The generalized criterion of multiaxial random fatigue based on conception proposed by prof. Macha

¹ Department of Mechanics and Machine Design, Opole University of Technology, 5 Mikołajczyka Street, 45-271 Opole, Poland
² Department of Mechanics, Materials Science and Engineering, Wrocław University of Science and Technology, Smoluchowskiego Street 25, Wrocław, Poland

Abstract

This criterion has been repeatedly verified, analyzed and special cases of this criterion reducing complex stress to equivalent uniaxial were taken into account. Since both normal and shear stress are vectors, we encounter the mathematical problem of adding these vectors, and the question arises how to understand the obtained equivalent stress, because two perpendicular vectors are added with weighting factors. Therefore, in this work it was proposed to adopt a system of complex numbers. Normal stress was defined as the real part and shear stress as imaginary part. As a result, on the basis of the defined complex number and basing on pure bending and pure torsion after transformations, the expression for equivalent stress was identical to the previously proposed criteria defined on the basis of the concept of prof. Macha.