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BY 4.0 license Open Access Published by De Gruyter September 26, 2018

On the accuracy of estimating fatigue notch factors

Dedicated to Professor Dr.-Ing. Harald Zenner on the occasion of his eightieth birthday

Zur zuverlässigen Schätzung von Kerbwirkungszahlen
Christian Müller , Michael Wächter , Rainer Masendorf and Alfons Esderts
From the journal Materials Testing

Abstract

The fatigue notch factor is the quotient of the nominal stress endurance limits of unnotched and notched specimens. It represents the notch sensitivity of a material or a component under cyclic loading. For example, the fatigue notch factor is used in analytical strength assessments with nominal stress and is also suitable as a quality criterion for materials and entire components. On the one hand, an analytical approach to rate the reliability of the fatigue notch factor is derived assuming a log-normal distribution for the population of the endurance limits of the unnotched and notched specimens. The analytical approach provides the best achievable result and can be used to rate real experiments. On the other hand, the staircase method, which is often used to determine endurance limits, is simulated using Monte Carlo simulations. From the simulations, information about the reliability of the real test can be gathered, which can be compared to the analytical approach. In conclusion, in this paper the reliability of the fracture of two originally log-normally distributed random variables each used in an own staircase test is examined. The result is compared to an analytical approach. In former articles the scope has only been on single test series, the examination of error propagation, e.g, by using the staircase method and building the fracture of the two results afterwards, is missing in former examinations. The staircase method is a procedure to estimate fatigue notch factors with reliabilities comparable to those of the analytical approach. To increase the number of evaluable tests, runouts should be reused.

Kurzfassung

Die Kerbwirkungszahl ist das Verhältnis der Nennspannungslangzeitfestigkeiten von ungekerbter und gekerbter Probe. Sie stellt ein Maß für die Kerbempfindlichkeit eines Werkstoffs oder Bauteils unter schwingender Belastung dar. Sie wird u.a. in rechnerischen Festigkeitsnachweisen mit Nennspannungen verwendet und kann auch als Qualitätskriterium für Werkstoffkennwerte und ganze Bauteile dienen. Unter der Annahme von logarithmischen Normalverteilungen für die Grundgesamtheiten der Langzeitfestigkeiten von ungekerbter und gekerbter Probe wird zunächst eine analytische Lösung für die Zuverlässigkeit der Kerbwirkungszahl hergeleitet. Die analytische Lösung stellt den Idealwert dar, mit dem der ausgeführte Versuch verglichen werden kann. Weiterhin wird durch den Einsatz von Monte-Carlo-Simulationen das in der Betriebsfestigkeit häufig zur Ermittlung von Langzeitfestigkeiten verwendete Treppenstufenverfahren am Rechner nachgebildet. Durch die Simulation lassen sich Aussagen über die Zuverlässigkeit des realen Versuchs ableiten und mit der analytischen Ideallösung vergleichen. Letztendlich lässt sich die Zuverlässigkeit der Kerbwirkungszahlschätzung bewerten, die aus der Verhältnisbildung zweier Zufallsexperimenten (Treppenstufenversuche) resultiert. In bisherigen Untersuchungen lag der Fokus auf separat betrachteten Treppenstufenversuchen. Die Fehlerfortpflanzung durch die Ergebnisverrechnung wurde bisher nicht betrachtet. Das Treppenstufenverfahren stellt eine Möglichkeit dar, Kerbwirkungszahlen mit ähnlichen Güten wie der analytischen Ideallösung zu schätzen. Um den Anteil nicht auswertbarer Versuchsfolgen im Treppenstufenversuch zu minimieren, sollten Durchläufer wiedereingesetzt werden.


*Correspondence Address, Dr.-Ing. Christian Müller, Hopfenstraße 20, 85114 Buxheim, Germany, E-mail:

Dr.-Ing. Christian Müller, born in 1984, studied Mechanical Engineering at Clausthal University of Technology (TUC), Germany and was a scientific employee at the Institute for Plant Engineering and Fatigue Analysis (IMAB) of TUC between 2010 and 2015. He completed his PhD thesis on the statistical evaluation of S-N curves in 2015. Since then, he has worked in the field of the fatigue strength of high-voltage batteries at Audi Ingolstadt, Germany.

Dr.-Ing. Michael Wächter, born in 1986, studied Mechanical Engineering at Clausthal University of Technology (TUC) and has been a scientific employee at the Institute for Plant Engineering and Fatigue Analysis (IMAB) of TUC in Clausthal, Germany since 2011. He completed his PhD thesis on the determination of cyclic material properties and S-N curves for damage parameters in 2016.

Dr.-Ing. Rainer Masendorf, born in 1964, studied Mechanical Engineering at Clausthal University of Technology (TUC) in Clausthal, Germany and has been a scientific employee at the Institute for Plant Engineering and Fatigue Analysis (IMAB) of TUC since 1994. His PhD thesis (2000) considered the influence of prestraining on cyclic material properties of thin sheets. He has been a leading engineer at IMAB since 2000. The focus of his work is fatigue testing of materials and components to determine fatigue properties.

Professor Dr.-Ing. Alfons Esderts, born in 1963, studied Mechanical Engineering at Clausthal University of Technology (TUC) and completed his PhD thesis in 1995. Between 1995 and 2003, he was head of the “Fatigue Analysis” department at Deutsche Bahn AG in Minden, Germany. Since 2003, he has been a professor at TUC and the head of the Institute for Plant Engineering and Fatigue Analysis (IMAB). In addition, he has been vice president for research and technology transfer at TUC since 2015.


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Published Online: 2018-09-26
Published in Print: 2018-10-27

© 2018, Carl Hanser Verlag, München

This work is licensed under the Creative Commons Attribution 4.0 International License.

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