Tube inflation of viscoelastic fluids at a constant growth rate

The simultaneous radial inflation and axisymmetric extension of an incompressible viscoelastic tube is modeled analytically as an idealization of the blow-molding process. The working fluid is assumed to obey a single integral constitutive model with a power-law damping function, accommodating behavior ranging from extreme strain hardening (akin to the Lodge–Maxwell model) to strain thinning leading to plastic flow. The tube is sufficiently long so that end effects can be neglected. The axial and radial extension rates at the outer tube radius are assumed to be constant in time. Exact analytical expressions are derived for the tube thickness H, the pressure difference ΔP across the tube wall, and the axial force F required for sustaining the tube inflation with constant stretch history. Their evolution is studied over a variety of deformation intensities, operating conditions, and flow geometries. A valuable insight in the effects of rheology on the blow-molding process is gained.