# Stress Strain Behaviour of Rubber

The stress-strain behaviour of both filled and unfilled incompressible rubbers, and a rubber containing a compressible filler, are examined. Experiments are also carried out on partially crystalline rubber. An assessment of theoretical equations relating the compression stiffness of rubber pads to the bulk and shear moduli of the rubber is made from an experimental study of an elastomer containing a compressible filler, and the volume fraction of filler is estimated using a simple model. Characterisation of the first cycle stress-strain behaviour of incompressible rubbers is carried out using a novel experimental technique in which both non-zero principal stresses in pure shear are measured. From this, combined with a series of uniaxial tests, it is concluded that the strain energy of filled natural rubber is a function only of the first strain invariant to an acceptable degree of accuracy. In addition, explicit functions for the strain energy are assessed.

The behaviour of rubber in simple shear is modelled using finite element analysis and the results compared with experiment. It is found that in conventional test pieces the stresses or deflection in the thickness direction are influenced by the size of the dW/dI2 term but not by dW/dI1, as is predicted theoretically, and also by the proximity of the free edges. Measurements in combined torsion and extension serve to show the limitations of a strain energy approach for describing the behaviour of filled rubber. Moreover, using the split pure shear technique, it is found that the amounts of stress softening and stress relaxation are liable to be different in the two principal directions, and the amount of stress softening depends on the direction of previous stresses, so these effects are not describable by an isotropic damage or time dependent model. Nevertheless, simple isotropic models for some of these inelastic effects, based on a suitably modified function of the strain energy, are found to give a reasonable approximation to the behaviour.

Simultaneous measurement of the modulus and volume change of rubber, crystallised at low temperature, enables the relationship between the crystallinity and modulus to be obtained. The reinforcing effect of the crystalline phase is found to be independent of the modulus of the rubber and of the detailed morphology of the crystals and cannot, therefore, be modelled as a rigid filler. Finally, studies. of yielding of partially crystalline natural rubber show that the yield strain is largely independent of the amount of crystallinity, whereas the yield stress increases with increasing crystallinities. The behaviour is ualitatively similar to that observed in other crystalline polymers.