Stress softening, rubber

It is demonstrated in Figure 22.11 that the quasi-static stress-strain cycles at different prestrains of silica-filled rubbers can be well described in the scope of the above-mentioned dynamic flocculation model of stress softening and filler-induced hysteresis up to large strain. Thereby, the size distribution < ( ) has been chosen as an isotropic logarithmic normal distribution (< ( i) = 4> ) = A( 3)) ... 

FIGURE 22.11 Uniaxial stress-strain data (up-cycles) of solution-based styrene-butadiene rubber (S-SBR) samples with 60 phr silica at different prestrains s =100%, 150%, 200%, 250%, and 300% (symbols) and fittings (lines) with the stress-softening model Equations 22.19-22.24. The fitting parameters are indicated. The insert shows a magnification of the small-strain data. (From Kliippel, M. and Heinrich, G., Kautschuk, Gummi, Kunststojfe, 58, 217, 2005. With permission.)... 

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]. 

There are various test methods, one being the De Mattia Flex Test method which is suitable for rubbers that have reasonably stable stress-strain properties, at least after a period of cycling, and do not show undue stress softening or set, or highly viscous behaviour. The results obtained for some thermoplastic rubber should be treated with caution if the elongation at break is below,... 

Work done by L. Mullins on the prestressing of filler-loaded vulcanisates showed that such prestressing gives a stress-strain curve approaching that of an unfilled rubber. This work has thrown much light on so called permanent set and the theory of filler reinforcement. See Stress Softening. 

An important feature of filled elastomers is the stress softening whereby an elastomer exhibits lower tensile properties at extensions less than those previously applied. As a result of this effect, a hysteresis loop on the stress-strain curve is observed. This effect is irreversible it is not connected with relaxation processes but the internal structure changes during stress softening. The reinforcement results from the polymer-filler interaction which include both physical and chemical bonds. Thus, deforma-tional properties and strength of filled rubbers are closely connected with the polymer-particle interactions and the ability of these bonds to become reformed under stress. 

Natural rubber exhibits unique physical and chemical properties. Rubbers stress-strain behavior exhibits the Mullins effect and the Payne effect. It strain crystallizes. Under repeated tensile strain, many filler reinforced rubbers exhibit a reduction in stress after the initial extension, and this is the so-called Mullins Effect which is technically understood as stress decay or relaxation. The phenomenon is named after the British rubber scientist Leonard Mullins, working at MBL Group in Leyland, and can be applied for many purposes as an instantaneous and irreversible softening of the stress-strain curve that occurs whenever the load increases beyond... 

The Payne effect of carbon black reinforced rubbers has also been investigated intensively by a number of different researchers [36-39]. In most cases, standard diene rubbers widely used in the tire industry, bke SBR, NR, and BR, have been appbed, but also carbon black filled bromobutyl rubbers [40-42] or functional rubbers containing tin end-modified polymers [43] were used. The Payne effect was described in the framework of various experimental procedures, including pre-conditioning-, recovery- and dynamic stress-softening studies [44]. The typically almost reversible, non-linear response found for carbon black composites has also been observed for silica filled rubbers [44-46]. 

The above interpretations of the Mullins effect of stress softening ignore the important results of Haarwood et al. [73, 74], who showed that a plot of stress in second extension vs ratio between strain and pre-strain of natural rubber filled with a variety of carbon blacks yields a single master curve [60, 73]. This demonstrates that stress softening is related to hydrodynamic strain amplification due to the presence of the filler. Based on this observation a micro-mechanical model of stress softening has been developed by referring to hydrodynamic reinforcement of the rubber matrix by rigid filler... 

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. 

In view of an illustration of the viscoelastic characteristics of the developed model, simulations of uniaxial stress-strain cycles in the small strain regime have been performed for various pre-strains, as depicted in Fig. 47b. Thereby, the material parameters obtained from the adaptation in Fig. 47a (Table 4, sample type C60) have been used. The dashed lines represent the polymer contributions, which include the pre-strain dependent hydrodynamic amplification of the polymer matrix. It becomes clear that in the small and medium strain regime a pronounced filler-induced hysteresis is predicted, due to the cyclic breakdown and re-aggregation of filler clusters. It can considered to be the main mechanism of energy dissipation of filler reinforced rubbers that appears even in the quasi-static limit. In addition, stress softening is present, also at small strains. It leads to the characteristic decline of the polymer contributions with rising pre-strain (dashed lines in... 

It is important to note that stress softening is also present during dynamic stress-strain cycles of filled rubbers at small and medium strain. In particular, this can be concluded from the dynamic mechanical data of the S-SBR samples filled with 60 phr N 220 as shown in Fig. 48. In the framework of the above model, the observed shift of the center point of the cycles to smaller stress values with increasing strain amplitude or maximum strain and the accompanied drop of the slope of the hysteresis cycles can be related to a de-... 

Kliippel M, Schramm J (1999) An advanced micromechanical model of hyperelasticity and stress softening of reinforced rubbers. In Dorfmann A, Muhr A (eds) Constitutive models for rubber. A.A. Balkema, Rotterdam... 

Molecular mechanisms for stress-softening are also discussed. It is shown that this phenomenon is not related to the chain slippage or to a conversion of a "hard" adsorbed phase to a soft one. The obtained results assume that the stress-softening in silicon rubbers is caused by two possible reasons changes in the positions of filler particles relative to the direction of stretching at the first deformation and by a re-distribution of the topological hindrances. It is shown that the tensile strength at break as a fiinction of temperature is closely related to the chain dynamics at the elastomer-filler interface. 

Stress-Softening of Silicone Rubbers (Mullins Effect)... 

When a strip of a filler-reinforced rubber is extended, returned to the unstressed state and then re-extended, the second stress-strain curve is found to lie below the original one, at least up to the elongation of the first extension. This phenomenon, known as stress-softening, has been the subject of much study as well as controversy. It is frequently referred to as the Mullins Effect, although it was well known even before the extensive work of Mullins and collaborators. The subject was thoroughly reviewed by Mullins (181) in 1969 and no attempt will be made here to cover it in detail. Instead, only a brief summary will be given, along with some relevant observations not emphasized in the Mullins review. 

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. 

Fig. 17. Stress-softening in unfilled and filled natural rubber vulcanizates after extension to equal stress (on original cross-section) a initial extension, b first retraction, c second extension, d second retraction. After Harwood, Mullins and...

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