Ranges of the validity of power scaling laws in the description of scale effects of the strength of extended elements of machines and structures

Abstract

The ranges of the validity of power laws to describe the scale effect of the strength of machine parts and structural elements are evaluated based on the probabilistic-statistical approach to analyzing the scale effect. For small structures, it is necessary to refute the basic assumption of Weibull’s theory on the statistical independence of the values of local strength at various points of structures and transition to using the mathematical model of random field of local strength, which makes it possible to take into account the correlation of strength properties of material in closely spaced points of structure. The derived results underlay the creation of the combined probabilistic scaling law of strength.