Stafford (1969) has suggested that the multiple integral constitutive equation of nonlinear viscoelasticity is reduced to a single integral form when kernel functions are expressible as products of functions of single argument, and that stress relaxation experiments at various strains are sufficient to evaluate the kernel functions. In this paper, we examined applicability of the Stafford model for high density polyethylene (HDPE) and poly(vinyl chloride) (PVC). It was assumed that the kernel function was simply expressed by a power of time t-β (power-low model). The kernel functions were evaluated from previous stress relaxation data in uniaxial elongation up to the fourth order for HDPE and up to the second order for PVC, respectively. These values of kernel functions based on the power-law model were used to predict nonlinear behavior at uniaxial strains with various histories : two strains applied successively, loading and unloading at constant strain rate, and stress relaxation after elongation of constant rate. In the stress relaxation under two-step strain (i. e., two strains applied at an interval), the calculated values were in rough agreement with observed values when the second additional strain Δε was positive, while the calculated values were remarkably greater than the observed values when Δε was negative. In tensile behavior at constant strain rate, the calculated values of stress agreed with the observed values in the loading and relaxation processes, but they were greater than the experimental values in the unloading process. When the strain decreased after attaining a certain value, the applicability of the Stafford model was poor compared with that of the Schapery type equation (i. e., time-strain reduced model) discussed in the previous paper (this journal, 4, 72 (1976)).
A new method (Raised Cosine Pulse Method) of measurements of viscoelasticity is presented, which is based on the Fourier analysis of the after-effect function related to a shear strain pulse of cosine type. According to the Boltzmann superposition principle, the shear stress is represented by a convolution integral of the rate of strain and the after-effect function, and the complex shear modulus can be determined from the Fourier transform of the after-effect function. Thus, the Fourier transform of the stress obtained as the response to a given strain function allows us to evaluate the complex shear modulus over a wide range of frequency. In the presented method, a small shear strain pulse of cosine type is imposed on samples, and the measured stress is analyzed following the above principle. Tests of the Raised Cosine Pulse method were made on a 20% polystyrene solution in diethylphthalate and a 20% glass beads suspension in the polystyrene solution. In the former system, the viscoelastic functions obtained by this method were in close agreement with those obtained by the conventional dynamic measurement. In the latter system, the conventional method was not applicable because of the structural change of suspension occuring in the measurement, while the presented pulse method enabled us to evaluate the viscoelastic function at various phases in the course of the structural change.