Nonlinear Viscoelasticity of Rubber Materials: Payne Effect and Differential Dynamic Modulus

Abstract

Rubber materials are used normally in large deformations, that is, in nonlinear conditions. So, nonlinear viscoelasticity is important for the characterization of rubber materials. So-called Payne effect, strain amplitude dependence of dynamic modulus, is one of the examples for nonlinear behaviors in rubber materials.In linear viscoelasticity, we can determine experimentally peak stress, peak strain, and phase angle difference in stress and strain waves. Hence we can define storage and loss modulus, GЈ and GЉ, respectively. In nonlinear viscoelasticity, however, stress wave deviates from a simple sinusoidal wave. Therefore, we may discuss Payne effect on rubber materials by absolute values of dynamic modulus, |G*|. We need additional information on viscoelasticity to discuss Payne effect.In this work, strain amplitude, g L, and phase angle, wt, dependence of differential dynamic modulus, G*(w, g L ; t) for carbon black filled, cured and unfilled, cured SBRs were tested in large amplitude oscillatory shear (LAOS) at g L ϭ0.005 Ϫ2.0 and n L ϭ0.001 Hz (period Tϭ1000 s) using self-made biaxial rheometer. Small oscillations (g S ϭ0.005, n S ϭ0.2 Hz) were superposed orthogonally on LAOS. Strain softening in G* was found depending on both g L and wt. Unfilled, cured rubber showed affine-like change with LAOS in both GЈ and GЉ, while filled, cured rubber did partial recovery in GЈ at peak position of LAOS and additional enhancement in GЉ. As a result, filled, cured rubber showed much higher values of differential loss tangent (DLT) in LAOS than unfilled, cured one, indicating that DLT may be useful for novel index of heat generation in periodical deformations of rubber materials.

Evidence of the Transition from a Flexible to Rigid Percolating Network in Polymer Nanocomposites

“…The addition of solid nanoparticles into polymers is an indispensable step toward improving their mechanical, thermal, and other physical properties for many industrial applications. − Together with the hydrodynamic effect induced by the presence of nanoparticles, the formation of an interfacial region surrounding the nanoparticle with structural and dynamic properties different from the neat polymer is thought to be the origin of the mechanical reinforcement of polymer nanocomposites (PNCs) at low filler loadings. ,,− As the filler volume fraction increases by more than 10%, an abrupt enhancement in the mechanical reinforcement has been frequently reported, which cannot be simply interpreted by relying on the hydrodynamic and interfacial layer effects. ,,− , Instead, this enhancement is largely related to the formation of a percolating filler network (PFN) within the polymer matrix. ,,,− The presence of such a PFN in various PNCs has been revealed using different techniques. − In addition, many physical phenomena, including the Payne and Mullins effects, , which have been widely observed in PNCs at high filler loadings, have been proven to mainly result from the formation and breakdown of PFNs. ,,,,,, …”

“…16−19 In addition, many physical phenomena, including the Payne and Mullins effects, 20,21 which have been widely observed in PNCs at high filler loadings, have been proven to mainly result from the formation and breakdown of PFNs. 9,10,13,14,18,22,23 Over the past few decades, many attempts have been made to better understand how nanoparticles are connected in a PFN. 2,13−15,23−28 Although there is a growing consensus that the formed PFN consists of fillers as the nodes and interfacial polymer layers as the bridges, 15−19,23,25−28 several fundamental questions concerning the dynamic nature of the polymer bridges and its relation to the mechanical reinforcement are still in active debate.…”

Filler Network Recovery of Carbon Black Filled Rubber

“…The nonlinearity observed in unfilled polymer is much weaker than that in filled rubber [6][7][8][9][10][11][12][13][14][15] . For example, unfilled polymers show linear viscoelastic behaviors even at shear strain =0.1 [8][9][10][11][12][13] , while filled rubbers show nonlinear viscoelastic behaviors at shear less than =0.01 6,7,14,15) . This strain-sensitive nature may be due to filler effect.…”