抄録
Taking into account the effects of the flow history on the rate of formation and breaking of junction points, the memory function in Lodge's equation is modified as follows:
μ(t;t')=∫∞-∞H(λ)/λR(t';λ)/R0(λ)e-1/λ[(t-t')+β∫tt'h(t", t')dt"]d ln λ
h(t;t')=√Tr(C-1(t')-I)
here H(λ), λ and β are relaxation spectrum in the linear region, relaxation time and a dimension less parameter respectively. R(t';λ) and R0(λ) are the rate of formation of junction points at time t' in the nonlinear and linear region, respectively. C-1(t') is the Finger strain tensor and I is the unit tensor.
Using this memory function, the integral constitutive equation is represented by
τ=pI+∫t-∞μ(t;t')[(l+ε)(C-1(t')-I)+ε(C(t')-I)]dt'
where τ, p and ε are stress tensor, hydrostatic pressure and dimensionless parameter respectively. C(t') is the Cauchy-Green strain tensor.
In the case of R(t';λ)=R0(λ), this constitutive equation makes the following predictions.
(1) The non-Newtonian viscosity curve for the broad box type relaxation spectrum is nearly the same as the Bueche-Harding stand curve7).
(2) The non-Newtonian viscosity curve for the narrow box type relaxation spectrum (including the case of single relaxation time) properly represents non-Newtonian viscosities of monodisperse polystyrene melts8)9).
(3) The first normal stress coefficient is proportional to γ-1.5 for large shear rate γ.
