Stresses and volume changes in a polymer loaded axially in a rigid die

Abstract

We consider the boundary value problem of an isotropic, linearly elastic or linearly viscoelastic material constrained in a rigid die and loaded by a uniform axial stress σ 33 (‘piston/die’ problem). The elastic solution is obtained in terms of the shear and bulk modulus of the material, and the Laplace-transformed form of the viscoelastic solution in terms of the Laplace transforms of the shear and bulk relaxation moduli. Solutions to the viscoelastic problem at t = 0 and for t → ∞ are found, which involve only values of the relaxation moduli at these times. The complete solutions in time space for a viscoelastic material which has a time-independent bulk modulus, and behaves like a Maxwell or Voigt model in shear, are calculated and discussed. For typical elastic and solid viscoelastic materials, the volume change in the ‘piston/die’ situation is only 60–80% of that observed in the hydrostatic case with P = − σ 33. The ‘piston/die’ geometry is therefore not a universally applicable method for pressure-volume-temperature ( PVT) studies. Methods in which a material is subjected to true hydrostatic pressures (achieved through the use of a confining fluid) must be preferred.