Mullins’ effect

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 

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L. Mullins, Effect of fillers in rubber, Chap. 11 in The Chemistry and Physics of Rubber-Like Substances, ed. by L. Bateman, Wiley, New York, 1963. 

FIGURE 18.12 Mullins effect (schematic) loading (Hrst.ll second, 21) and unloading (Hrst, lu second, 2u). 

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. 

L. Mullins, Rubber Chem. Technol., 42, 339 (1969). J.A.C. Harwood and A.R. Payne, Journal of Applied Polymer Science 10,315,1966 "http // en.wikipedia.org/wiki/Mullins effect. 

It will be appreciated that in the relations considered above the rubber has been treated as a perfectly elastic material, whereas in practice there several factors that cause departure from pure elastic behaviour. Hysteresis and the Payne effect are considered in Chapter 9, set, stress relaxation and creep in Chapter 10 and the Mullins effect was covered in Chapter 5. 

It was shown that the stress-induced orientational order is larger in a filled network than in an unfilled one [78]. Two effects explain this observation first, adsorption of network chains on filler particles leads to an increase of the effective crosslink density, and secondly, the microscopic deformation ratio differs from the macroscopic one, since part of the volume is occupied by solid filler particles. An important question for understanding the elastic properties of filled elastomeric systems, is to know to what extent the adsorption layer is affected by an external stress. Tong-time elastic relaxation and/or non-linearity in the elastic behaviour (Mullins effect, Payne effect) may be related to this question [79]. Just above the melting temperature Tm, it has been shown that local chain mobility in the adsorption layer decreases under stress, which may allow some elastic energy to be dissipated, (i.e., to relax). This may provide a mechanism for the reinforcement of filled PDMS networks [78]. 

The Italian authors have also studied the effect of the annealing and of the solvent evaporation rate on the morphology and on the mechanical properties of different Kratons114-117. Kraton 1102 exhibits a Mullins effect which increases with annealing. Films with thickness between 0.2 and 0.4 mm, cast from dilute solution (1%) in cyclohexane and methylethyl ketone (MEK) at different rates have been... 

To our knowledge, very few results have been published concerning the morphology of star SB copolymers. In 1975, Pedemonte et al,153) studied two copolymers (SB)4Si called Europrene T 161 and Europrene T 162 containing, respectively, 35% and 49% polystyrene. For the annealed samples, a disordered cylindrical structure was found in T 161 and a lamellar structure in T 162. In 1976, Pedemonte et al.ls4) published the results of a more detailed study performed on compression-moulded films of T 162. These films deformed increasing step by step the maximum strain value exhibit the Mullins effect. If in the original compression moulded film rods of polystyrene were arranged almost perpendicular to the compression plane, the de-... 

So far the micro-mechanical origin of the Mullins effect is not totally understood [26, 36, 61]. Beside the action of the entropy elastic polymer network that is quite well understood on a molecular-statistical basis [24, 62], the impact of filler particles on stress-strain properties is of high importance. On the one hand the addition of hard filler particles leads to a stiffening of the rubber matrix that can be described by a hydrodynamic strain amplification factor [22, 63-65]. On the other, the constraints introduced into the system by filler-polymer bonds result in a decreased network entropy. Accordingly, the free energy that equals the negative entropy times the temperature increases linear with the effective number of network junctions [64-67]. A further effect is obtained from the formation of filler clusters or a... 

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] ... 

The plots in Figure 6 show stress strain curves for two optimised PDMS systems formulated with 6% dihydroxyhexamethyl- and octaphenyl- modified POSS. Although somewhat softer than the silica filled equivalent, also shown, plots indicate a far simpler behaviour with no obvious Mullins effect and little... 

Stress strain curves for silica nano fibre, CNF and systems formulated with more refined single and multi walled nano tubes are shown in Figure 12. The further simplification of the stress strain response over the PDMS formulated with fumed silica is apparent. There is no Mullins effect, in any of the tubular carbon modified systems, they all have a non complex modulas and a highly linear stress strain response. 

Figure 8. Stress strain curves for a PDMS formulated with fumed silica. The plots show a large Mullins effect and complex modulas.

The nano modified PDMS systems discussed have properties that enable a more confident prediction of ageing trends. The properties of the carborane modified system change in a linear fashion with radiation dose as opposed to the nonlinear trend observed for conventional particulate filled PDMS. The silica and carbon nano tubular systems display simplified mechanical properties. The reduction in Mullins effect or move to a more linear, less complex stress strain behavior, allows increased accuracy in property measurements. 

Decrease in Mullins effect silica hexadecanol, silanes 76... 

Webber RE, Creton C, Brown HR, Gong JP (2007) Large strain hysteresis and Mullins effect of tough double-network hydrogels. Macromolecules 40 2919-2927... 

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