A simple finding on variable amplitude (Gassner) fatigue SN curves obtained using Miner’s rule for unnotched or notched specimen

We provide a very simple result for a problem which has been often neglected (variable amplitude loading) in academia, but which is of paramount importance in real engineering situations, where fatigue is almost never "constant amplitude".

We found few cases where we could check this extremely simple result, but it worked very well.  We would welcome further verifications.

The paper is in press here.

Engineering Fracture Mechanics

Available online 10 March 2017

In Press, Accepted Manuscript — Note to users

 A simple finding on variable amplitude (Gassner) fatigue SN curves obtained using Miner’s rule for unnotched or notched specimen

• M. Ciavarella, , 
• P. D’Antuono, 
• G.P. Demelio

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http://dx.doi.org/10.1016/j.engfracmech.2017.03.005

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Abstract

In this note, starting from the SN curve under Constant Amplitude (CA) for the fatigue life of the uncracked (plain) specimen, we obtain that Gassner curves for Variable Amplitude (VA) loading using the simple Palmgren-Miner’s law are simply shifted CA curves. Further, using the Critical Distance Method in a very clean and powerful form proposed by Susmel and Taylor for VA loading, we find similar result for notched specimen, the spectrum loading results in the same multiplicative term for notched, cracked and unnotched specimen. Hence, the present proposal can be considered as a simple empirical unified approach for rapid assessment of the notch effect under random loading, which simplifies the recent proposal by Susmel and Taylor. To their extensive validations, we add some specific comparison with experimental data from the Literature on our further findings.

Keywords

• Fatigue; 
• Notches; 
• Medium-Cycle fatigue; 
• Critical distance approach; 
• Random loading

Highlights

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We obtain Gassner curves using the simple Palmgren-Miner’s law and Point Critical Distance Method

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We find (either analytically or numerically) Gassner curve are simply shifted CA curves.

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Spectrum loading results in the same multiplicative term for notched, racked and unnotched specimen.

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A simple empirical unified approach for rapid assessment of the notch effect under random loading is proposed

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Experimental data from the Literature seem to confirm these simple findings, despite the strong assumptions

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The iterative solution suggested by Susmel and Taylor seems not needed.