Multiaxial Fatigue: A Survey of the State of the Art

Abstract

This paper surveys the current state of knowledge concerning multiaxial fatigue. Developments are presented in chronological order and are discussed so as to supplement existing reviews in this field. Emphasis is placed primarily on the criteria or methods of evaluation of fatigue strength under general multiaxial loading at room temperature. The survey indicates that the early development of the criteria was based on extensions of static yield theories to fatigue under combined stresses. These are stress-based criteria limited primarily to high-cycle fatigue. Most of the later criteria are strain-based. These criteria fall into two broad groups: the equivalent stress or strain type and the critical plane type. Most of these criteria commonly lack considerations of the cyclic stress-strain response. Their application to nonproportional loading suffers from difficulties in implementation or from inconsistencies with results of experiments. Recent approaches fall in the category of continuous damage evaluation methods. At present, these appear to be abstract or difficult to implement. All the above criteria are critically examined and compared. With this background, a new plastic work approach, proposed by the author, is discussed briefly.

Evaluation of finite high cycle fatigue life of hard steels using the elliptical curve method

“…1 Several reviews of these models can be found in the literature. [2][3][4][5][6] In general terms, critical plane stress-based criteria are designed to assess the fatigue behavior considering an infinite fatigue life approach, where loading histories and material properties are taken into account to determine whether or not fatigue failures are to be expected. In this case, attention is focused on guaranteeing a good margin of safety against failure by admitting loading conditions in proximity with the fatigue resistance limit, above which fatigue failure can occur and below which fatigue life extends over a very high number of cycles (theoretically infinite).…”

“…The large number of models belonging to this approach can be typically classified into four divisions based on empirical equivalent stress, stress invariants, average stress, and critical plane stress 1 . Several reviews of these models can be found in the literature 2–6 …”

Dynamic finite element modeling and fatigue damage analysis of thermite welds

“…Therefore, fatigue damage criterions have been adopted to investigate the fatigue failure mechanism. Several multiaxial fatigue criterions have been investigated in this study using the 3D multiaxial stress state condition . The orientation of the planes where the fatigue cracks initiate cannot be explicitly obtained in some cases such as in the stress invariant criteria, which is a distinguishable factor from uniaxial fatigue criterions.…”

“…Several multiaxial fatigue criterions have been investigated in this study using the 3D multiaxial stress state condition. [17][18][19][20][21] The orientation of the planes where the fatigue cracks initiate cannot be explicitly obtained in some cases such as in the stress invariant criteria, which is a distinguishable factor from uniaxial fatigue criterions. Therefore, critical plane-based criterions are applied in this study to investigate the orientations of the planes for initiated cracks.…”

Energy-Saving Mechatronic System for Fatigue Tests of Materials under Variable-Amplitude Proportional Bending and Torsion

“…Multiaxial fatigue of materials and structures has been investigated for about 120 years and many different mathematical models of the limit state of strength have been formulated. At present, we know more than 60 criteria of fatigue strength under multiaxial loading [2][3][4]. There are stress-, strain-, and energy-based fatigue failure criteria, but there are no universal criterion for different structural materials and loading conditions [4].…”