A new distortion energy-based equivalent stress for multiaxial fatigue life prediction Onome Scott-Emuakpor a,n , Tommy George a , Charles Cross a , John Wertz b , M.-H. Herman Shen b a Air Force Research Laboratory, Wright-Patterson AFB, OH 45433, United States b Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210, United States article info Article history: Received 27 April 2010 Received in revised form 1 December 2011 Accepted 18 December 2011 Available online 27 December 2011 Keywords: Multiaxial Non-linear strain energy Fatigue abstract A new equivalent stress amplitude expression has been developed for the assessment of fatigue life in components under multiaxial loading. The expression was generated by incorporating non-linear/ plastic stress–strain relation into a mechanical energy calculation, and then applying the calculation to the distortion energy theory for a cyclic loading case. Therefore, the new uniaxial equivalent stress expression determines an appropriate stress amplitude value for multiaxial cyclic loading. The purpose of the equivalent stress value is to determine multiaxial fatigue failure using an energy-based fatigue life prediction criterion. The governing understanding behind the criterion states that the physical damage quantity for failure is equal to the accumulated strain energy in a monotonic fracture, which is also equal to the accumulated strain energy during fatigue failure. Using the new equivalent stress amplitude expression and the energy-based life prediction method, a comparison is made between prediction results and multiaxial empirical data. The multiaxial data was acquired by a vibration-based biaxial bending fatigue test and a torsion fatigue test with an assumed axial misalignment. The results of the comparison provide encouragement regarding the capability of the newly developed equivalent stress amplitude expression for fatigue life prediction. Published by Elsevier Ltd. 1. Introduction Fatigue-failure behavior of rotating components is often deter- mined using uniaxial stress design tools such as the modified Goodman diagram or a stress versus cycles to failure (S–N) curve [1, 2]; however, there are many cases where fatigue occurs under a multiaxial loading state. In these cases, fatigue life behavior is assessed by using an equivalent uniaxial stress value that represents multiaxial stresses. The conventionally used expression for equivalent stress is derived by incorporating the phase difference between each load direction into a von Mises stress calculation for alternating and mean stresses, where the resulting values are plotted on a Goodman diagram or an S–N curve [3]. With sufficient empirical results, this equivalent stress value is capable of expressing fatigue life behavior of multiaxially stressed components. Though the aforementioned equivalent stress value is acceptable for observing empirical fatigue life results graphically, it cannot be applied to the energy-based life prediction method developed in [4] to assess fatigue life without substantial experimental fatigue data. Therefore, an equivalent stress amplitude expression capable of predicting multiaxial fatigue life using this uniaxial energy-based method was necessary. The motivation behind the energy-based fatigue life prediction method comes from the Engine Structural Integrity Program (EnSIP) High Cycle Fatigue (HCF) evaluation guidelines, which requires that the fatigue life threshold of gas turbine engine components be defined as high as 10 9 cycles and characterized using empirical results [5]. Of the existing experimental HCF procedures, however, the maximum attainable cycling frequency is roughly around 20 kHz: ultrasonic piezoelectric horn-excitation experiments on a fixed-free coupon specimen [2]. This means it would take nearly 14 h to generate one empirical fatigue life data point for 10 9 cycle HCF characterization; thus, hundreds to thousands more hours of testing would be required to fully characterize HCF behavior using gas turbine engine design tools such as Goodman Diagrams and Random Fatigue Life (RFL) models. Based on the large time consumption of HCF testing, a helpful approach would be an empirically based model that can significantly reduce the amount of fatigue life data necessary to accurately assess HCF. In other words, it is necessary to have a physical damage quantity that is capable of correlating fatigue life and loading amplitude in an empirically based fatigue life prediction model which does not require hundreds to thousands of experimental hours to generate. The energy-based method is built according to these necessities. The energy-based life prediction method comes from a long line of energy/failure correlation research stating that strain Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/nlm International Journal of Non-Linear Mechanics 0020-7462/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.ijnonlinmec.2011.12.002 n Corresponding author. Tel.: þ1 937 255 6810; fax: þ1 937 656 5532. E-mail address: onome.scott-emuakpor@wpafb.af.mil (O. Scott-Emuakpor). International Journal of Non-Linear Mechanics 47 (2012) 29–37