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A critical plane criterion to multiaxial fatigue of metals containing small defects

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Abstract

A critical plane criterion for the fatigue limit of metals with small defects is developed based on the \(\sqrt{\mathrm{area}}\) parameter. The criterion is designed to reflect the Mode I-dominated physical damage mechanism of small defects. The concept of directionally dependent fatigue strength is introduced to extend the critical plane definition to defects whose projected area varies with the plane. The Walker relation with a critical plane interpretation is used to account for the mean stress effect. The criterion is evaluated using available experimental data of steels containing artificial surface defects and a ductile cast iron having inherent graphite nodules. The experiments include different proportional and nonproportional axial-torsional loading conditions and defect types (cylindrical, hemispherical, and tilted hemiellipsoidal holes). The criterion is found to give good estimates of both fatigue limits and crack directions. A discussion on the physical interpretation of critical plane criteria in the context of the small defect fatigue problem is presented.

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Abbreviations

A :

Fitting constant

\(\sqrt {{\text{area}}}\) :

Projected defect area

\(\sqrt {{\text{area}}} _{{{\text{max}}}}\) :

Largest projected defect area

b :

Fitting constant

FP:

Fatigue parameter

\(H_{{\text{v}}}\) :

Vickers hardness

\(k\) :

Defect sensitivity to biaxial stresses

\(m\) :

Constant of the Walker relation

θ :

Plane angle

\(\sigma _{{\text{a}}}\) :

Axial stress amplitude

\(\sigma _{{\text{m}}}\) :

Mean axial stress

\(\sigma _{{\text{w}}}\) :

Uniaxial fatigue strength

\(\sigma _{{{\text{w}^{\prime}}}}\) :

Uniaxial fatigue strength as a function of \(\sqrt {{\text{area}}}\)

\(\sigma _{{\text{x}}}\) :

Axial stress

\(\sigma _{{{\text{x}^{\prime}}}}\) :

Normal stress acting perpendicular to a plane θ

\(\sigma _{{{\text{y}^{\prime}}}}\) :

Normal stress acting parallel to a plane θ

\(\bar{\sigma }\) :

Linear combination of normal stresses at a plane θ

\(\tau _{{\text{a}}}\) :

Shear stress amplitude

\(\tau _{{\text{m}}}\) :

Mean shear stress

\(\tau _{{\text{w}}}\) :

Fatigue strength in shear

\(\tau _{{{\text{xy}}}}\) :

Shear stress

\(\varphi\) :

Phase angle

\(\omega\) :

Angular frequency

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Acknowledgements

Fábio Castro and Edgar Mamiya would like to thank the support from the National Council for Scientific and Technological Development – CNPq (contracts 308126/2016-5 and 310063/2018-3). Fábio Castro also acknowledges the support from FAP-DF under contract number 0193.001583/2017. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Brasilia, Brasilia, DF, 70910-900, Brazil

    F. C. Castro, E. N. Mamiya & C. Bemfica

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  1. F. C. Castro
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  2. E. N. Mamiya
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Correspondence to F. C. Castro.

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Appendix

Appendix

A summary of the fatigue limit data and mechanical properties of the materials used in this work are provided below.

See Tables 3, 4, 5 and 6.

Table 3 Fatigue limit data of S35C steel*
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Table 4 Fatigue limit data of SCM435 steel*
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Table 5 Fatigue limit data of FCD400 ductile cast iron*
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Table 6 Fatigue limit data of C36 steel*
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Castro, F.C., Mamiya, E.N. & Bemfica, C. A critical plane criterion to multiaxial fatigue of metals containing small defects. J Braz. Soc. Mech. Sci. Eng. 43, 517 (2021). https://doi.org/10.1007/s40430-021-03246-4

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