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Assessing Phase Relationships Between Stress Components in Statistical Fatigue Evaluations

Random vibration loading commonly induces non-proportional multiaxial stress states. Their evaluation requires sophisticated methods, which often entail high computational demands. To address this, statistical characterizations of loading and stresses have emerged as a powerful approach, enabling highly efficient evaluations across entire finite element (FE) models, including parametric analyses of critical planes.

These statistical characterizations combine two key aspects: frequency-domain characterizations, which account for structural dynamics and cycle counting, and correlation statistics, such as the covariance matrix, to describe interactions between stress components. However, traditional covariance matrix analysis fails to capture the full phase information necessary…

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Description

To overcome this limitation, we introduce a complex-valued covariance matrix as an extension of the well-know covariance matrix. We demonstrate its utility in characterizing multiaxial stress states through a comparative study of time- and frequency-domain approaches. Our contribution will focus on accurately considering the interactions between shear and normal stresses on critical planes and proposing an extension of a widely used critical plane criterion for random vibration fatigue.

In summary, this work highlights the potential of statistical-based fatigue evaluations as a fast alternative to time-domain assessments of multiaxial stress states. Such an approach can serve as a pre-processing step to identify critical nodes and plane orientations for subsequent time-domain analyses or as input for fatigue damage estimations using statistical damage models.

Reference: ICMFF14-2025-46

Title: Assessing Phase Relationships Between Stress Components in Statistical Fatigue Evaluations
Author(s): A. Trapp, K. Rother
DOI: 10.48447/ICMFF14-2025-46
Event: 14. International Conference on Multiaxial Fatigue and Fracture 2025
Year of publication: 2025
Publication type: conference paper (PDF)
Language: English
Keywords: Variable Amplitude Loading,Random Vibration Loading,Critical Plane Approach,Statistical Fatigue Assessment

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Author(s): S. J. Duda, M. Smolnicki, G. Lesiuk, A. Fatemi

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Fatigue life prediction of continuous fiber reinforced polymers under multiaxial loading conditions based on the critical plane approach

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Author(s): A. Chiocca, F. Frendo, M. Sgamma

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Author(s): N. Santos, R. Costa, F. Castro

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Author(s): M. Müller, D. Knabner, L. Suchy, A. Hasse

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Author(s): S.S. Penkulinti, N. Saintier, M. Bonneric, B. Verquin, T. Palin-Luc, F. Lefebvre

Numerical Analysis of Defect Population Influence on the Multiaxial High-cycle Fatigue Strength Anisotropy of Ti64 Manufactured by Laser Powder Bed Fusion (L-PBF)

Publication type: conference paper (PDF)

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Author(s): A. Zaiat, A. Blug, G. Laskin, A. Bertz, F. Conrad, C. Kontermann, M. Oechsner

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Author(s): G. A. Brito Oliveira, I. M. Matos, R. A. Cardoso, J. A. Araújo

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Author(s): A. Trapp, K. Rother

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Author(s): M. Wächter, R. Wuthenow, C. Fällgren, H.-T. Beier, M. Obermayr, R. Rennert, M. Vormwald, A. Esderts

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Evaluation of multi-axial stresses using the FKM guideline - status quo and how it can be improved

Publication type: conference paper (PDF)

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€25.00

Online only New

Author(s): N. B. Winther, M. L. Larsen, S. M. Jenson, J. H. Andreasen, J. Schjødt-Thomsen

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Multiaxial Fatigue Testing of Welded Steel Joints Subjected to Non-Proportional Stress States Induced by Frequency Difference Between Normal and Shear Stresses

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€25.00

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Author(s): J.-A. Meis

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Interior fatigue of gears under special consideration of multiaxial stresses and local material properties

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English

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