Behavior of Elastic Networks of Various Degrees of Orientation in the Kinetic Theory of Fracture

Abstract

This paper describes a kinetic theory of fracture initiation using a linear elastic network as an approach to represent the strength and elastic properties of oriented materials. Emphasis has been placed on the questions as to whether the assumptions of small strains and invariant molecular orientational distribution are valid for the whole period of fracture initiation. The decrease of the modulus of elasticity resulting from the breakage of molecular elements during this period was found to be less than 1%. For brittle materials with high velocities of crack tip propagation the initiation period covers most of the lifetime of a sample. The logarithms of time to break calculated accordingly for network systems of different degrees of orientation are linear functions of applied stress over a wide range of stress. The slopes of these linear curves are inversely proportional to the modulus of elasticity of the network at zero time. Therefore, if the calculated curves of the logarithm of time are plotted versus the applied stress divided by the initial modulus of elasticity the linear portions of all curves reduce to one. For very small or large stresses the curves deviate from linearity.