A deviatoric version of the SWT parameter Daniel Kujawski Department of Mechanical and Aerospace Engineering, Western Michigan University, Kalamazoo, MI 49008, USA article info Article history: Received 4 October 2013 Received in revised form 19 November 2013 Accepted 1 December 2013 Available online xxxx Keywords: Fatigue life analysis SWT parameter Neuber’s rule Mean stress Deviatoric strain energy abstract The Smith–Watson–Topper parameter (SWT = r max e a ) was originally suggested and is still widely used to account for the mean stress effects in fatigue life analysis. It is well recognized however, that the SWT parameter might be a non-conservative description for cyclic loads that involve relatively large compres- sive mean stresses that can develop in samples/components with notches after overloads. In such situa- tions r max tends to be small resulting in underestimating the SWT parameter. It is shown that the SWT parameter can be interpreted in terms of the sum of strain energy and complementary strain energy den- sities supplemented by the strain energy density associated with a mean stress in the cycle. Using this energy interpretation and its analogy with the Neuber’s rule a deviatoric version of the SWT parameter called SWT D is proposed. It is found that for positive mean stresses and moderate negative mean stresses the original SWT parameter and the proposed deviatoric SWT D parameter yield similar results. At large compressive mean stresses, the deviatoric SWT D parameter demonstrates a fairly good correlation while the original SWT parameter is unable to correlate the data. Although the proposed approach seems to be very promising, based on the limited data of this study, it should be further re-examined using more experimental data sets, in particular for multiaxial in-phase and out-of-phase loadings. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Engineering components subjected to cyclic loading often expe- rience mean stresses effects on fatigue life. It is well known that the tensile mean stress is detrimental, whereas the compressive mean stress is beneficial [1,2]. Fig. 1 depicts the typical notation used in the description of a fatigue hysteresis loop showing the key parameters used in fatigue life analysis. In the past, various ap- proaches have been proposed for estimating mean stress effect on stress-life, strain-life, and stress/strain-life relationships. In this section a brief review of the selected and most widely used models and some recent approaches is summarized. 1.1. Stress-life models In general, the stress-life (or S–N) formulations have been used at high-cycle fatigue (HCF). The first stress-life relationship was proposed by Basquin [3] r a ¼ AðN f Þ B ð1Þ where r a is a stress amplitude, N f is a number of cycles to failure whereas A and B are fitting constants to experimental data. Follow- ing Morrow [4], the Basquin’s relationship is customarily used in terms of reversals to failure, 2N f , and for a fully-reversed stress amplitude, r ar , has the following form r ar ¼ r 0 f ð2N f Þ b ð2Þ where r 0 f is the fatigue strength coefficient, which corresponds to the failure stress amplitude for a single reversal, and b is the fatigue strength exponent or the slope of the best fit line in log r ar  log 2N f plot. In order to account for the combined effect of the stress ampli- tude, r a , and the mean stress, r m , the following models are often used, which allow to estimate the corresponding equivalent fully- reversed stress amplitude, r ar : Gerber [5] r a r ar þ r m r u  2 ¼ 1 ð3aÞ Goodman [6] r a r ar þ r m r u ¼ 1 ð3bÞ Soderberg [7] r a r ar þ r m r 0 ¼ 1 ð3cÞ Morrow [4] r a r ar þ r m r 0 f ¼ 1 ð3dÞ 0142-1123/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2013.12.002 E-mail address: daniel.kujawski@wmich.edu International Journal of Fatigue xxx (2014) xxx–xxx Contents lists available at ScienceDirect International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue Please cite this article in press as: Kujawski D. A deviatoric version of the SWT parameter. Int J Fatigue (2014), http://dx.doi.org/10.1016/ j.ijfatigue.2013.12.002