Elastic Properties

In a tensile test carried out in quasi-static conditions (at low crosshead speed), the specimen is stretched at constant crosshead speed until fracture (ASTM D412). Most of the characteristic parameters of a tensile test are defined in terms of the so-called “engineering stress” (force per unit original cross sectional area) and “engineering strain” (elongation per unit original length, l0). At very low (infinitesimal) strain, there is no significant difference between the “engineering stress” and the Cauchy stress or “true stress” which is given by force per unit actual cross sectional area. Metals, ceramics, glassy polymers, and thermosets, present a low value elongation at break, so the error in using “engineering data” instead of “true data” is almost negligible. For materials able to hold up large strains without breaking, as it is the case of elastomers, flexible foams, thermoplastics presenting “cold drawing”, and so on, “engineering stress” can differ from “true stress” by a factor of 5,10 or even more. The same holds for strain: Hencky strain or “true strain” [ln(l/l0)] and “engineering strain” values are quite different. For an extension ratio (l/l0) equal to 10, the “engineering strain” is 9 and the Hencky strain or “true strain” is 2.3.

Therefore quantities such as the yield stress, the ultimate tensile strength (maxi­mum value of “engineering stress”), the fracture stress (“engineering stress” at fracture) and the corresponding “engineering strain” values are of little help for characterisation of elastomers, flexible foams or ductile thermoplastics.

Elastomers are non-linear. To account for non-linear elastic behaviour, “moduli” at 100,200 and 300 % strain are taken. As pointed before, care has to be taken with the definition of strain for large strains. Very small strains are described by a unique measure, the infinitesimal strain; moreover, infinitesimal strains are additive. On the contrary, finite strains are non-additive, and several measures of strain may be considered. Since the elastic energy does not depend on the particular measure of strain chosen, for finite strains the value of the stress depends on the chosen measure of strain.

The tensile test for foams is described in standards DIN 53430 (rigid foams) and DIN 53571 (flexible foams).

Figures 10.3 and 10.4 display the results of a tensile test in natural rubber (Fig. 10.3) and in a high performance nitrile rubber (Fig. 10.4). Notice that natural rubber can be extended up to seven times the initial length and the nitrile rubber shown can be extended up to 13 times the initial length.