Normal stress ratio predicted by viscoelastic constitutive equations

Abstract

The first and second normal stress differences, N1 and N2 in steady shear flow are calculated using differential constitutive equations proposed by Leonov and Giesekus. At low shear rates, the Leonov model gives -N2/N1=0.25 for both single and multiple relaxation modes. In the Giesekus model, -N2/N1 increases with increasing anisotropy mobility parameter α. Both models predict that -N2/N1 is a decreasing function of the shear rate at high shear rates. The shear rate dependence of -N2/N1 becomes weaker with increasing width of relaxation time distribution. The BKZ type integral constitutive equation is employed to investigate the effect of a model parameter b (=N2/N1) on steady planar, uniaxial and biaxial extensional flows. It is found that the strain rate dependences of planar2 and biaxial extensional viscosities are very sensitive to the parameter b, where 2 in planar extension denotes the direction of constant width.