Citation: Wächter, M.; Linn, A.;
Wuthenow, R.; Esderts, A.; Gaier, C.;
Kraft, J.; Fällgren, C.; Vormwald, M.
On Scaled Normal Stresses in
Multiaxial Fatigue and Their
Exemplary Application to Ductile
Cast Iron. Appl. Mech. 2022, 3,
259–295. https://doi.org/10.3390/
applmech3010018
Received: 12 January 2022
Accepted: 5 March 2022
Published: 8 March 2022
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Article
On Scaled Normal Stresses in Multiaxial Fatigue and Their
Exemplary Application to Ductile Cast Iron
Michael Wächter
1,
* , Alexander Linn
1
, Ralf Wuthenow
1
, Alfons Esderts
1
, Christian Gaier
2
, Jan Kraft
3
,
Carl Fällgren
3
and Michael Vormwald
3
1
Institute for Plant Engineering and Fatigue Analysis, Clausthal University of Technology,
38678 Clausthal-Zellerfeld, Germany; alexander.linn@tu-clausthal.de (A.L.);
ralf.wuthenow@tu-clausthal.de (R.W.); alfons.esderts@tu-clausthal.de (A.E.)
2
Engineering Center Steyr Gmbh & Co. KG, 4300 St. Valentin, Austria; christian.gaier@magna.com
3
Materials Mechanics Group, Technical University of Darmstadt, 64287 Darmstadt, Germany;
kraft@wm.tu-darmstadt.de (J.K.); faellgren@wm.tu-darmstadt.de (C.F.);
vormwald@wm.tu-darmstadt.de (M.V.)
* Correspondence: michael.waechter@tu-clausthal.de
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.
Keywords:
multiaxial fatigue; critical plane; scaled normal stresses; proportional loading; nonpro-
portional loading; ductile cast iron
1. Introduction
Fatigue assessments for components relevant to safety are conducted either on an
experimental basis or by using calculation approaches. From an economic point of view,
calculation appears preferable at first glance. However, with regard to accuracy, the
experimental approach is superior. Therefore, a combination of calculation and experiment
is often used.
Service loads that are the reason for fatigue assessments usually consist of several
components (e.g., different force and moment channels), which only behave proportionally
to each other in special cases. Therefore, assessments of analytical fatigue strength need to
be able to handle multiaxial nonproportional loads while producing reliable results.
This objective contrasts with the fatigue strength data commonly available in practice:
1.
Strain–life curve: These Wöhler curves are determined in axial strain-controlled
tests on unnotched material specimens [
1
,
2
], allowing the uniaxial stress state to be
tested. As an alternative to experimental determination, these properties can also be
estimated using statistical dependencies (see, for example, [
3
,
4
]). However, this does
not change the range of validity of the properties.
Appl. Mech. 2022, 3, 259–295. https://doi.org/10.3390/applmech3010018 https://www.mdpi.com/journal/applmech
