Accessible Requires Authentication Published by De Gruyter August 18, 2021

Evaluation of S-N curves including failure probabilities using short-time procedures

Ruth Acosta, Christian Boller, Markus Doktor, Haoran Wu, Hanna Jost, Fabian Weber and Peter Starke
From the journal Materials Testing


In recent years, different short-time procedures have been developed that significantly reduce the experimental effort required to generate S-N curves and thus S-N databases. Methods like StressLife, StrainLife, and SteBLife are some of those which have shown enormous potential in this respect. In this contribution, the practicability of the SteBLife method is shown. Two S-N curve evaluation strategies based on temperature and magnetic field measurements are presented. These take statistical evaluation into account, describing a material’s scatter in terms of fatigue life. In order to demonstrate the versatility of the approach and to underline the advantages in terms of effort saved when compared to conventional procedures, the process on how to get the required information obtained is shown for three unalloyed and low-alloyed steels under different heat treatment conditions.

University of Applied Sciences Kaiserslautern Department of Materials Science and Materials Testing Institute Quality, Modeling, Machining & Materials Schoenstr.11 D-67659 Kaiserslautern Germany


The authors would like to thank the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG STA 1133/ 6-1 and STA 1133/10-1) and the University of Applied Sciences Kaiserslautern for financial support for this research.

The authors would also thank Shimadzu Germany/Europe and Micro-Epsilon for their support in technical equipment provision.


1 R. Masendorf, C. Müller: Execution and evaluation of cyclic tests at constant load amplitudes – DIN 50100:2016, Materials Testing 60 (2018), No. 10, pp. 961-968 DOI:10.3139/120.111238 Search in Google Scholar

2 P. Starke, H. Wu: Use of non-destructive testing methods in a new one-specimen test strategy for the estimation of fatigue data, International Journal of Fatigue 111 (2018), pp. 177-185 DOI:10.1016/j.ijfatigue.2018.02.011 Search in Google Scholar

3 H. Wu, A. Bäumchen, A. Engel, R. Acosta, C. Boller, P. Starke: SteBLife – A new short-time procedure for the evaluation of fatigue data, International Journal of Fatigue 124 (2019), pp. 82-88 DOI:10.1016/j.ijfatigue.2019.02.049 Search in Google Scholar

4 P. Starke, A. Bäumchen, H. Wu: SteBLife – A new short-time procedure for the calculation of S-N curves and failure probabilities, Materials Testing 60 (2018), No. 2, pp. 121-127 DOI:10.3139/120.111139 Search in Google Scholar

5 P. Starke, H. Wu, C. Boller: SteBLife – The enhanced short-time evaluation procedure for materials fatigue data generation, Materials Science Forum 941 (2019), pp. 2395-2400 DOI:10.4028/ Search in Google Scholar

6 R. Acosta, H. Wu, R. Sridaran Venkat, F. Weber, J. Tenkamp, F. Walther, P. Starke: SteBLife, a new approach for the accelerated generation of metallic materials’ fatigue data, Metals 10 (2020), No. 798, pp. 1-17 DOI:10.3390/met10060798 Search in Google Scholar

7 A. Piotrowski, D. Eifler: Characterization of cyclic deformation behaviour by thermometrical and electrical methods, Materialwissenschaft und Werkstofftechnik 26 (1995), No. 3, pp. 121-127 DOI:10.1002/mawe.19950260305 (in German) Search in Google Scholar

8 M. D. Sangid: The physics of fatigue crack initiation, International Journal of Fatigue 57 (2013), pp. 58-72 DOI:10.1016/j.ijfatigue.2012.10.009 Search in Google Scholar

9 I. Altpeter, G. Dobmann, NDE of material degradation by embrittlement and fatigue, D. O Thompson, D. E. Chimenti (Eds.): Proc. of Review of Quantitative Nondestructive Evaluation 22 (2003), pp. 15-21 DOI:10.1063/1.1570115 Search in Google Scholar

10 P. Starke, D. Eifler, C. Boller: Fatigue assessment of metallic materials beyond strain measurement, International Journal of Fatigue 82 (2016), pp. 274-279 DOI:10.1016/j.ijfatigue.2015.03.018 Search in Google Scholar

11 N. Kasai, H. Koshino, K. Sekine, H. Kihira, M. Takahashi: Study on the effect of elastic stress and microstructure of low carbon steels on Barkhausen noise, Journal of Nondestructive Evaluation 32 (2013), No. 3, pp. 277-285 DOI:10.1007/s10921-013-0180-1 Search in Google Scholar

12 M. Küpferling, F. Fiorillo, V. Basso, G. Bertotti, P. Meilland: Barkhausen noise in plastically deformed low-carbon steels, Journal of Magnetism and Magnetic Materials 320 (2008), No. 20, pp. e527-e530 DOI:10.1016/j.jmmm.2008.04.009 Search in Google Scholar

13 C. C. H. Lo, E. Kinser, D. C. Jiles: Modeling the interrelating effects of plastic deformation and stress on magnetic properties of materials, Journal of Applied Physics 93 (2003), No. 10, pp. 6626-6628 DOI:10.1063/1.1557356 Search in Google Scholar

14 J. M. Makar, B. K. Tanner: The in situ measurement of the effect of plastic deformation on the magnetic properties of steel, Journal of Magnetism and Magnetic Materials 184 (1998), No. 2, pp. 193-208 DOI:10.1016/s0304-8853(97)01129-3 Search in Google Scholar

15 J. M. Makar, B. K. Tanner: Effect of plastic deformation and residual stress on the permeability and magnetostriction of steels, Journal of Magnetism and Magnetic Materials 222 (2000), No. 3, pp. 291-304 DOI:10.1016/S0304-8853(00)00558-8 Search in Google Scholar

16 J. Li, M. Xu, J. Leng, M. Xu: Modeling plastic deformation effect on magnetization in ferromagnetic materials, Journal of Applied Physics 111, 063909 (2012), No. 6 DOI:10.1063/1.3695460 Search in Google Scholar

17 S. M. Thompson, B. K. Tanner: The magnetic properties of plastically deformed steels, Journal of Magnetism and Magnetic Materials 83 (1990), No. 1-3, pp. 221-222 DOI:10.1016/0304-8853(90)90493-A Search in Google Scholar

18 J. D. Morrow: Cyclic plastic strain energy and fatigue of metals, Internal Friction, Damping, and Cyclic Plasticity, American Society for Testing and Materials (1964), pp. 45-87 DOI:10.1520/STP43764S Search in Google Scholar

19 O. H. Basquin: The exponential law of endurance, American Society for Testing and Materials 10 (1910), pp. 625-630 Search in Google Scholar

20 R. Marek, K. Nitsche: Heat Transfer – Practice – Fundamentals – Applications – Exercises, 3rd Ed., Hanser, Munich, Germany (2012) (in German) DOI:10.3139/9783446433205 Search in Google Scholar

21 P. Böckh, T. Wetzel: Heat Transfer – Fundamentals and Practice, 6th Ed., Springer Vieweg, Berlin, Germany (2015) (in German) DOI:10.1007/978-3-662-44477-1 Search in Google Scholar

22 N. Hannoschöck: Heat Conduction and Transport – Fundamentals of Heat and Mass Transfer, 1st Ed., Springer Vieweg, Berlin, Germany (2018) (in German) DOI:10.1007/978-3-662-57572-7_1 Search in Google Scholar

23 C. Müller: About the Statistical Evaluation of Experimental S-N Lines, Dissertation, Clausthal University of Technology (2015) (in German) Search in Google Scholar

24 ASTM E739-10(2015): Standard Practice for Statistical Analysis of Linear or Linearized Stress-Life (S-N) and Strain-Life (ε-N) Fatigue Data, ASTM International, West Conshohocken, PA, USA (2015) DOI:10.1520/E0739-10R15 Search in Google Scholar

25 DIN50100 : 2016-12: Load Controlled Fatigue Testing – Execution and Evaluation of Cyclic Tests at Constant Load Amplitudes on Metallic Specimens and Components, Beuth, Berlin, Germany (2016) Search in Google Scholar

26 ISO 12107 : 2012: Metallic Materials – Fatigue Testing – Statistical Planning and Analysis of Data – International Organization for Standardization, Geneva, Switzerland (2012) Search in Google Scholar

27 J. A. Villaseñor-Alva, E. González-Estrada: A bootstrap goodness of fit test for the generalized Pareto distribution, Computational Statistics and Data Analysis 53 (2009), No. 11, pp. 3835-3841 DOI:10.1016/j.csda.2009.04.001 Search in Google Scholar

28 G. M. Goerg: Lambert W random variables-a new family of generalized skewed distributions with applications to risk estimation, The Annals of Applied Statistics 5 (2011), No. 3, pp. 2197-2230 DOI:10.1214/11-AOAS457 Search in Google Scholar

29 J. Shao: Mathematical Statistics, 2nd Ed., Springer Science+Business Media, LLC, New York, USA (2003) Search in Google Scholar

30 L. Györfi, M. Kohler, A. Krzyzak, H. Walk: A distribution-free theory of nonparametric regression, Springer, New York, USA (2002) DOI:10.1007/b97848 Search in Google Scholar

31 B. W. Silverman: Density estimation for statistics and data, Monographs on Statistics and Applied Probability, Chapman and Hall, London (1986) Search in Google Scholar

32 R Core Team: R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, 2017, Online available at: Search in Google Scholar

33 A. Baddeley, E. Rubak, R. Turner: Spatial point patterns: methodology and applications with R, Chapman and Hall CRC Press, New York, USA (2015) DOI:10.1201/b19708 Search in Google Scholar

34 A. Martin, K. Hinkelmann, E. Clausthal-Zellerfeld: On the evaluation of fatigue tests in the time strength range – Part 1: how reliably can 50 % S-N lines be estimated from experimental data?, Materials Testing 53 (2011), No. 9, pp. 502-512 DOI:10.3139/120.110255 (in German) Search in Google Scholar

35 M. Weber, M. Doktor, J.-P. Stockis, C. Glock, W. Kurz, C. Fox: Outlier tests in the determination of the in-situ concrete compressive strength – Applicability of the Grubbs test and other outlier tests, Beton 6 (2019), Verlag Bau+Technik GmbH, pp. 212 (in German) Search in Google Scholar

36 M. S. Doktor, C. Fox, W. Kurz, J. P. Stockis: Characterization of steel buildings by means of non-destructive testing methods, Journal of Mathematics in Industry 8 (2018), No. 10 DOI:10.1186/s13362-018-0052-5 Search in Google Scholar

37 P. Ruckdeschel, B. Spangl, D. Pupashenko: Robust Kalman tracking and smoothing with propagating and non-propagating outliers, Statistical Papers 55 (2014), No. 1, pp. 93-123 DOI:10.1007/s0036201204964 Search in Google Scholar

Published Online: 2021-08-18
Published in Print: 2021-08-31

© 2021 Walter de Gruyter GmbH, Berlin/Boston, Germany