Deformation of elastomers

Top An electrical connection positioned within a section of as-received polymer shrink-tubing. Center, Bottom Application of heat to the tubing caused its diameter to shrink. In this constricted form, the polymer tubing stabilizes the connection and provides electrical insulation. (Photograph courtesy of Insulation Products Corporation.) 

The crosslinking process in elastomers is called vulcanization, which is achieved by a nonreversible chemical reaction, typically carried out at an elevated temperature. In most vulcanizing reactions, sulfur compounds are added to the heated elastomer chains of sulfur atoms bond with adjacent polymer backbone chains and crosslink them, which is accomplished according to the following reaction  

Unvulcanized rubber, which contains very few crosslinks, is soft and tacky and has poor resistance to abrasion. Modulus of elasticity, tensile strength, and resistance to degradation by oxidation are all enhanced by vulcanization. The magnitude of the modulus of elasticity is directly proportional to the density of the crosslinks. 

Concept Check 15,5 For the following pair of polymers, plot and label schematic stress-strain curves on the same graph. 

Concept Check 15.6 In terms of molecular structure, explain why phenol-formaldehyde (Bakelite) will not be an elastomer. (The molecular structure for phenol-formaldehyde is presented in Table 14.3.) 

The properties of elastomeric materials are controlled by their molecular structure which has been discussed earlier (Section 4.5). They are basically all amorphous polymers above their glass transition and normally crosslinked. Their unique deformation behaviour has fascinated scientists for many years and there are even reports of investigations into the deformation of natural rubber from the beginning of the nineteeth century. Elastomer deformation is particularly amenable to analysis using thermodynamics, as an elastomer behaves essentially as an entropy spring . It is even possible to derive the form of the basic stress-strain relationship from first principles by considering the statistical thermodynamic behaviour of the molecular network. 

The first law of thermodynamics establishes the relationship between the change in internal energy of a system dU and the heat SQ absorbed by the system and work SW done by the system as 

The bars indicate that 3Q anddW are inexact differentials because Q and W, unlike U, are not macroscopic functions of the system. If the length of 

The deformation of elastomers can be considered as a reversible process and so d 0 can be evaluated from the second law of thermodynamics which states that for a reversible process 

Most of the experimental investigations on elastomers have been done under conditions of constant pressure. The thermodynamic function which can be used to describe equilibrium under these conditions is the Gibbs free energy (Equation 4.1), but since elastomers tend to deform at constant volume it is possible to use the Helmholtz free energy, A in the consideration of equilibrium. It is defined as 

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Although traditionally the thermodynamic treatment of the deformation of elastomers has been centered on the force, the alternative condition of keeping the force (or tension) constant and recording the sample length as a function of temperature at constant pressure is even simpler 23,271. 

The success of the developed model in predicting uniaxial and equi-biaxi-al stress strain curves correctly emphasizes the role of filler networking in deriving a constitutive material law of reinforced rubbers that covers the deformation behavior up to large strains. Since different deformation modes can be described with a single set of material parameters, the model appears well suited for being implemented into a finite element (FE) code for simulations of three-dimensional, complex deformations of elastomer materials in the quasi-static Emit. 

One experimental observation which allows the analysis to be simplified is that the deformation of elastomers takes place approximately at constant volume, i.e., the deformation is nearly isovolume. For such a deformation at ambient pressure (P = 1 atm), the contribution of PdV to dW will be small and so the work done on the system in creating an elongation dl is... 

PROPERTIES OF SPECIAL INTEREST Low glass transition temjjerature, mesophase behavior including reversible stress-induced mesophase formation accompanied by necking-denecking phenomena in cyclic deformation of elastomers at room temperature and above. 

The usefulness of this model can be evaluated by comparison of calculation results with experimental data obtained for PBU and PDUE (Figures 10.63, 10.64). The model adequately describes the deformation behavior of elastomers in a wide range of strain rates. The main shortcoming of the model is that it does not describe a final stage of deformation of elastomers having S-shape strain curve. 

In addition to the two mechanisms of comminution and stretching, elastomer and carbon black have to be compacted.Compaction, or massing, is the displacement of entrapped air in the machine by applied compressive force. This requires deformation of elastomer domains to match the shape of the carbon black, followed by relaxation of the elastomer in the deformed state. In another case study, Nakajima and Harrell estimated that about 6% of the energy used in incorporation was required for compaction. 

MOLECULAR BOND RUPTURE IN INELASTIC DEFORMATION OF ELASTOMERS... 

Orientation of the polymer may also influence the permeation properties. However, the overall effect is highly dependent upon crystallinity. For example, deformation of elastomers-has little effect on permeability until crystallization effects occur. " Orientation of amorphous polymers can result in a reduction in permeability of around 10-15%, whereas in crystalline polymers, e.g, poly(ethylene terephthalate), reductions of over 50% have been observed. At high degrees of orientation, time-dependent effects on permeability occur in both glassy and semi-crystalline polymers. These effects have been related to the relaxation recovery of strain-induced areas of free volume generated during orientation. ... 

Not represented in Figure 2.10 is the deformation behavior of cross-linked networks of highly flexible elastomeric chains. The characteristic tensile deformation of elastomers is not based on energy elasticity but rather on the change of entropy accompanying the deformation and orientation of randomly coiled chain molecules... 

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