Biaxial Propertis of Rubber Balloons

INTRODUTION

Constitutive models for rubbery material have been used to simulate the finite deformation response of rubber network. The classical constitutive equations were mainly based on statistical approach assuming the Gaussian distribution for randomly-oriented long chains of network. This attitude led to rather good prediction on tensile stretch-strain behaviour at low and moderate strains. However, Constitutive models based on the Gaussian distribution assumption fail to predict tensile stress-strain behaviour of network at large strains, owing to, orientation on macro molecules in the direction of stretch. The statistical approaches have been mainly modified by using inverse Langevin distribution function instead of the Gaussian function. Inverse Langevin distribution function successfully recognises finite extensibility of material and hence models that correspond the change of individual chain to applied deformation show an upturn in tensile stress –strain curve. But this model can not successfully describe other states of deformation e.g. biaxial deformation. 3-chain model is the simplest model of the non-Gaussian network. This model based on the assumption that the real network can be replaced by three sets of chains parallel to the axes of a rectangular coordinate system. A source of error in 3-chain model is affine presumption i.e. this model assumes the effect of the deformation is to change a single network in the same ratio of the bulk rubber. The four-chain model is a better estimation of the conditions existing in an actual network. This model considers a cell of network containing four chains emanating from a common junction point to each edge. Comparing to the 3-chain model, this model has the advantage of non-affine approach. In the 8-chain model the chains are located inside the diagonals of the unit cell and deforms with cell. The chains in this non-affine model undergo tensile deformation for all imposed deformation. In the full-network...