ON THE MATHEMATICAL GENERALIZATION OF S. YA YAREMA FORMULA

Abstract

The goal of the article is a mathematical generalization of S. Ya Yarema formula derived for approximation of the experimental diagrams of the fatigue fracture and subsequent analysis of the capabilities of the formula. The analysis is performed on the basis of the operator for smooth transition from one mathematical function to another. Formula of S. Ya Yarema is shown to be a special case of this mathematical operator when a smooth differentiable transition occurs from one constant level of the amplitude of stress intensity factor to another constant level. The obtained mathematical expressions can be interpreted as the cumulative probability and the probability density of random values of the fatigue crack rate. This allowed us to give a statistical interpretation of the fatigue fracture diagrams. On this basis we developed a methodology for estimation of the residual resource of a structural part containing a fatigue crack.