Rubber elasticity stress softening

In particular it can be shown that the dynamic flocculation model of stress softening and hysteresis fulfils a plausibility criterion, important, e.g., for finite element (FE) apphcations. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. From the simulations of stress-strain cycles at medium and large strain it can be concluded that the model of cluster breakdown and reaggregation for prestrained samples represents a fundamental micromechanical basis for the description of nonlinear viscoelasticity of filler-reinforced rubbers. Thereby, the mechanisms of energy storage and dissipation are traced back to the elastic response of tender but fragile filler clusters [24]. 

So far, we have considered the elasticity of filler networks in elastomers and its reinforcing action at small strain amplitudes, where no fracture of filler-filler bonds appears. With increasing strain, a successive breakdown of the filler network takes place and the elastic modulus decreases rapidly if a critical strain amplitude is exceeded (Fig. 42). For a theoretical description of this behavior, the ultimate properties and fracture mechanics of CCA-filler clusters in elastomers have to be evaluated. This will be a basic tool for a quantitative understanding of stress softening phenomena and the role of fillers in internal friction of reinforced rubbers. 

A difficulty in comparing stress-softening data of various authors is the different degree of emphasis given by them to the extent of recovery of the sample before determination of the softening effect. When the sample is swelled in the vapor of a good solvent, elastic recovery should be very nearly complete and, indeed, there is very little permanent set, even under conditions of severe pre-strain. Under these conditions amorphous gum rubbers show no detectable softening, but black rubbers do. 

The predictions of the classical models of rubber elasticity correspond to horizontal lines in a Mooney-Rivlin plot (C2 = 0). Plots for experimental data show a positive slope (C2 > 0). This indicates a stress softening with increasing deformation (as the reciprocal deformation 1 /X decreases). A comparison of (4) and (6) shows that, for the classical models, the Mooney-Rivlin coefficient 2Ci, corresponds to the shear modulus G given by (5), and the Mooney-Rivlin plot presents another method to determine crosslink density Vc or the average molecular mass of a network chain Me ... 

Kluppel M, Schramm M (2000) A generalized tube model of rubber elasticity and stress softening of filler reinforced elastomer systems. Macromol Theory Simul 9 742-54... 

The Mullins effect, which can be considered as a hysteretic mechanism related to energy dissipated by the material during deformation, corresponds to a decrease in the number of elastically effective network chains. It results from chains that reach their limit of extensibility by strain amplification effects caused by the inclusion of undeformable filler particles [24,25]. Stress-softening in filled rubbers has been associated with the rupture properties and a quantitative relationship between total hysteresis (area between the first extension and the first release curves in the first extension cycle) and the enei-gy required for rupture has been derived [26,27]. 

L. Mullins, N.R. Tobin. Stress softening in rubber vulcanizates. Part I. Use of s strain amplitude factor to describe the elastic behaviour of filler-reinforced vulcanized rubber. /. Appl. Polym. Sci., 9,2993-3009,1965. 

The situation for amorphous linear polymers is sketched in Fig. 2.8a. If a polymeric glass is heated, it will begin to soften in the neighbourhood of the glass-rubber transition temperature (Tg) and become quite rubbery. On further heating the elastic behaviour diminishes, but it is only at temperatures more than 50° above the glass-rubber transition temperature that a shear stress will cause viscous flow to predominate over elastic deformation. 

Vulcanised rubbers show viscoelasticity and the departure from perfect elasticity are evaluated by measurement of resilience, creep and stress relaxation. Compounding which contributes to a more tightly knit crosslinking system occupying the maximum possible volume proportion of the vulcanisate will enhance the elastic properties as displayed by resilience. Appropriate antioxidant protection of the polymer will give further improvement. At normal levels of addition softeners and plasticisers have little effect [7]. 

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