Subject Mullins effect

After a test specimen of an elastomer has been subjected to repeated deformation, the modulus at some lesser deformation is lower than the initial value. The modulus after such stress softening has been termed the degraded modulus. See 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. 

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]. 

The problem at hand is not reversible behavior, but instead is irreversible phenomenon such as the Mullins Effect". Consider that N(t) and f(xe) are arbitrary but non-zero, and the material was subjected to the strain history given below, it can be shown that the Mullins type hysteresis is contained in equation (3.4). 

Hilsmann (16) found no effect on two-point tactile discrimination, while Kremer (17) recorded a definite increase in the minimal distance for two-point discrimination throughout the surface of the body after 10-15 mg. of morphine was administered subcutaneously. David (11) reported recently that tactile discrimination was decreased in 6 of 10 subjects with 10 mg. (0.14 mg./kg.) and was uniformly decreased in all subjects by 15 mg. (0.22 mg./kg.). Mullin and Luckhardt (18, 19) claimed that tactile sensitivity was not appreciably affected by doses of morphine (35-30 mg.) which reduced sensitivity to pain. Further, according to Wikler et al. (5), the administration of morphine did not alter thresholds of perception for touch, vibration, two-point discrimination, or hearing in man, and hence morphine specifically alters pain thresholds. Wikler felt that this inference was open to question because of the variable effects of analgesics on pain as reported by different investigators (5). 

There has long been an interest in the potential effects on the nucleation process of externally applied electrostatic or magnetic fields. There is evidence that both homogeneous nucleation and the duration of the nucleation induction period (section 5.5) can be influenced. However, the relevance of experimental data, obtained from small-scale investigations under controlled laboratory conditions, to bulk solutions in flow or agitated conditions normally encountered in industrial practice (section 9.5) is still the subject of considerable controversy (Sohnel and Mullin, 1988c). A detailed account of recent theor-... 

The effect of an externally applied magnetic field on crystalline scale deposition, typically of CaCOs from hard water flowing in metal pipes, still remains a controversial subject despite the considerable number of investigations made over the past thirty years or so. There is still no general agreement on either the efficacy of commercially available devices or on the speculative mechanisms that have been proposed to explain their action (Sohnel and Mullin, 1988 Prasad et al., 1999 Kotsinaris et al., 1999). 

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