Volume 22, Issue 1, February 1978
Index of content:
22(1978); http://dx.doi.org/10.1122/1.549470View Description Hide Description
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 deformationrelaxationmodulus 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.
22(1978); http://dx.doi.org/10.1122/1.549471View Description Hide Description
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.
22(1978); http://dx.doi.org/10.1122/1.549500View Description Hide Description
A multiple integral expansion of the Boltzmann superposition principle when applied to sinusoidal shear oscillations becomes We have evaluated this constitutive equation with hollow cylinders of polycarbonate and polymethylmethacrylate at 1 Hz from to below their β transitions. Shear strain amplitude, 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. and vs temperature compare excellently to the literature and our own small strain measurements of and on rectangular bars in free and forced torsion. and higher harmonic terms were found to be small. All nonlinearity in the range studied can be modeled by and is in the range is negative and for both materials. and show a glass transition similar to For polycarbonate they show a very large transition at the of 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.
22(1978); http://dx.doi.org/10.1122/1.549472View Description Hide Description
A nonisothermal theory of viscoelastic media, motivated by thermomechanical behavior of polymericmaterials 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.