Fracture and mechanical behavior of rubber-like polymers under finite deformation in biaxial stress field

A study on the mechanical properties of rubbery polymers under finite deformation is presented here using the biaxial stress relaxation method for the experimental study. In the first part the gradient functions of the strain energy density function are determined as functions of I1 and I2, which are the invariants of the deformation sensor, by biaxial stress relaxation testing. The following results were found for both vulcanized natural rubber and SBR. 1. Each ∂W/∂I1 and ∂W/∂I2 is a function of both I1 and I2, especially in the small deformation region. However, the functions take on almost constant values and become flat for relatively large deformations. 2. The temperature dependence of these functions are such that ∂W/∂I1 is proportional to the absolute temperature in the rubbery region whereas ∂W/∂I2 is almost independent of temperature. 3. The relaxation properties of both functions are very close and have almost the same relaxation rate. In the second part some discussion on the cause of the functional forms of these functions are presented using a structural model composed of 16 stretchable elements. The result is that ∂W/∂I, can be related to the energy required for the elongation of these elements, and aW/aI, corresponds to the energy required for the expansion of surfaces which are formed by the elements. This implies that ∂W/∂I2 corresponds to an intramolecular energy, such as entropy elasticity, and ∂W/∂I1 to the energy caused by intermolecular forces in the body. This estimation is also supported by an experiment in which ∂W/∂I2 took a negative value in the small deformation region. Finally, the fracture properties of the rubber-like polymers are observed by using both the biaxial tensile tester and the thin film inflation method. The fracture criterion of constant stretch ratio is proposed. This simple criterion can be deduced from the structural model presented here. It is also shown, using plasticized polyvinyl chloride, that if the material changes its property from rubbery to glassy, this simple relation is no longer applicable.