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Journal of Fuel Cell Science and Technology | Volume 12 | Issue 6 | research-article
Research Papers

Development and Validation of a Uniaxial Nonlinear Viscoelastic Viscoplastic Stress Model for a Fuel Cell Membrane

[+] Author and Article Information
Jessica A. May, Michael W. Ellis

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061

David A. Dillard, Scott W. Case

Department of Biomedical Engineering and Mechanics,
Virginia Tech,
Blacksburg, VA 24061

Robert B. Moore

Department of Chemistry,
Virginia Tech,
Blacksburg, VA 24061

Yonqiang Li, Yeh-Hung Lai, Craig A. Gittleman

General Motors Research and
Development Center,
Warren, MI 48093

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF FUEL CELL SCIENCE AND TECHNOLOGY. Manuscript received July 3, 2015; final manuscript received December 3, 2015; published online January 29, 2016. Assoc. Editor: Dirk Henkensmeier.

J. Fuel Cell Sci. Technol 12(6), 061011 (Jan 29, 2016) (10 pages) Paper No: FC-15-1044; doi: 10.1115/1.4032491 History: Received July 03, 2015; Revised December 03, 2015
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Proton exchange membranes (PEMs) in operating fuel cells are subjected to varying thermal and hygral loads while under mechanical constraint imposed within the compressed stack. Swelling during hygrothermal cycles can result in residual in-plane tensile stresses in the membrane and lead to mechanical degradation or failure through thinning or pinhole development. Numerical models can predict the stresses resulting from applied loads based on material characteristics, thus aiding in the development of more durable membrane materials. In this work, a nonlinear viscoelastic stress model based on the Schapery constitutive formulation is used with a viscoplastic term to describe the response of a novel membrane material comprised of a blend of perfluorocyclobutane (PFCB) ionomer and poly(vinylidene fluoride) (PVDF). Uniaxial creep and recovery experiments characterize the time-dependent linear viscoelastic compliance and the fitting parameters for the nonlinear viscoelastic viscoplastic model. The stress model is implemented in a commercial finite element code, abaqus®, to predict the response of a membrane subjected to mechanical loads. The stress model is validated by comparing model predictions to the experimental responses of membranes subjected to multiple-step creep, stress relaxation, and force ramp loads in uniaxial tension.
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Figures

Grahic Jump Location
Fig. 1

Geometry of tensile specimen

+Geometry of tensile specimen
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Geometry of tensile specimen
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Fig. 2

Regions of applicability of model parameters during creep and recovery

+Regions of applicability of model parameters during creep and recovery
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Regions of applicability of model parameters during creep and recovery
Grahic Jump Location
Fig. 6

Constitutive model calculations and experiments for creep and recovery tests. For each stress level, the dashed-dotted line represents the average experimental response, the dashed lines represent the 95% confidence interval for the experiments, and the solid line represents the fitted model.

+Constitutive model calculations and experiments for creep and recovery tests. For each stress level, the dashed-dotted line represents the average experimental response, the dashed lines represent the 95% confidence interval for the experiments, and the solid line represents the fitted model.
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Constitutive model calculations and experiments for creep and recovery tests. For each stress level, the dashed-dotted line represents the average experimental response, the dashed lines represent the 95% confidence interval for the experiments, and the solid line represents the fitted model.
Grahic Jump Location
Fig. 5

Finite element geometry used for evaluating the constitutive model

+Finite element geometry used for evaluating the constitutive model
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Finite element geometry used for evaluating the constitutive model
Grahic Jump Location
Fig. 4

Graphical demonstration of strain hardening

+Graphical demonstration of strain hardening
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Graphical demonstration of strain hardening
Grahic Jump Location
Fig. 3

Graphical demonstration of time hardening

+Graphical demonstration of time hardening
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Graphical demonstration of time hardening
Grahic Jump Location
Fig. 7

Constitutive model calculations and experiments for multiple-step stress loading “profile A.” The solid line represents the predicted response with time hardening, the dashed-dotted line represents the predicted response with strain hardening, and the dashed lines represent the independent experiments.

+Constitutive model calculations and experiments for multiple-step stress loading “profile A.” The solid line represents the predicted response with time hardening, the dashed-dotted line represents the predicted response with strain hardening, and the dashed lines represent the independent experiments.
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Constitutive model calculations and experiments for multiple-step stress loading “profile A.” The solid line represents the predicted response with time hardening, the dashed-dotted line represents the predicted response with strain hardening, and the dashed lines represent the independent experiments.
Grahic Jump Location
Fig. 8

Constitutive model calculations and experiments for multiple-step stress loading “profile B.” The solid line represents the predicted response with time hardening, the dashed-dotted line represents the predicted response with strain hardening, and the dashed lines represent the independent experiments.

+Constitutive model calculations and experiments for multiple-step stress loading “profile B.” The solid line represents the predicted response with time hardening, the dashed-dotted line represents the predicted response with strain hardening, and the dashed lines represent the independent experiments.
View Large  |  Save Figure  |  Download Slide (.ppt)
Constitutive model calculations and experiments for multiple-step stress loading “profile B.” The solid line represents the predicted response with time hardening, the dashed-dotted line represents the predicted response with strain hardening, and the dashed lines represent the independent experiments.
Grahic Jump Location
Fig. 9

Constitutive model calculations and experiments for 0.5%, 1%, and 3% stress relaxation. For each strain level, the solid line represents the predicted stress relaxation profile and the patterned lines represent the independent experiments.

+Constitutive model calculations and experiments for 0.5%, 1%, and 3% stress relaxation. For each strain level, the solid line represents the predicted stress relaxation profile and the patterned lines represent the independent experiments.
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Constitutive model calculations and experiments for 0.5%, 1%, and 3% stress relaxation. For each strain level, the solid line represents the predicted stress relaxation profile and the patterned lines represent the independent experiments.
Grahic Jump Location
Fig. 10

Constitutive model calculations and experiments for 0.01 N/min, 0.1 N/min, and 1.0 N/min force ramps. For each ramp rate, the solid line represents the predicted stress–strain curve and the patterned line represents the independent experiment.

+Constitutive model calculations and experiments for 0.01 N/min, 0.1 N/min, and 1.0 N/min force ramps. For each ramp rate, the solid line represents the predicted stress–strain curve and the patterned line represents the independent experiment.
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Constitutive model calculations and experiments for 0.01 N/min, 0.1 N/min, and 1.0 N/min force ramps. For each ramp rate, the solid line represents the predicted stress–strain curve and the patterned line represents the independent experiment.

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