Journal
RHEOLOGICA ACTA
Volume 56, Issue 12, Pages 955-970Publisher
SPRINGER
DOI: 10.1007/s00397-017-1046-8
Keywords
Large-amplitude oscillatory extension; LAOE; Styrene-butadiene rubber; SBR; Steady uniaxial extension strain-hardening spring; Voigt element; Treloar spring; Modified Treloar spring
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Funding
- Canada Research Chairs program of the government of Canada
- Faculty of Applied Science and Engineering of Queen's University at Kingston through a Research Initiation Grant (RIG)
- Greek General Secretariat for Research and Technology [Thalis-380238 COVISCO]
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In this work, we subject elastomers to a fixed pre-stretch in uniaxial extension, epsilon (p) , upon which a large-amplitude, epsilon (0), oscillatory uniaxial extensional (LAOE) deformation is superposed. We find that if both epsilon (p) and epsilon (0) are large enough, the stress responds with a rich set of higher harmonics, both even and odd. We further find the Lissajous-Bowditch plots of our measured stress responses versus uniaxial strain to be without twofold symmetry and, specifically, to be shaped like convex bananas. Our new continuum model for this behavior combines a new nonlinear spring, in parallel with a Newtonian dashpot, and we call this the Voigt model with strain-hardening. We consider this three-parameter (Young's modulus, viscosity, and strain-hardening coefficient) model to be the simplest relevant one for the observed convex bananas. We fit the parameters to both our LAOE measurements and then to our uniaxial elongation measurements at constant extension rate. We develop analytical expressions for the Fourier components of the stress response, parts both in-phase and out-of-phase with the extensional strain, for the zeroth, first, second, and third harmonics. We find that the part of the second harmonic that is out-of-phase with the strain must be negative for proper banana convexity.
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