A formulation of the criterion for multiaxial fatigue in terms of complex number as proposed by Macha. (April 2020)

• Record Type: Journal Article
• Authors: Łagoda, Tadeusz; Kurek, Marta; Głowacka, Karolina
• Is Part Of: International journal of fatigue. Volume 133(2020)
• Publication Date: 2020-04
• Subjects: Multiaxial criteria -- Stress state -- Random loading; Materials -- Fatigue -- Periodicals; Materials -- Fatigue; Periodicals; 620.1122
• DOI: 10.1016/j.ijfatigue.2019.105430
• Languages: English
• ISSNs: 0142-1123

Abstract

Highlights: We often deal with the combination of mutually perpendicular vectors of the normal and shear stress. Although this is inconsistent with the principles of mathematics. Mathematical compatibility is not fully valid in the criterion based on the concept by Macha. It turns out that treating stress in the critical plane as a complex number results in an expression identical to Macha's criterion. Abstract: This criterion by Macha has been repeatedly verified, analyzed and special cases of this criterion have been taken into account, reducing the complex stress to its uniaxial equivalent. Since both normal and shear stresses are vectors, we encounter the mathematical problem of adding these vectors, and the question arises how to consider the obtained equivalent stress, because two perpendicular vectors are added with weighting factors. Therefore, in this work it is proposed to adopt a system of complex numbers. Normal stress is defined here as a real part and shear stress as an imaginary part. As a result, on the basis of the defined complex number and based on pendulum bending and double-sided torsion, after transformations, the expression for equivalent stress proves to be identical to those previously defined on the basis of the concept of Macha.