Carbon-black-filled rubber stress-strain relation

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. [Pg.239]

Figure 18.1 is the typical stress-strain curves of the filled rubber (SBR filled with fine carbon black, HAF),

$Figure 18.1 is the typical stress-strain curves of the filled rubber (SBR filled with fine carbon black, HAF), <p the volume fraction of carbon black, showing the above three criteria from 1 to 3. The most characteristic point in stress-strain relation of the filled rubber is first, that the stress increase becomes larger and larger as extension increases (called the stress upturn), in addition to the initial stress (modulus) increase at small extension. Second, the tensile strength is 10-15 times larger than that of the unfilled rubber vulcanizate whose strength is in the order of 2 or 3 MPa ( = 0 in Figure 18.1). Moreover, the tensile strain is also quite large, compared with the unfilled rubber of the same modulus, as shown in Figure 18.1.$

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... [Pg.7]

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