Carbon black stress-strain behavior

Fig. 10 Stress-strain behavior of CR gum, CR-clay (CRLDH and CRMMT), CR-modified clay ( CROLDH and CROMMT), and CR-carbon black (CRN220) composites...

It was shown, on the one hand, that gum-filler interactions are associated with the immobilization of a certain amount of rubber on the surface or inside the carbon black aggregates, and, on the other hand, that the corresponding bound or occluded rubbers play important roles in the reinforcement process due either to a restriction of elastomer chain mobility in the vicinity of the filler or to an increase of the effective volume of the latter. What are now the effects exerted by a filler on the stress-strain behavior and the modulus of cured rubbers ... 

Figure 16. Comparison of effects of fiber reinforcement vs. high modulus carbon black on stress-strain behavior of rubber...

The reinforcing effect of carbon black on stress-strain behavior of natural rubber is depicted in Figure 10.1. The reinforced material has a higher modulus (is stiffer) and is less extensible. 

The effect of filler structure on the rubber properties of filled rubber has been explained by the occlusion of rubber by filler aggregates (45). When stmctin-ed carbon blacks are dispersed in rubber, the polymer portion filling the internal void of the carbon black aggregates, or the polymer portion located within the irregular contours of the aggregates, is imable to participate fully in the macrodeformation. The partial immobilization in the form of occluded rubber causes this portion of rubber to behave like the filler rather than like the polymer matrix. As a result of this phenomenon, the effective volume of the filler, with regard to the stress-strain behavior and viscoelastic properties of the filled rubber, is increased considerably. 

The effects of fillers on the behavior of elastomers are summarized in Figure 3.22. In this figure the stress-strain curves of both natural rubber reinforced with 50% carbon black and a nonreinforced natural rubber are compared. An inspection of the curves highlights three important characteristics ... 

The effects of secondary aggregation of small particle carbon blacks on the elastic modulus at small strains are large. They have been studied primarily in dynamic oscillatory loading experiments and are discussed in Section VII, dealing with viscoelastic behavior. The effects of prior deformation on stress-strain relationships (stress softening) are also time-dependent phenomena, consideration of which is postponed to a later point in this review. 

The response of unvulcanized black-filled polymers (in the rubbery zone) to oscillating shear strains (151) is characterized by a strong dependence of the dynamic storage modulus, G, on the strain amplitude or the strain work (product of stress and strain amplitudes). The same behavior is observed in cross-linked rubbers and will be discussed in more detail in connection with the dynamic response of filled networks. It is clearly established that the manyfold drop of G, which occurs between double strain amplitudes of ca. 0.001 and 0.5, is due to the breakdown of secondary (Van der Waals) filler aggregation. In fact, as Payne (102) has shown, in the limit of low strain amplitudes a storage modulus of the order of 10 dynes/cm2 is obtained with concentrated (30 parts by volume and higher) carbon black dispersions made up from low molecular liquids or polymers alike. Carbon black pastes from low molecular liquids also show a very similar functional relationship between G and the strain amplitude. At lower black concentrations the contribution due to secondary aggregation becomes much smaller and, in polymers, it is always sensitive to the state of filler dispersion. 

A reduction of the required energy could be reached by the incorporation of conductive fillers such as heat conductive ceramics, carbon black and carbon nanotubes [103-105] as these materials allowed a better heat distribution between the heat source and the shape-memory devices. At the same time the incorporation of particles influenced the mechanical properties increased stiffness and recoverable strain levels could be reached by the incorporation of microscale particles [106, 107], while the usage of nanoscale particles enhanced stiffness and recoverable strain levels even more [108, 109]. When nanoscale particles are used to improve the photothermal effect and to enhance the mechanical properties, the molecular structure of the particles has to be considered. An inconsistent behavior in mechanical properties was observed by the reinforcement of polyesterurethanes with carbon nanotubes or carbon black or silicon carbide of similar size [3, 110]. While carbon black reinforced materials showed limited Ri around 25-30%, in carbon-nanotube reinforced polymers shape-recovery stresses increased and R s of almost 100% could be determined [110]. A synergism between the anisotropic carbon nanotubes and the crystallizing polyurethane switching segments was proposed as a possible... 

The viscoelastic analysis for DMA requires that the sample be in the linear viscoelastic range. In practice, this means that the strain/stress behavior is independent of the strain/stress level. Unmodified polymers, such as PMMA and PC, which are amorphous, are not likely to exhibit strain-dependent behavior as long as the strain amplitude is kept below about 0.3%. However, certain filled materials, especially carbon black or sUica-filled rubbers, may... 

Another softening phenomenon which manifests the dependence of the stress upon the entire history of deformation is the so-called Payne effect. Like the Mullins effect, this is a softening phenomena but it concerns the behavior of carbon blackfilled rubber subjected to oscillatory displacement. Strain dependence of the storage and loss moduli (Payne effect) at 70 °C and 10 Hz for a rubber compotmd with different concentration of carbon black filler [7] (Fig. 26). Indeed, the dynamic part of the stress response presents a rather strong nonlinear amplitude dependence, which is actually the Payne effect [8, 16, 43]. 

Indeed, carbon black-filled rubber, when loaded with time-dependent external forces, suffers a state of stress which is the superposition of two different aspects a time independent, long-term, behavior (sometimes improperly called hyperelastic ) opposed to a time dependent, short-term, response. Step-strain relaxation tests suggest that short term stresses are larger than the long term or quasi-static ones [117]. Moreover, oscillatoiy (sinusoidal) tests indicate that dissipative anelastic effects are significant, which leads to the consideration of a constitutive relation which depends not only on the current value of the strain but on the entire strain history. This assumption must be in accordance with some principles which restrict the class of rehable constitutive equations. These restrictions can be classified as physical and constitutive . The former are restrictirMis to which every rational physical theory must be subjected to, e.g., frame indifference. The latter, on the other hand, depends upon the material under consideration, e.g., internal symmetries. 

Figure 2.8 (a) Influence of carbon black particle size on tensile properties of rubber vulcanizates [95] (b) Stress-strain softening behavior (Mullins effect) of carbon blackfilled natural rubber compound... 

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