Description of the non-linear shear behaviour of a low density polyethylene melt by means of an experimentally determined strain dependent memory function

Abstract

The applicability of a single integral constitutive equation with strain dependent memory function for the description of the nonlinear shear behaviour of a LDPE melt is examined. The generalized memory function is expressed as a product of Lodge's rubberlikeliquid memory function $$\mathop \mu \limits^ \circ (t - t\prime )$$ and a damping function h(γt, t′). $$\mathop \mu \limits^ \circ $$ characterizes the time dependence of the linear viscoelastic behaviour and is determined by measurements of the frequency dependence of the complex shear modulus. The damping function describes the nonlinearity of the shear behaviour and can directly be determined by measurements of the shear relaxation modulus. From the temperature invariance of the damping function it follows that also in the nonlinear range a variation of temperature only corresponds to a shift in time scale which can be described by the shift factora T (T). By means of the experimentally determined memory function the shear viscosity and the primary normal stress coefficient as functions of shear rate and temperature can be predicted. The time dependence of the shear stress and of the primary normal stress difference in stressing tests and the relaxation behaviour is described correctly.