Mullin effect, phenomenon

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... 

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. 

Examination of the stress as a function of time during retraction at constant strain rate following extension, and in particular for several successive cycles of elongation and retraction, reveals some further complications. The stresses during retraction are smaller than would be calculated on the basis of equation 8, and are smaller during extension in the second cycle than in the first. (This phenomenon, known as the Mullins effect, is particularly evident in filled rubbers, but appears also in the absenee of filler. )... 

The Mullins effect [79] is a strain induced softening phenomenon, which is associated mainly with a significant reduction in the stress at a given level of strain during the unloading path as compared with the stress on initial loading in stress-strain cyclic tests [80] (Fig. 18). 

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]. 

There is considerable evidence that all the hysteresis effects observed in these materials and most of the viscoelastic behavior can be caused by the time dependent failure of the polymer on a molecular basis and are not due to internal viscosity [1,2]. At near equilibrium rates and small strains filled polymers exhibit the same type of hysteresis that many lowly filled, highly cross-linked rubbers demonstrate at large strains [1-8]. This phenomenon is called the "Mullins Effect" and has been attributed to micro-structural failure. Mullins postulated that a breakdown of particle-particle association and possibly also particle-polymer breakdown could account for the effect [3-5]. Later Bueche [7,8] proposed a molecular model for the Mullins Effect based on the assumption that the centers of the filler particles are displaced in an affine manner during deformation of the composite. Such deformations would cause a highly non-uniform strain and stress gradient in the polymer... 

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). 

Mass transport processes in ceramics are of interest due to their importance in materials preparation techniques. The phenomenon of sintering by diffusion is reasonably well understood for metallic systems.For 2-component ionic systems two additional features must be considered. (i) In order to produce an overall transfer of material a net flux of each component will occur, the components having in general unequal mobilities. These fluxes are interdependent since, locally, certain concentration ratios must be maintained. (ii) The concentration of defects will vary with distance from the free surface. As an example of the incorporation of these effects we may consider the changes in morphology of a nearly planar surface to which Mullins theory of mass transport may be applied. For the two component case, eg. NaCl, the equation describing the surface evolution by volume diffusion processes may be written as( )... 

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