THE MULLINS EFFECT IN EQUIBIAXIAL EXTENSION AND ITS INFLUENCE ON THE INFLATION OF A BALLOON

It is a common practice to manually stretch a toy balloon several times prior to inflation. This preconditioning reduces the pressure required to fully inflate the balloon, and thus eases the task of inflation. The reduction in pressure required to inflate the balloon is mainly a result of the Mullins effect. The Mullins effect, also known as stress softening, refers to a change in material behavior resulting from prior deformation. The results of cyclic inflation experiments performed with latex rubber balloons are presented. Some interesting aspects of the inflation behavior are noted, and the effect of preconditioning on the inflation behavior is quantified. The balloons are modeled as incompressible, spherical membranes which undergo an equibiaxial extension during inflation. This mode is used to calculate the stress-strain behavior of the balloon material in an equibiaxial extension. We generalize a constitutive equation for the Mullins effect in uniaxial extension, first proposed by Johnson and Beatty [1], to an equibiaxial extensional deformation. We are able to make certain predictions about the results of our balloon inflation experiments without specification of the two functions which comprise the constitutive equation. Our method of interpretation of experimental results from the balloon inflation tests is similar to the method in [1] for the small transverse vibration of a stretched rubber cord. Finally, we demonstrate that the equibiaxial extensional deformation of an isotropic, incompressible material is kinematically equivalent to the uniaxial compression of that material. The results of our balloon inflation experiments are used to calculate the stress softening behavior of latex rubber in uniaxial compression. The calculated behavior indicates that latex rubber does indeed stress soften in uniaxial compression. This observation confirms the early experimental findings of Mullins [2], but contradicts the analytical predictions of Lee and Williams [3].