Scaled empirical fatigue laws

Abstract

A geometric size effect is evident in fatigue loading with a scaled cracked component of the same material appearing stronger in the sense of increased fatigue resistance. The number of cycles to failure can increase markedly with reduction in the size of a component and consequently, the use of scaled components to gauge fatigue life is invariably conservative. A question of some interest however and the focus of this work is whether it is possible to establish a precise analytical relationship between fatigue life and scale. This is shown possible on application of the new scaling theory finite similitude, which connects information across scales and links more than one scaled experiment. Through the design of two scaled-down experiments it is established that the Paris law empirical power-law relationship is precisely a first-order finite similitude identity. The practical applicability of the approach is demonstrated by means of experimental and numerical case studies, which confirm that the complete fatigue response of a structure described by key-fatigue parameters can be captured using two smaller scaled down experiments. High levels of accuracy are shown possible with the two-experiment approach with results returned up to 99% accurate.