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Feb 1978

Volume 22, Issue 1, pp. 1-89


The Behavior of Rubberlike Materials in Moderately Large Deformations

R. Bloch, W. V. Chang, and N. W. Tschoegl

J. Rheol. 22, 1 (1978); http://dx.doi.org/10.1122/1.549470 (32 pages) | Cited 1 time

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Introduction of the nonlinear n‐measure of strain into the Boltzmann superposition integral allows accurate prediction of the viscoelastic behavior of soft (rubberlike) materials if the relaxation spectrum remains unchanged during the deformation. This condition is generally satisfied in moderately large deformations (typically about 150% strain in simple tension). Apart from the strain parameter n, only the small deformation relaxation modulus is required by the theory. Both pieces of information are obtained from the response to a step of strain in simple tension. Data obtained in the temperature range −40 to 23°C on a dicumyl‐peroxide‐cured styrene‐butadiene rubber (SBR), lightly plasticized with silicone oil (1.5%), gave excellent agreement with the theory in various strain histories including sensitive tests in which small deformations were superposed on a finite stretch. Published data were used to corroborate the theory further. The temperature dependence of n was obtained from the authors' data on SBR and from published data on Viton A‐HV. The dependence of n on crosslink density and swelling ratio was also examined.
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83.80.Va Elastomeric polymers
83.60.Df Nonlinear viscoelasticity

Strain Independent Nonlinearity in Peroxide‐Cured Styrene‐Butadiene Rubber

R. Bloch, W. V. Chang, and N. W. Tschoegl

J. Rheol. 22, 33 (1978); http://dx.doi.org/10.1122/1.549471 (19 pages)

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Emulsion polymerized compression molded dicumyl‐peroxide‐cured SBR does not obey Boltzmann's principle for the superposition of time effects at very small strains at which the true stress‐strain relation is linear. Normally, nonpreservation of time shift invariance is linked with stress‐strain nonlinearity. In this anomalous styrene‐butadiene rubber (SBR) the former effect can be studied independently of the latter.
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83.80.Va Elastomeric polymers
83.60.Df Nonlinear viscoelasticity

Nonlinear Dynamic Mechanical Moduli for Polycarbonate and PMMA

W. M. Davis and C. W. Macosko

J. Rheol. 22, 53 (1978); http://dx.doi.org/10.1122/1.549500 (19 pages) | Cited 2 times

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A multiple integral expansion of the Boltzmann superposition principle when applied to sinusoidal shear oscillations becomes σ(t)=γ0[G1′ sinωt+G1″ cosωt]+γ03[G3′ sinωt+H3′ sin3ωt+G3″ cosωt+H3″ cos3ωt]+γ05[0]. We have evaluated this constitutive equation with hollow cylinders of polycarbonate and polymethylmethacrylate at 1 Hz from Tg to below their β transitions. Shear strain amplitude, γ0, was increased incrementally from the linear to the nonlinear region. Phase angles and harmonic content were determined with a Rheophasor digital cross correlator. At the maximum strain used, 2–4%, deformation was completely recoverable, after some time, upon returning to the linear region. G1′ and G1″ vs temperature compare excellently to the literature and our own small strain measurements of G′ and G″ on rectangular bars in free and forced torsion. H3′, H3″, and higher harmonic terms were found to be small. All nonlinearity in the range studied can be modeled by G3′ and G3″ is in the range 1010–1011 N∕m2. G3′ is negative and ∼10 (G3″) for both materials. G3′ and G3″ show a glass transition similar to G1″. For polycarbonate they show a very large transition at the Tβ of G1″. PMMA showed almost no β transition in the nonlinear constants. Molecular explanations and implications for impact and fatigue behavior are discussed as well as potential errors in typical dynamic mechanical data due to these nonlinearities.
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83.10.Gr Constitutive relations
83.80.-k Material type

On Thermomechanics of Polymers in the Transition and Rubber Regions

M. J. Crochet and P. M. Naghdi

J. Rheol. 22, 73 (1978); http://dx.doi.org/10.1122/1.549472 (17 pages)

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A nonisothermal theory of viscoelastic media, motivated by thermomechanical behavior of polymeric materials in the transition zone between the rubber and glassy states, was developed previously by Crochet and Naghdi and included as a special case a theory with small deformation suitable for thermorheologically simple materials. The object of the present paper is to modify the form of the previous constitutive equations slightly in order to extend the validity of the theory to the rubber region in which the medium behaves elastically.
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83.60.St Non-isothermal rheology
83.10.Gr Constitutive relations
83.80.-k Material type
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