Multiaxial vibration fatigue—A theoretical and experimental comparison

Abstract Random vibration excitation is a common cause of failure, especially if natural dynamics is excited. The high-cycle vibration-fatigue analysis typically requires the structural dynamics analysis, the response analysis and the fatigue analysis. The material parameters (S–N curve) are obtained at uniaxial stress state. However, in real structures the stress state is rarely uniaxial and the direct application of the S–N curve is difficult. The stress tensor is reduced to a more manageable representation using a multiaxial criterion. In this study, maximum normal stress, maximum shear stress, maximum normal-and-shear stress, C–S criterion, Projection-by- Projection and the Preumont and Piefort criterion for multiaxial stress state are compared theoretically and experimentally. The crack location and the time-to-failure were compared. The time-to-failure was found relatively accurate with all multiaxial criteria; however, the crack-location estimation was found not to be accurate enough for either of the compared criteria. The study proves the applicability of the vibration-fatigue analysis procedure on real vibrating structures with rich structural dynamics. Random vibration excitation is a common cause of failure, especially if natural dynamics is excited. The high-cycle vibration-fatigue analysis typically requires the structural dynamics analysis, the response analysis and the fatigue analysis. The material parameters (S–N curve) are obtained at uniaxial stress state. However, in real structures the stress state is rarely uniaxial and the direct application of the S–N curve is difficult. The stress tensor is reduced to a more manageable representation using a multiaxial criterion. In this study, maximum normal stress, maximum shear stress, maximum normaland-shear stress, C–S criterion, Projection-by-Projection and the Preumont and Piefort criterion for multiaxial stress state are compared theoretically and experimentally. The crack location and the time-to-failure were compared. The time-to-failure was found relatively accurate with all multiaxial criteria; however, the crack-location estimation was found not to be accurate enough for either of the compared criteria. The study proves the applicability of the vibration-fatigue analysis procedure on real vibrating structures with rich structural dynamics.

[1]  R. Brook,et al.  Cumulative Damage in Fatigue: A Step towards Its Understanding , 1969 .

[2]  Yi Sun,et al.  A hybrid frequency–time domain method for predicting multiaxial fatigue life of 7075-T6 aluminium alloy under random loading , 2015 .

[3]  W. Findley.  A Theory for the Effect of Mean Stress on Fatigue of Metals Under Combined Torsion and Axial Load or Bending , 1959 .

[4]  Chan-Jung Kim,et al.  Experimental spectral damage prediction of a linear elastic system using acceleration response , 2011 .

[5]  Roberto Tovo,et al.  A stress invariant based spectral method to estimate fatigue life under multiaxial random loading , 2011 .

[6]  Jorge Nocedal,et al.  Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization , 1997, TOMS.

[7]  Xu Chen,et al.  Evaluation of multiaxial fatigue criteria under irregular loading , 2002 .

[8]  Andrea Carpinteri,et al.  Reformulation in the frequency domain of a critical plane-based multiaxial fatigue criterion , 2014 .

[9]  Andrea Carpinteri,et al.  Multiaxial high-cycle fatigue criterion for hard metals , 2001 .

[10]  K. Kluger.  Fatigue life estimation for 2017A-T4 and 6082-T6 aluminium alloys subjected to bending-torsion with mean stress , 2015 .

[11]  Adam Niesłony,et al.  Comparison of some selected multiaxial fatigue failure criteria dedicated for spectral method , 2010 .

[12]  Igor Rychlik,et al.  Fatigue and stochastic loads , 1996 .

[13]  André Preumont,et al.  Spectral methods for multiaxial random fatigue analysis of metallic structures , 2000 .

[14]  Nuno M. M. Maia,et al.  Theoretical and Experimental Modal Analysis , 1997 .

[15]  J. Bendat,et al.  Random Data: Analysis and Measurement Procedures , 1987 .

[16]  D. Newland.  An introduction to random vibrations and spectral analysis , 1975 .

[17]  M. Matsuichi,et al.  Fatigue of metals subjected to varying stress , 1968 .

[18]  Bin Li,et al.  A Procedure for Fast Evaluation of High-Cycle Fatigue Under Multiaxial Random Loading , 2002 .

[19]  Shahram Sarkani,et al.  Random Vibrations: Analysis of Structural and Mechanical Systems , 2003 .

[20]  Tomokazu Matake.  An Explanation on Fatigue Limit under Combined Stress , 1977 .

[21]  A. Palmgren.  Die Lebensdauer von Kugellargern , 1924 .

[22]  Ed Habtour,et al.  Review of Response and Damage of Linear and Nonlinear Systems under Multiaxial Vibration , 2014 .

[23]  D. L. McDiarmid,et al.  A SHEAR STRESS BASED CRITICAL‐PLANE CRITERION OF MULTIAXIAL FATIGUE FAILURE FOR DESIGN AND LIFE PREDICTION , 1994 .

[24]  D. F. Socie,et al.  Benchmark Problems in Multiaxial Fatigue , 2015 .

[25]  Soon-Bok Lee,et al.  A critical review on multiaxial fatigue assessments of metals , 1996 .

[26]  Mauro Filippini,et al.  A comparative study of multiaxial high-cycle fatigue criteria for metals , 1997 .

[27]  Mark Edward Paulus.  Fatigue damage accumulation due to complex random vibration environments: Application to single-axis and multi-axis vibration , 2011 .

[28]  Yi Sun,et al.  Fatigue life estimation under multiaxial random loading by means of the equivalent Lemaitre stress and multiaxial S–N curve methods , 2015 .

[29]  Denis Benasciutti,et al.  Some analytical expressions to measure the accuracy of the “equivalent von Mises stress” in vibration multiaxial fatigue , 2014 .

[30]  Adam Niesłony,et al.  Spectral Method in Multiaxial Random Fatigue , 2007 .

[31]  Janko Slavič,et al.  Frequency-domain methods for a vibration-fatigue-life estimation – Application to real data , 2013 .

[32]  F. Roosevelt,et al.  Tools for a Multiaxial Fatigue Analysis of Structures Submitted to Random Vibrations , 2022 .

[33]  Angela Halfpenny,et al.  A Frequency Domain Approach for Fatigue Life Estimation from Finite Element Analysis , 1999 .

[34]  Jorge Nocedal,et al.  Large Scale Unconstrained Optimization , 1997 .

[35]  Turan Dirlik,et al.  Application of computers in fatigue analysis , 1985 .

[36]  Janko Slavič,et al.  A comparison of strain and classic experimental modal analysis , 2016 .

[37]  John W. Miles,et al.  On Structural Fatigue Under Random Loading , 1954 .

[38]  M.H.A. Bonte,et al.  Determining the von Mises stress power spectral density for frequency domain fatigue analysis including out-of-phase stress components , 2007 .

[39]  Janko Slavič,et al.  Uninterrupted and accelerated vibrational fatigue testing with simultaneous monitoring of the natural frequency and damping , 2012 .

[40]  Janko Slavič,et al.  Vibrational Fatigue and Structural Dynamics for Harmonic and Random Loads , 2013 .

[41]  André Preumont,et al.  Spectral methods to estimate local multiaxial fatigue failure for structures undergoing random vibrations , 2001 .

[42]  André Preumont,et al.  Predicting random high-cycle fatigue life with finite elements , 1994 .

[43]  Tadeusz Łagoda,et al.  Comparison of the fatigue characteristics for some selected structural materials under bending and torsion , 2011 .

[44]  Aleksander Karolczuk,et al.  Critical Planes in Multiaxial Fatigue , 2005 .

[45]  Murat Aykan,et al.  Vibration fatigue analysis and multi-axial effect in testing of aerospace structures , 2009 .

[46]  D. Benasciutti,et al.  Spectral methods for lifetime prediction under wide-band stationary random processes , 2005 .

[47]  Luca Susmel,et al.  A stress invariant based criterion to estimate fatigue damage under multiaxial loading , 2008 .

[48]  Norris Stubbs,et al.  Damage identification in beam-type structures: frequency-based method vs mode-shape-based method , 2003 .

[49]  Janko Slavič,et al.  Frequency-based structural modification for the case of base excitation , 2013 .