On Scaled Normal Stresses in Multiaxial Fatigue and Their Exemplary Application to Ductile Cast Iron

Abstract

The approaches used to calculate the fatigue life of components must inevitably consider multiaxial stresses. Compared to proportional loading, the calculation of nonproportional loading is particularly challenging, especially since different materials exhibit the effects of nonproportional hardening and shifts in fatigue life. In this paper, the critical plane approach of scaled normal stresses, first proposed by Gaier and Dannbauer and later published in a modified version by Riess et al., is investigated in detail. It is shown that, on the one hand, compatibilities exist or can be established with known proportional strength criteria that can account for the varying ductility of different materials. Furthermore, it is demonstrated that the scaled normal stress approach can be formulated in such a way that different strength criteria can be used therein. As an example, the generally formulated approach for scaled normal stresses is applied to test results from ductile cast iron material EN-GJS-500-14. Different correction factors accounting for nonproportional loading are investigated. Through appropriate parameterization of one of the studied corrections, proportional and nonproportional test results were observed to fall within one common scatter band.

Effects of non‐proportionality and tension–compression asymmetry on the fatigue life prediction of equivalent stress criteria

“…where τ y and σ y,t are the yield strengths in shear and tension. According to Wächter et al, 28 a fully brittle material is characterized by…”

“…The level of ductility can be estimated by the yield strength ratio given by where and are the yield strengths in shear and tension. According to Wächter et al, 28 a fully brittle material is characterized by , while either or classifies a fully ductile material. These ratios also reflect different equivalent stress hypotheses, that is, Rankine 29 ( ), Tresca 30 ( ), and von Mises 31 .…”

Effects of non-proportionality and tension-compression asymmetry on the fatigue life prediction of equivalent stress criteria

“…where τy and σy,t are the yield strengths in shear and tension. According to Wächter et al 28 , a fully brittle material is characterized by κτ = 1, while either κτ = 0.5 or κτ = 1/ √ 3 classifies a fully ductile material. These ratios also reflect different equivalent stress hypotheses, i.e., Rankine 29 (κτ = 1), Tresca 30 (κτ = 0.5) and von Mises 31 (κτ = 1/ √ 3).…”

Cyclic utilization rates of the FKM guidelines: Definition and proposal of an efficient iteration procedure

“…Zusätzlich wird ein Ansatz zur verbesserten Berücksichtigung des Einflusses der Oberflächenrauheit auf die Schwingfestigkeit durch Anpassung der Wöhlerlinienneigung vorgestellt. Aktuell werden Ansätze zur Berücksichtigung mehrachsig proportionaler und nichtproportionaler Beanspruchungszustände im Ermüdungsfestigkeitsnachweis nach FKM-Richtlinie nichtlinear genauer untersucht [25,26]. In der Literatur existieren Ansätze "skalierter Normalspannungen", bei denen der elastizitätstheoretisch berechnete, mehrachsige Spannungszustand zu jedem Zeitschritt mit einem Skalierungsfaktor gewichtet und in einen einachsigen Spannungsraum projiziert wird.…”

“…Ein Vorschlag für einen koordinateninvarianten Ansatz für den zyklischen Auslastungsgrad unter mehrachsiger Beanspruchung mit Hilfe von Vergleichsspannungen soll ebenfalls zukünftig den koordinatensystemabhängigen Ansatz des Rechnerischen Festigkeitsnachweises ersetzen [20].…”