Compression Stress Strain of Rubber
Authors: Sheppard J. R. , Clapson W. J. 
Published: February 2011

Abstract
1. A relation of simple form between compressive force and equivalent two-way tensile forces is developed. 2. Based on this relation, a new method for determining the compression stress strain of rubber is outlined, which avoids difficulties and errors inherent in direct compression. It consists in applying tensile forces simultaneously in two directions, and, from these and the strained dimensions, in computing the compressive force that would have produced the same deformation. 3. The mode of applying the two-way tensiles is to inflate a hollow sphere of rubber; the experimental data required to determine the compression stress strain are pressure of gas in, and dimensions of, the inflating hollow sphere. 4. The method has been applied to cold-cured pure-gum rubber in the form of toy balloons which, in its ordinary elongation stress strain, shows a breaking elongation of about 650 to 700 per cent and a tensile of 30 to 40 kg. per square centimeter. While the numerical values obtained on this stock have no special significance, as they will vary from stock to stock, the following are examples: breaking compression, about 97.3 per cent; breaking compressive force, 6000 to 9000 kg. per square centimeter (on original cross section); hysteresis, 29 to 35 per cent of work of compression to near rupture. 5. As a common measuring stick by which to gage degree of strain in deformations of different types—e. g., increasing one dimension (and diminishing the other two) as against diminishing one dimension (and increasing the other two)—energy seems the best. Energy at break for ordinary elongation stress strain was 50 to 70 kg. cm. per cubic centimeter, and for compression stress strain was 89 to 103 kg. cm. per cubic centimeter. 6. The compression stress-strain data may, if desired, be expressed in terms of two-way tensiles vs. two-way elongations. Energy of compression may be computed either as twice the area subtended between such a curve and the strain axis, or as the area between the compression stress strain and the strain axis. 7. It is strongly indicated that the compression stress strain of rubber is continuous with the ordinary elongation stress strain when both are plotted in the same units, and that the complete stress strain should accordingly be considered as a single continuous curve having an elongation branch and a compression branch with the origin as dividing point. 8. The analytic features of the complete stress strain are described. 9. Granting the observed concavity of the upper part of the elongation stress strain, and the thesis of continuity between elongation and compression, a point of inflection is bound to exist theoretically. 10. Implications of the thesis of continuity are: (1) An equation for the stress-strain curve must fit the complete curve; it is not sufficient that it fit the elongation branch only. (2) It is impossible to compute the compression stress strain from the ordinary (one-way) elongation stress-strain data. The two sets of data are related empirically. 11. When compressive force and equivalent two-way tensiles are based on actual cross sections, stress conditions at a point are expressed and we have the simple rule: Pressure at a point is numerically equal to the transverse tensions which, substituted therefor, will maintain the same strain.