Time Dependence of Mechanical Breakdown in Bundles of Fibers. II. The Infinite Ideal Bundle under Linearly Increasing Loads

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Abstract
This article contains an extension of the theory of the previous paper to the calculation of the behavior of an infinite ideal bundle in a constant rate of loading experiment. It is assumed throughout that the bundle is composed of filaments which have been randomly selected from a first‐order ensemble for which the average lifetime under separate dead loads is an exponential function of the applied load. The differential equation which describes the breakdown of such a bundle has been numerically investigated with a CPC digital computer using a fourth‐order Runge‐Kutta method. It has been found that, throughout the practical range in rates of loading, the bundle's tensile strength (units of force at break per initial unit area) is about 90% of the strength of the individual filaments. It also was found that the strength of the bundle is approximately an increasing linear function of the logarithm of the rate of loading.

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