The finding of the reciprocal relationship between fatigue (S-N) behavior and fatigue crack growth behavior enabling interconversion of data in structural materials

Abstract

The existence of a simple reciprocal relationship between the fatigue life (S-N) behavior and the fatigue crack growth (da/dN-∆K or FCG) behavior, in materials under cyclic loading, is demonstrated. This relationship has been found by an intuitive transformation of a S-N constitutive equation that was developed before from a physical model of fatigue. The transformation produces mathematically symmetric forms of constitutive equations and enables interconversion between the two sets of fatigue data. It is shown that one dataset (e.g., S-N fatigue data) can be transformed into the other (FCG data) and vice versa in a simple step. This is shown to work extremely well for metals, ceramics, and polymers, indicating the universal reciprocity between the two fatigue behaviors of materials. More powerfully, this also means that it is possible to generate the S-N fatigue data of specific material from the fatigue crack growth data of that material obtained from a few fracture mechanics specimens, thus potentially eliminating the need for elaborate S-N testing. Notably, the major impact of this work is the result of two simple equations, reciprocally related to each other, representing the two important fatigue behaviors very accurately over a wide range of data and across many materials.