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Mechanics of Composite Materials

, Volume 50, Issue 6, pp 763–776 | Cite as

A Three-Scale Model of Basic Mechanical Properties of Nafion

  • V. Kafka
  • D. Vokoun
Article
  • 109 Downloads

The mechanical properties of Nafion are explained and modeled on the basis of Kafka’s general mesomechanical model and confronted with experimental results. In this approach, Nafion is looked upon as a composite consisting of three constituents: a crystalline Nafion, amorphous Nafion, and water. Taking into account the degree of hydration, its elastic, elastic-plastic, and hysteretic properties are discussed and modeled. It is shown how the interaction between the three constituents manifests itself on the macroscale.

Keywords

Nafion mechanical properties mesomechanics material structure hydration 

Nomenclature

General mechanics

σij

stress tensor

δijσ

isotropic part of σ ij (σ = σ ii /3)

sij

deviatoric part of σ ij (σ ij − δ ij σ)

εij

strain tensor

δijε

isotropic part of ε ij (ε = ε ii /3)

eij

deviatoric part of ε ij (ε ij δ ij ε)

δij

Kronecker’s delta

E

Young’s modulus

ν

Poisson’s ratio

μ = (1+ν)/E

deviatoric elastic compliance

ρ = (1 − 2ν) / E

isotropic elastic compliance.

Specific symbols

\( \overline{\Big|} \)

overbar that relates the symbol | to its macroscopic value — the average in the representative volume element RVE

|ω or |ω

index that relates the symbol | to the ω -constituent — the average in the subvolume of RVE that is filled in by the ω -constituent

ω = e

elastic constituent in the general two-phase model

ω = n

inelastic constituent in the general two-phase model

ω = a

amorphous constituent in Nafion

ω = c

crystalline constituent in Nafion

ω = w

water comprised in Nafion

ω = wa

aggregate of two constituents in Nafion: of the amorphous Nafion with water

|ij

Einstein’s notation

\( {\varepsilon}_{ij}^{\prime }={\varepsilon}_{ij}-{\overline{\varepsilon}}_{ij}; \)

δijε

isotropic part of ε ij

eij

deviatoric part of ε ij

σij

stress related to ε ij similarly as σ ij is related to ε ij

δijσ

isotropic part of σ ij

sij

deviatoric part of σ ij

νe{νn}

volume fraction of the elastic {inelastic} constituent in the general two-phase model

νa{νw}

volume fraction of the amorphous Nafion {of water} in the aggregate of amorphous Nafion with water

Vω

volume fraction of the ω - constituent in the total Nafion (ω = a, c, w, wa);

\( {R}_a^c=\frac{V_c}{V_a}; \)

ca

elastic limit of s 11 a in the a -constituent

Cwa

elastic limit of s 11 wa in the wa -constituent

nω

structural parameter (ω = a, c, w, wa)

|Ω

superscript that relates the symbol | to the respective Ω -specimen of Nafion

Ω = H

hydrated specimen

Ω = D

dry specimen

p = V c H η c μ c  + V wa H η wa μ wa H

\( q=\frac{\mu_c}{V_c^H}\left(p\left|+{\eta}_c{\eta}_{wa}{\mu}_{wa}^H\right.\right) \).

\( \overset{\cdot }{h} \)

formal variable equal to 0 in elasticity and to \( \overset{\cdot }{\lambda } \) in plasticity

|L

value of | at the elastic limit.

Notes

Acknowledgements

This work was supported by the Czech Science Foundation within projects P108/10/1296 and 103/09/2101. Acknowledged is also the support through the Institutional Project RVO: 68378297. D. Vokoun would like to thank Dr. M. Paidar for fruitful discussions.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute of Theoretical and Applied Mechanics ASCRPragueCzech Republic
  2. 2.Institute of Physics ASCRPragueCzech Republic

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