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Considerations about the existence or non-existence of the fatigue limit: implications on practical design

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Abstract

In practical design, the question of existence or non-existence of fatigue limit seems little more than an irrelevant academic discussion. Nevertheless, the answer affects many aspects of the fracture mechanics, such as, the calculation of damage accumulation; recognition of the multiplicity of fatigue mechanisms (and consequently, the multiplicity of S–N fields); interpretation of non-propagating cracks; and repercussion on the Kitagawa-Takahashi diagram. Various prestigious scientists deny the existence of a fatigue limit based on the results of failures in very high cycle fatigue (VHCF) regime, far below the high cycle fatigue (HCF) limit. However, the asymptotic extrapolation of the experimental results beyond the scope of testing with S–N models, cannot confirm or deny this hypothesis if those models do not fulfil indispensable physical and statistical requirements. Some phenomenological models based on solid statistical conditions (stability, limit conditions and compatibility), ensure the necessary existence of an asymptotic fatigue limit for each of the possible failure mechanisms. This may or may not be zero according to the experimental results but only the presence of an asymptotic fatigue limit can avoid the absurdity of fatigue failure under zero load value.

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Abbreviations

\({a}_{i}\)::

Initial crack size

FS::

Fatemi-Socie

\(F(N;\,\varDelta \sigma )\)::

Cumulative distribution function of the number of cycles for a given stress range

\(F(\varDelta \sigma ;\,N)\)::

Cumulative distribution function of the stress range for a given number of cycles

GP::

Generalized parameter (driving force)

HCF::

High cycle fatigue

K–T::

Kitagawa-Takahashi (K–T)

N::

Generic number of cycles

\(N_{0}\)::

Limit number of cycles according to the Castillo-Canteli model

\(N_{F}\)::

Number of cycles to failure

\(N_{L}\)::

Limiting number of cycles specified in the fatigue design

\(N_{T}\)::

Total number of cycles corresponding to the load spectrum

SIF::

Stress intensity factor

SWT::

Smith-Watson-Topper

VHCF::

Very high cycle fatigue

\(V=(log\,N/N_{0})\,(log\,\varDelta \sigma \,/\,\varDelta \sigma _{0})\)::

Normalized variable of the S–N field according to the Castillo-Canteli model

\(\beta \)::

Weibull shape parameter

\(\lambda \)::

Weibull location parameter

\(\delta \)::

Weibull scale parameter

\(\varDelta \sigma _{lim}\)::

Fatigue limit

\(\varDelta \sigma _{lim,fct}\)::

Factual fatigue limit, i.e. fatigue resistance for a defined number of cycles \(N_{L}\)

\(\varDelta \sigma _{max}\)::

Maximum stress range

\(\varDelta \sigma \)::

Generic stress range

\(\varDelta \sigma _0\)::

Asymptotic fatigue limit, as a model parameter of the model of Castillo-Canteli

\(\varDelta K_{th}\)::

Threshold value of the stress intensity factor

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Authors and Affiliations

  1. Faculty of Engineering, University of Oviedo, Gijón, Spain

    A. Fernández-Canteli, S. Blasón & M. Muniz-Calvente

  2. Dept. of Mechanical and Plastics Engineering, Hochschule Darmstadt, Darmstadt, Germany

    B. Pyttel

  3. Spanish Royal Academy of Engineering, Madrid, Spain

    E. Castillo

  4. Spanish Royal Academy of Sciences, Madrid, Spain

    E. Castillo

Authors
  1. A. Fernández-Canteli
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  2. S. Blasón
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  3. B. Pyttel
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  4. M. Muniz-Calvente
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  5. E. Castillo
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Correspondence to S. Blasón.

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Fernández-Canteli, A., Blasón, S., Pyttel, B. et al. Considerations about the existence or non-existence of the fatigue limit: implications on practical design. Int J Fract 223, 189–196 (2020). https://doi.org/10.1007/s10704-019-00413-6

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