Elastomers strain amplification

In this connection, Fig. 2 provides a qualitative illustration for interpreting modulus change of an elastomer upon filler blending 9). A hydrodynamic or strain amplification effect, the existence of filler-elastomer bonds, and the structure of carbon black 10) all play a part in this modulus increase. 

In this relation, 2C2 provides a correction for departure of the polymeric network from ideality, which results from chain entanglements and from the restricted extensibility of the elastomer strands. For filled vulcanizates, this equation can still be applied if it can be assumed that the major function of the dispersed phase is to increase the effective strain of the rubber matrix. In other words, because of the rigidity of the filler, the strain locally applied to the matrix may be larger than the measured overall strain. Various strain amplification functions have been proposed. Mullins and Tobin33), among others, suggested the use of the volume concentration factor of the Guth equation to estimate the effective strain U in the rubber matrix ... 

The influence of filler is not limited to this enhancement of the non-Newtonian behavior of elastomers. At very small shear rates, filled green compounds also exhibit an additional increase of viscosity that cannot be explained by strain amplification. This effect is usually attributed to the existence of the filler network the direct bonding of reinforcing objects by adsorbed chains implies a increased force to be broken. Obviously this influence can be observed only at very low strain, because a very small increase of interaggregate distances immediately implies a desorption of the bridging elastomeric chains. 

O At equilibrium, elastomer chains are adsorbed onto filler surface (state ). When strain increases, it induces a progressive extension of elastomer chain segments that bridges filler particles (state O). Obviously, this extension is much greater than macroscopic deformation because of strain amplification. At very low strain, the macroscopic deformation energy is stored in elongated chains as elastic energy and so can be fully recovered when strain decreases G" is low and constant. 

The presence of reinforcing fiUers also increases the non-Newtonian behavior of elastomers. This effect is mainly due to the fact that the incorporation of fillers in elastomers decreases the volume of the deformable phase. As discussed in the following text, this decrease is not limited to the actual volume of the filler, but must also include the existence of occluded rubber. So, when filled mixes are submitted to shear forces, because of the lower deformable volume, the actual deformation and speed of deformation are much higher than in unfilled mixes [1,134]. This phenomenon is usually called strain amplification effect, obviously strain amplification is not specific to reinforced systems but to any filled polymer. 

To reproduce the complex response at a start up of shear flow for a series of the LDPE/LDH nanocomposites (Fig. 20), it is necessary to take into account the shift of the second stress overshoot to smaller deformations with increasing LDH loading. To our knowledge, this shift can be explained by the effect of strain amplification in the polymer matrix foxmd previously in the case of filled elastomers [103]. Upon shearing, the hard filler particles cannot be stretched however, they can reorganize their positions in the polymer matrix, which hence experiences a noticeably higher effective deformation, yeff> than the strain externally applied to the sheared sample, yo [103] ... 

Within identical validity limits, Mullins and Tobin have shown that the stress-strain behavior of black-loaded rubber vulcanizates corresponds to the stress-strain response of pure gum vulcanizates multiplied by a suitable strain amplification factor X, which expresses the fact that the average strain supported by the rubber phase, is increased by the presence of filler. In other terms, the effective strain of the elastomer matrix X is given by X =X.xX, where X is the overall measured deformation of the filled material. 

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