PSI - Issue 19

Edrissa Gassama et al. / Procedia Structural Integrity 19 (2019) 711–718 Gassama et al./ Structural Integrity Procedia 00 (2019) 000 – 000

715

5

1 h S N  −  = 

(12)

where S  is the alternating stress range and N is the number of cycles. In this study, to account for nonlinearity, an additional parameter is added to the model, yielding the following form:

h S N  −

(13)

 = 

+

2 

1

To solve the above nonlinear equation using linear least-squares regression, a two-step approach was taken, wherein the value of h was first determined by taking the logarithm of Equation (12) and performing least-squares regression on the dataset absent any run-out points. The resulting solution for h was then substituted into Equation (13) and the dataset containing run-out points was fit using the procedure outline in Section 2.2.

3. Data Collection

The dataset used to fit the Master S-N curve in API 579 was extracted from reliable sources, with comprehensively documented experimental procedures (some of which include: Andrews (1996), Baptista et al. (2008), Bell and Vosikovsky (1993), Bell et al. (1989), Booth and Wylde (1990), Buitrago et al. (2003), ECSC (1975), Gioielli and Zettlemoyer (2007), Gioielli and Zettlemoyer (2008), Hechmet and Kuhn (1998), Hong (2010), Huo et al. (2005), Kang et al. (2011), Kang and Kim (2003), Kang et al. (2001), Kassner et al. (2010), Kihl and Sarkani (1997), Kihl and Sarkani (1998), Kim and Kang (2008), Kim and Yamanda (2005), Kim et al. (2006), Kim and Lotsberg (2005), Kirkhope et al. (1999), Kitsunai et al. (1998), Koenigs et al. (2003), Lindqvist (2002), Lotsberg (2009), Martinez and Blom (1997), Maddox (1982), Markl and George (1960), Mashiri et al. (2002), Mashiri et al. (2004), Mori et al. (2012), Mori et al. (2015), Ohta and Kudo (1980a), Ohta and Kudo (1980b), Okawa et al. (2013), Pook (1982), Rörup and Petershagen (2000), Sørenon et al. (2006), Spadea and Frank (2002), Tai and Miki (2014), Togasaki et al. (2010), Ting et al. (2009), Xiao and Yamada (2004), Xiao and Yamada (2005), Yagi and Tomita (1991), Yagi et al. (1991), Yagi et al. (1993), Yee et al. (1990)). However, run-out information was not originally published in the Master S-N Curve background documentation. In this study, we reviewed the same sources, both to verify the accuracy of the database and to document the run-out points that were left out of the original documentation. Some sources were not able to be retrieved as they were proprietary, internal reports which were not publicly accessible at the time of this publication. In total, approximately 1291 failure data points and 64 run-out data points were used in this analysis.

4. Results and Discussion

The procedure outlined in Section 2.2 is applied to the collected fatigue data with the form of the model expressed in Equation (13). The converged mean values for the parameters in the model are as follows:

1

N −

(14)

S  =

20475.8

15.48078



+

3.079355

The results of the fitting procedure are illustrated in Figure 1. The censored lives for the run-out points are shown in orange, and the estimated lives shown in green. From the inclusion of censored points alone, there is some indication that the lives at lower stresses deviate from the assumption of linearity, this becomes amplified when the lives at these stresses are estimated using the iterative solution procedure in 2.2. Interestingly, the nonlinear fit demonstrates good agreement with the bilinear curve with a slope of 5 m = after 10 7 cycles, a common approximation in various codes and standards. The lives predicted from the three forms of the curve (single slope, bilinear slope, and those from Equation (14)) are summarized for a select number of cases in Table 1.