Elastomers, large strain behaviour

It is possible to take the equations of linear spring and dashpot models and adapt them to nonlinear conditions. Thus, Smith [16] has described the large-strain behaviour of elastomers by taking as his starting-point the (linear) Maxwell element. Rewriting Equation (5.15), we have... 

These are essentially independent effects a polymer may exhibit all or any of them and they will all be temperature-dependent. Section 6.2 is concerned with the small-strain elasticity of polymers on time-scales short enough for the viscoelastic behaviour to be neglected. Sections 6.3 and 6.4 are concerned with materials that exhibit large strains and nonlinearity but (to a good approximation) none of the other departures from the behaviour of the ideal elastic solid. These are rubber-like materials or elastomers. Chapter 7 deals with materials that exhibit time-dependent effects at small strains but none of the other departures from the behaviour of the ideal elastic sohd. These are linear viscoelastic materials. Chapter 8 deals with yield, i.e. non-recoverable deformation, but this book does not deal with materials that exhibit non-linear viscoelasticity. Chapters 10 and 11 consider anisotropic materials. 

The non-linearity may arise for a variety of reasons. First, the linear theory has been developed for small strains, and to generalise it to large strain requires decisions on the appropriate definitions of both strain and stress, in effect making it necessary to create a new theory. Typical polymer applications may require the material to operate at strains in excess of 10%, and for elastomers the strains may be up to several hundred percent. Secondly, even at small strains linear behaviour may not be obtained. The behaviour may be quite rich, with the possibility of the polymer being initially linear but becoming non-linear at large times. 

Crosslinked polymers can be characterised conveniently by defining their crosslink density as branch points per unit volume or average molecular weight between crosslinks. This parameter in conjunction with the molecular nature of the polymer defines whether the material will behave as an elastomer or as a rigid material, which shows either ductile or brittle failure behaviour. Fillers can be used to modify properties further across the whole range of polymer behaviour. Because inorganic fillers are, compared to most polymers, much stiffer and less extensible materials, their incorporation into a polymer will usually produce a composite material of reduced strain to failure and increased stiffness relative to the polymer, i.e., the composite will be less elastomeric or less ductile. Nevertheless, large quantities of fillers are used in polymers that already have low strains to failure and show brittle failure behaviour. This chapter will confine itself to a discussion of the use of fillers in ductile and brittle crosslinked polymers. 

Contrary to metals and ceramics, the elastic strains in elastomers can become very large and attain values of several hundred percent. The reason is that the molecules are straightened during deformation, but the cross-links prevent the molecules from shding past each other and thus inhibit plastic deformation. Upon unloading, entropy-elasticity completely restores the initial arrangement of the molecules. This behaviour is called hyperelasticity. 

To describe the creep behaviour of glassy or tough polymers where the creep strains involved are small ( 5% say), as distinct from elastomers where the deformations are large ( 100% say), separable stress and time functions have been proposed. 

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