Viscoelastic Properties of a Rubber Vulcanizate Under Large Deformations in Equal Biaxial Tension, Pure Shear, and Simple Tension

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Abstract
Stress‐strain data were determined on an unfilled styrene‐butadiene rubber vulcanizate in equal biaxial tension (EBT) at deformations up to rupture. Tests were made at temperatures from −43° to 90°C and at extension rates from 0.15 to 4 min −1 . The data are represented in terms of a time‐ and temperature‐independent function, Ω(χ), the reduced modulus, T 0 F(t/a T )/T, and the maximum extensibility, λ m (t/a T ), the latter two quantities being functions of the temperature‐reduced time, t/a T . The function Ω(χ) gives the stress‐strain relationship for the material in a reference state for which the modulus is unity and λ m =λ m 0 , the equilibrium value. The maximum extensibility equals the extension ratio at which the slope of a stress‐strain curve from isochronal data becomes infinite; it cannot be measured directly because rupture always occurs at an extension less than λ m . Data from extensive tests in simple tension (ST) have been reported previously, as well as data in pure shear (constrained biaxial tension, CBT) at 1<λ<2.5, where λ is the extension ratio. The three Ω(χ) functions, which represent stress‐strain behavior in ST, CBT, and EBT, were considered in terms of the Valanis‐Landel theory of finite elasticity, which is based on the assumed validity of the strain‐energy function W=ω(λ 1 )+ω(λ 2 )+ω(λ 3 ). In this way, the characteristic function λω′(λ)/F was evaluated over the range 0.028<λ<7.5. From this function along with the modulus, the stress‐strain behavior in any pure homogeneous deformations can be calculated readily over extended ranges of temperature and extension rate. Because λ m (t/a T ) depends somewhat on the type of deformation ( λ m 0 in ST is at least 30% greater than in EBT), data at very large deformations under an arbitrary pure homogeneous deformation can be derived only if λ m is known as a function of both t/a T and the type of deformation.

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