulation is discussed and model improvements needed are suggested.

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## Figures

Figure 1

Specimen design, dimension, and gripping. (a) 2D sketch showing dimensions (in mm) of the specimen. (b) 3D view of the specimen. (c) End collate used in gripping the specimen using ring-feeders at each end of the specimen. (d) Photograph of a specimen gripped in the testing machine along with the extensometer for recording axial strain.

Figure 2

UHMWPE material responses (true stresses and strains) under monotonic and cyclic, strain-controlled loading (strain rate=0.1%): (a) monotonic response from test 1 in Table 1, (b) hysteresis loops under symmetric, strain-controlled cycle with amplitudes 0.5%, 1%, and 2% (15 cycles each) from test 2 in Table 1, (c) stress amplitude (σxa) and mean (σxm) of the hysteresis loops as a function of the number of cycles N from test 2 in Table 1, and (d) stable hysteresis loops under strain-controlled cycle with amplitudes 2%, 4%, and 6% from test 3 in Table 1.

Figure 3

UHMWPE experimental and simulation responses (true stresses and strains) under symmetric, strain-controlled cyclic loading (strain rate=0.1%): (a) stable hysteresis loops under strain-controlled cycle with amplitudes 2%, 4%, and 6% from test 3 in Table 1, (b) stress amplitude (σxa) and mean (σxm) of the hysteresis loops as a function of the number of cycles N from test 3 in Table 1, (c) stable hysteresis loops under strain-controlled cycle with amplitudes 1.0%, 1.5%, 2.0%, 2.5%, 3.0%, 3.5%, 4.0%, and 4.5% from test 4 in Table 1, and (d) σxa and σxm of the hysteresis loops as a function of the number of cycles N from test 4 in Table 1.

Figure 4

Experimental and simulation responses (true stresses and strains) of UHMWPE under stress-controlled cycle: (a) experimental hysteretic response with amplitude 12.5 MPa and mean 0 MPa for the first 10 cycles and 4.5 MPa for the subsequent 90 cycles, and stress rate of 0.87 MPa/s, test 5 in Table 1, (b) hysteresis response simulation of test 5 in Table 1 using the refined model parameters in Table 3, (c) strain amplitude versus the number of cycle N for tests 5 and 6 in Table 1, and (d) strain mean versus the number of cycle N for tests 5 and 6 in Table 1.

Figure 5

VBOP model parameter determination using strain-controlled responses. (a) Fitting of the stable hysteresis loops from 0.5%, 1%, and 2% strain amplitude cycles (test 2 in Table 1) and (b) fitting of stress amplitudes (σxa) from test 2 in Table 1.

Figure 6

Simulation by VBOP model using the strain-controlled response determined model parameters in Table 2. (a) Experimental and simulated monotonic responses and (b) hysteresis response simulation of test 5 in Table 1 using the model parameters in Table 2.

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