Mullins softening

Mullins softening may be defined as the reduction of modulus caused by successive stretching (Bachmann et al, 1959 Boonstra, 1965 Bueche, F., 1965 Dannenberg, 1966 Harwood et al, 1967 Mullins, 1969 Mullins and Tobin, 1956 Sellers and Toonder, 1965). This phenomenon is characteristic of truly reinforcing fillers, but occurs to a lesser extent in gums and non-reinforced systems (Kraus, 1971). 

Figure 10.14. Characteristic types of Mullins softening in silica-filled rubber vulcanizates. Highly reinforcing fillers give more stress-softening than slightly reinforcing or nonreinforcing materials. (Sellers and Toonder, 1965.)...

Table 2 Examples of materials showing some Mullins softening...

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. 

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. 

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 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... 

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

The data in Table 1 indicates that the deformation energy is lower for the second deformation compared with the first one. This effect is called the Mullins effect or stress-softening. Two explanations of this effect are given for the case of complete elastic recovery of a sample before its second deformation [39-43] ... 

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. 

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...

It seems that the Mullins mechanism may, indeed, be the dominant one in experiments in which no special precautions are made to facilitate recovery before the second extension cycle. It is difficult to see, however, how large degrees of softening can persist in pre-stretched carbon black filled vulcanizates which have been swelled and de-swelled to ensure recovery. Amorphous gum rubbers show no softening under these conditions. It would appear that caution remains indicated against the total abandonment of alternative mechanisms. 

Another important effect of fillers is stress softening, or the Mullins effect. If a filled sample is stretched for the first time to 100%, the stress-strain curve27 will follow that illustrated in Figure 6-11. Now the strain is removed, and the sample is restretched to 200%. The stress in the second cycle is lower than that in the first up to 100%, after which it continues in a manner following the first cycle. If we repeat the stress-strain in a third cycle, we again see a softening up to 200% due to the previous strain history. This stress-softening effect was first discovered by Mullins, after whom it is named. 

Figure 6-11. Stress softening of natural rubber filled with MPC carbon black (Mullins effect). Numerals indicate the stress-strain cycles. [After F. Bueche, J. Appl. Polym. Sci., 4, 107 (1960) by permission of John Wiley Sons.]...

Blanchard developed the model in additional studies4 s and explained certain behaviour as the result of the existence of two phases in the matrix — a hard phase and a soft phase. This model was also proposed by Mullins and Tobin64. As a result of stressing, increasing proportions of the hard phase become softened. The subsequent behaviour is then controlled by the model described by Takayanagi et al.95, which was also used by Gent28 and Blanchard6. ... 

Brennan, J. J., Jermyn, T. E., Perdigao, M. F. Influence of carbon black on stress softening (Mullins effect). Paper no. 36, Division of Rubber Chemistry, ACS, Detroit, Michigan, 1964... 

Equation (1.5) has also been used to estimate the force at which a rubber molecule will become detached from a particle of a reinforcing filler (e.g., carbon black) when a filled rubber is deformed (Bueche, 1960, 1961). In this way, a general semiquantitative treatment has been achieved for stress-induced softening (Mullins effect) of filled mbbers (shown in Figure 1.5). 

A very significant observation is the stress softening effect, also called the Mullins effect (Mullins and Tobin, 1965 Mullins, 1969). In this experiment, a compound sample is stretched to ei and returned to zero strain, then stretched again. For strain below si, its stress-strain curve is significantly below the first one but rejoins it at si. Stress softening is dependent on the initial strain level it can be partially reduced by thermal treatment but not be totally effaced (Figure 8.7). 

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