PSI - Issue 17

Juan Cruz Castro et al. / Procedia Structural Integrity 17 (2019) 115–122 Juan Cruz Castro et al./ Structural Integrity Procedia 00 (2019) 000 – 000

119

5

Table 4 shows the number of cycles to failure N f for carbon steel with S u <552MPa (ASME, 2004). The vast majority of fatigue curves and tables have been determined for completely reversed sinusoidal stress, that is, with a mean stress equal to zero σ m =0 . An additional equation is needed when such curves have a non-zero mean stress. The mean stress, σ m , has a substantial influence on fatigue behaviour (Dowling, 2004; Dowling et al. , 2009). Different theories have been reported in the literature, such as Goodman (Eq. 1) and Gerber (Eq. 2).



(1)



=

a

ar

1

m u  

−

a 

(2)



=

ar

(

) 2

1

m u  

−

According to Dowling (Dowling, 2004; Dowling et al. , 2009), the equation of Walker (Eq. 3) and the equation of Morrow (Eq. 4) give a good estimate for the adjustment of the Stress-Life curve with a non-zero mean stresses for steels, where a σ Equivalent completely reversed stress amplitude is estimated. It is obtained with the combination of alternating stress σ =(1/2)( σ max - σ min ) , and mean stress σ =(1/2)( σ max + σ min ) . ' 1 a ar m f     = − (3) The disadvantage of the equation of Morrow is the true fracture strength. It is not available for several materials. An estimate, which has been used for the case of steels, is to obtain the true fracture strength based on the ultimate tensile strength. This is σ ' f = σ u +345 MPa (Dowling et al. , 2009). On the other hand, the equation of Walker (Eq. 4) requires the constant γ. A linear relationship (Eq. 5) has been used for the determination of γ for steel (Dowling et al. , 2009). ( ) 1 2 ar m a R      −  = +     (4) 0.0002 0.8818 u   = − + (5) The tabulated values of the fatigue curve of the ASME – BPVC are shown in Table 4 (ASME, 2004). The number of the cycles to failure N f for diverse cyclic loads can be obtained. The intermediate values can be estimated by interpolation. This is based on the Equivalent completely reversed stress amplitude σ ar through Eq. 6. log ( / ) log ( / ) i ar i j S S S f j       

i i N N N N

  =    

(6)

Table 4. Tabulated Values of σ ar for carbon steel with S u <552MPa, according to BPVC (ASME, 2004)

N f

1e1

2e1

5e1

1e2

2e2

5e2

1e3 572

2e3 441

5e3 331

1e4 262

2e4 214

5e4 159

1e5 138

2e5 114

5e5

1e6

σ ar [MPa]

3999 2827 1896 1413 1069 724

93

86

Finally, the determination of the Cumulative Usage Factor is through the rule of Miner Eq. 7, performing the summation of the cycle relation for each of the cyclic loads. (7) The number of cycles were estimated for 60 years of operation of the BWR reactor building crane. It was based on the reported data for the renewal of operational license of the Limerick (USNRC, 2014) and LaSalle (USNRC, 2016) plants. In Table 3, it can be observed the load cycles n and the different loads considered. i i n CUF N = 

5. RESULTS

The maximum and minimum stresses for every case were calculated based on Maximum-Shear-Stress theory by means of ANSYS code. Subsequently, the Equivalent completely reversed stress amplitudes of the critical regions of