PSI - Issue 38

Alexander Raßloff et al. / Procedia Structural Integrity 38 (2022) 4–11 A. Raßlo ff et al. / Structural Integrity Procedia 00 (2021) 000–000

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6

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0 . 2 0 . 8 Ranking parameter P FS 0 . 6 0 . 7

0 . 8

0 . 6

CDF of FS-FIP

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0.56

0.66

0.80

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0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 Fatemi-Socie FIP

Porosity φ in %

Fig. 5. (Left) Cumulative distribution of highest Fatemi-Socie FIPs and fitted distribution function (dashed line) for three exemplary SVE sets of di ff ering porosity; (right) associated Fatemi-Socie ranking parameter based on extreme value distribution. f ( x ; a , c , l , s ) = | c | Φ FS s − l ca − 1 exp − Φ FS s − l c Γ − 1 ( a ) , Φ FS ≥ 0 , a > 0 , c 0 , (4) where l and s denote the shift and scale parameters, a and c the shape parameters and Γ is the already introduced gamma function. A ranking parameter P is now introduced to describe the fatigue proneness of the SVE set. It is defined as the FIP that will not be exceeded with a probability of 99 . 5 %, i.e. P = F − 1 EVD (0 . 995). In Figure 5 this ranking parameter is shown. To allow for a better comparison, a relative ranking parameter ˜ P = P ref / P is introduced. Murakami’s √ area estimation. To serve as a comparative value, an empirical method for the estimation of the fatigue strength is additionally employed. The Kitagawa-Takahashi diagram established by Liu et al. (2020) is used here. It can be expressed as ∆ σ w = ∆ σ w0 a 0 a + a 0 = ∆ σ w0 √ area e ff 0 √ area e ff + √ area e ff 0 . (5) The fatigue limit ∆ σ w of the AM structure can be calculated based on the fatigue limit of the defect-free structure ∆ σ w0 and two size parameters a and a 0 . Liu et al. (2020) substituted the latter ones by the √ area parameter introduced by Murakami (1989). Based on the work of Leuders et al. (2013), the specific value of ∆ σ w0 = 420MPa was chosen. For defects within the specimen, √ area e ff 0 = 102 . 6 µ m was determined. Comparing this empirical determination of a fatigue property to the FIPs is facilitated by defining the ranking parameter as ˜ P √ area = ∆ σ w / ∆ σ w,ref , analogously to the FIP-based one, so that higher values indicate a better fatigue performance. Three exemplary studies are conducted to illustrate the presented approach. For this purpose, three pore structure descriptors are chosen and varied, namely (a) the scale parameter of the ESD s esd , (b) the size of the largest pore √ area and (c) the porosity φ . Figure 4 shows the local spatial distribution of the highest FS FIP. It can be seen that they locate at the pores as expected. The results of the studies are shown in Figure 6 in terms of the ranking parameter. The scale parameters are presented as relative values to allow for a better evaluation. Per study only one parameter is varied and the others are set to constant values as given in the same figure. The study on the ESD as shown in Figure 6(a) indicates that the proneness to fatigue increases for higher scale parameters ˜ s esd . As can be seen from the associated plot of the gamma PDF, a high value of ˜ s esd means that there 3. Results