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RESEARCH PAPERS

Constitutive Modeling of a Thermoplastic Olefin Over a Broad Range of Strain Rates

[+] Author and Article Information
Yan Wang1

Macromolecular Science and Engineering, University of Michigan, Ann Arbor, MI 48109-1055

Ellen M. Arruda2

Department of Mechanical Engineering, Macromolecular Science and Engineering, University of Michigan, Ann Arbor, MI 48109-2125arruda@umich.edu

1

Currently at PPG Industries, Glass Technology Center, Pittsburgh, PA 15238.

2

Corresponding author.

J. Eng. Mater. Technol 128(4), 551-558 (Jul 13, 2006) (8 pages) doi:10.1115/1.2349501 History: Received October 25, 2005; Revised July 13, 2006

A microstructually motivated, three-dimensional, large deformation, strain rate dependent constitutive model has been developed for a semi-crystalline, blended, thermoplastic olefin (TPO) (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). Various experiments have been conducted to characterize the TPO and to verify the modeling approach (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). The model includes a quantitative rate-dependent Young’s modulus, a nonlinear viscoelastic response between initial linear elastic response and yield due to inherent microstructural irregularity, rate and temperature dependent yield with two distinctive yield mechanisms for low and high strain rates, temperature-dependent strain hardening, plastic deformation of crystalline regions, and adiabatic heating. It has been shown to accurately capture the observed TPO stress-strain behavior including the rate-dependent initial linear elastic response; temperature, strain rate, and deformation state-dependent yield; temperature and deformation state-dependent strain hardening; and pronounced thermal softening effects at high (impact) strain rates. The model has also been examined for its ability to predict the response in plane strain compression based on material parameters chosen to capture the uniaxial compression response. The model is predictive of the initial strain rate dependent stiffness, yield, and strain hardening responses in plane strain. Such predictive capability demonstrates the versatility with which this model captures the three-dimensional anisotropic nature of TPO stress-strain behavior.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Dynamic mechanical analysis spectra of the TPO. Loss modulus (E″) and damping (tanδ) peaks denote the glass transition temperatures of the distinct HDPE (−120°C), EPDM (−45°C), and PP (10°C) phases in the TPO. The sharp transition at 165°C denotes the PP melting temperature.

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Figure 2

Experimental true stress versus true strain curves under uniaxial compression loading and unloading at constant true strain rates from −0.001 to −10s−1, and 23°C ambient. Strain rate dependent initial modulus, yield strength, and strain hardening are all evident in this strain rate range.

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Figure 3

The compression stress-strain response of TPO from ASHPB tests at average strain rates from −450 to −3520s−1 and 23°C ambient. Strain rate dependent response as in Fig. 2 is also evident here, along with thermal softening due to adiabatic heating effects.

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Figure 4

The rate dependent stress-strain behavior of TPO over a broad range of strain rates. Results from Figs.  23 are here combined to demonstrate the transition in the large deformation response over more than seven decades in strain rate.

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Figure 5

The strain rate dependence of the TPO Young’s modulus at 23°C. The trendline highlights the nonlinear dependence of the modulus on rate or on inverse time.

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Figure 6

The dependence of yield stress in compression on strain rate. Two distinct mechanisms exist; one dominates at low strain rates, the other at high rates.

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Figure 7

Experimental stress versus strain curves under isothermal uniaxial compression loading and unloading at constant strain rate of −0.01s−1 and various temperatures. The temperature dependent yield strength (horizontal lines on graph) and strain hardening (arrow lengths) are clearly evident for this TPO.

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Figure 8

A schematic of TPO plastic deformation mechanisms in compression including amorphous chain orientation and crystallographic slip

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Figure 9

A one-dimensional analog of the TPO constitutive model showing elastic and inelastic deformation mechanisms

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Figure 10

Finite deformation kinematics. The total deformation gradient F maps the reference configuration to the deformed (or current) configuration. It is decomposed into elastic, Fe, and plastic Fp, parts. Fp is further decomposed into crystallographic flow, Ff, and orientation strain hardening of the amorphous phase, Fh.

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Figure 11

Simulation results for the stress-strain response of the TPO at low strain rates at 23°C and under uniaxial compression

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Figure 12

Comparison between modeling results and predictions and experimental data of the TPO at high strain rates and 23°C ambient. The thin black lines are the simulations and the red symbols are the experimental curves.

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Figure 13

Comparison between modeling result and experimental data for the TPO under uniaxial compression at ε̇=0.001s−1 and 23°C

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Figure 14

Comparison between modeling prediction and experimental data of the TPO under uniaxial compression at ε̇=0.01s−1 and 23°C

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Figure 15

Comparison between modeling result and experimental data of the TPO under uniaxial compression at ε̇=0.1s−1 and 23°C

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Figure 16

Comparison of the modeling results and predictions and experimental data of the TPO under uniaxial compression and plane strain compression at ε̇=−0.01s−1 and ε̇=−0.001s−1 and at 23°C

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