1 STRESS-STRAIN RELATIONSHIPS

Stress/strain relationships are commonly studied in tension, compression, shear or indentation. Because in theory all stress/strain relationships except those at breaking point are a function of elastic modulus, it can be questioned as to why so many modes of test are required. The answer is partly because some tests have persisted by tradition, partly because certain tests are very convenient for particular geometry of specimens and partly because at high strains the physics of rubber elasticity is even now not fully understood so that exact relationships between the various moduli are not known. A practical extension of the third reason is that it is logical to test using the mode of deformation to be found in practice.

It is not necessary to be expert in the theory of rubber elasticity to test rubbers but it is a distinct advantage to be conversant with the main principles. A classic account of the development of the basic theories is given by Treloar ^[1] which, if not digested from cover to cover, should be compulsory reading for those concerned with physical testing.

Statistical network theory leads to the expression of the strain energy density (energy stored in unit volume of the rubber) in terms of the extension ratios:

where W = strain energy density and ? ₁, ? ₂, ? ₃ are extension ratios in the three principal axis.

Also, because the assumption is made that the rubber is incompressible:

Statistical network theory then leads to...