Fourier transform mechanical analysis for determining the nonlinear viscoelastic properties of polymers

Abstract

Fourier Transform Mechanical Analysis (FTMA) has been used to study the strain amplitude dependent nonlinear dynamic mechanical properties of two elastomer compounds, nitrile rubber (NBR) and Neoprene, at various frequencies up to 750 Hz. Basic theory and experimental results are presented for one‐dimensional isothermal single frequency simple shear deformation. The Green‐Rivlin constitutive equation was used to model the observed behavior. The energy dissipation mechanism and a physical meaning for the material functions in the Green‐Rivlin representation have also been examined. The stress Fourier spectrum contained terms at the input frequency and its higher harmonics. It can qualitatively indicate the type of mathematical mode that best describes the observed behavior. The first harmonic storage and loss moduli showed strong dependence on the strain amplitude and frequency. The FTMA methodology presented can be used to systematically conduct nonlinear dynamic mechanical studies on any polymer. It can provide enough insight which, along with a knowledge of the molecular structure, may indicate a path for developing a better representative continuum constitutive model of these complex materials.

Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials

“…The local shape of a Lissajous curve depends on all of the harmonics, but the total energy dissipated per cycle by any harmonic strain-controlled LAOS response is only a function of the first-order viscous Fourier coefficient (Ganeriwala and Rotz (1987)), and is given by…”

Strain-rate frequency superposition in large-amplitude oscillatory shear

“…In all three test configurations, we note that the points cluster about the expected value of 1, with a maximum deviation of approximately 2%, the residual difference being attributed to experimental uncertainty in the measurement of G ′′ 1 . The energy-dissipation rate per unit volume in LAOS can be shown [7] to equalǫ(t; ω, γ 0 ) = ωγ…”

“…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. It is plausible that the other harmonic moduli are involved in reversible exchanges of energy in LAOS.…”

“…Most LAOS studies to-date have been restricted to the study of stress-strain curves [2,5,8,11] or the ratios of the harmonics of the stress amplitude spectrum [4,6,7]. In occasional studies [9], the harmonic moduli have been calculated in a strain amplitude or an angular frequency sweep test.…”

“…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).…”