Non-Linear Behavior of Viscoelastic Materials. I. Disperse Systems of Polystyrene Solution and Carbon Black

Abstract

To determine non-linear viscoelasticity parameters for disperse and high-polymeric systems, some fundamental relations have been derived between these parameters and the experimental quantities by viscoelastometry, particularly with a torsionally oscillating rheometer, on the basis of the general theory presented by Green and Rivlin. The non-linear viscoelasticity of several disperse systems consisting of polystyrene solutions and carbon black has been measured by means of the torsionally oscillating rheometer at various temperatures ranging from 100 to 170°C, and in a frequency range from 2×10−3 to 0.5 cycle per sec. As a result of harmonic analysis of the experimental results, it has been revealed that the resultant torque consists of the fundamental component and odd harmonics, and that the energy dissipated during one cycle is the same as that calculated from the fundamental component alone. Frequency dependence curves at various temperatures for G1′ and G1″, which correspond to G′ and G″ for linear viscoelastic materials, can be superposed into master curves by horizontal and vertical shifts. The master curves manifest a plateau lower than the ordinary rubbery plateau on the low frequency side.

Viscoelastic properties of rubber-modified polymeric materials at elevated temperatures

“…C' curves as well as C" curves exhibit the "second plateau", which was first named for disperse systems of solid particles in polymer liquids (39). The second plateau becomes clear and the intensity becomes higher with increasing particle content, as seen from Figs.…”

“…The effect of the particles on C" at low frequencies is much less than that on C'. This behavior is quite different from that for solid particlecontaining polymeric systems (39), which have a higher-order structure of the particlesso called agglomerated structure, skeleton structure or network structure. Another difference between the rubber-modified systems and solid particle-dispersed systems is that the former still shows a linear viscoelastic behavior for strain amplitudes of 10 % and higher, while the latter shows a remarkable non-linear viscoelasticity and a plastic flow (very flat C" curves in the low frequency region) under a strain of less than 3 Z.…”

A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)

“…From the 1960's to 1970's, early publications [9][10][11][12][13][14][15][16][17][18][19] investigated nonlinear phenomena for various viscoelastic materials under oscillatory shear and proposed the methods of Fourier transform analysis and stress waveform analysis. Technical problems severely hindered further progress at that time, specifically hardware and software limitations such as torque transducer resolution and computational power.…”

Strain-rate frequency superposition in large-amplitude oscillatory shear

“…The energy dissipated per unit volume per cycle of strain oscillation is ǫ(t; ω, γ 0 ) ≡ 2π/ω 0 σdγ [3]. Ganeriwala and Rotz [7] have shown that on substituting the one-dimensional Green-Rivlin constitutive equation [33] for the stress into this formula and assuming a sinusoidal strain one obtains ǫ = πγ itive, but places no restriction on the sign of the other moduli.…”

“…In order to probe their linear viscoelastic response, materials are frequently subject to small-amplitude oscillatory shear, wherein an applied sinusoidal strain γ(t) = γ 0 sin(ωt) (here γ 0 is the strain amplitude, ω is the angular frequency, t is the time) results in a stress response σ(t; ω) = γ 0 [G [1], and are functions of the angular frequency. By contrast, the resultant stress from a large-amplitude oscillatory shear (LAOS) [2][3][4][5][6][7][8][9][10][11] test contains higher harmonics which may be interpreted in terms of harmonic moduli G ′ n and G ′′ n (subscript n refers to the n-th harmonic, see Section III(A) for the definition), which are functions of both the strain amplitude and the angular frequency. The moduli G ′′ 1 may be physically interpreted [7] in terms of the energy dissipated per unit volume per cycle of strain oscillation (see Section III(E) below).…”