PSI - Issue 45

Teresa Magoga et al. / Procedia Structural Integrity 45 (2023) 28–35 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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5

The fatigue relationship between 5x10 6 and 10 8 cycles is defined by Equation 2: =5×10 6 ( ∆ ∆ ) 2 ( 2 5 ) 2 1

(2)

In Eurocode 9, the modified nominal stresses should be used when there are gross geometrical effects present in the vicinity of the initiation site. Gross geometrical effects include cut-outs, re-entrant corners, and gross changes in stiffness at junctions between open or hollow sections. For example, Fig. 1 reveals a significant stress concentration at detail of interest ID-1 (circumferential weld at the top of a pillar) under the wave crest landing condition. There is no clear nominal stress in the pillar. Therefore, it is judicious to use the modified nominal stress.

 max

 min

Fig. 1. Distribution of normal stress under wave crest landing condition at detail of interest ID-1

The ratio between  max at the detail of interest to that at the reference location is denoted by K, in Equation 3: = ( − ℎ ) ( − ℎ ) = (∆ ) (∆ ) (3) The factor K is applied to  i in Equations 2 and 3. Eccentricity in the butt weld of detail of interest ID-2 is also taken into account according to Det Norske Veritas (2010). To calculate the fatigue damage at a detail of interest, a reference stress spectrum is translated to the detail of interest. To do this, the stresses at the strain gauge location and the detail of interest are determined from Finite Element Analysis (FEA) under a unit load. Two quasi-static load cases are considered that represent the design Wave Crest Landing and Wave Hollow Landing conditions defined in DNV High Speed Light Craft rules (2011). The fatigue damage (D) can be predicted using cumulative damage theory (Miner 1945), where  denotes the number of stress ranges identified in a stress time history and n i denotes the number of cycles at the ith stress range: =∑  =1 (4) The fatigue life (FL) in years is the ratio of the service life in years to the fatigue damage: ( ) = ( ) (5) Approximately 4500 hours of strain measurements at different locations on the ship are available (Magoga et al. 2016). The strains are assumed to be the responses to the dominant wave loads applied to the ship structure. The strain gauge locations and stress spectra and are shown in Fig 2.a and b, respectively.