PSI - Issue 38

246 Hamza Abbad El Andaloussi et al. / Procedia Structural Integrity 38 (2022) 238–250 Hamza Abbad El Andaloussi, Luc Mouton, Firas Sayed Ahmad, Xabier Errotabehere, Stéphanie Mahérault-Mougin, Stéphane Paboeuf/ Structural Integrity Procedia 00 (2021) 000 – 000 9 5. Statistical analysis The combination of the fatigue tests results and the numerical analyses allows to determine the number of cycles at failure for each stress range at the interface Substrate/Adhesive for a peak stress value at the edge of the reinforcement. This data is then processed as per [10] “ISO12107:2012 Metallic materials — Fatigue testing — Statistical planning and analysis of data”. Even though reference [10] is focused on metallic materials, the statistical approach is relevant for the analysis of the data gathered from the experimental fatigue tests campaign. In fact, there are – according to the present literature review- no guidance notes or standards regarding the statistical analysis of the fatigue results for bonded reinforcements. Thus, a special care has been paid to the consistency of the data gathered from the fatigue tests campaign. Indeed, all the points considered for the statistical analysis result from the same type of test – Tensile fatigue test- and present the same type of failure – interfacial failure at bondline. One should also note that, the fatigue tests campaign is extensive as it respects the requirements Standard “12107” [10] in terms of number of tests performed (25 fatigue tests). Standard “12107” [10] presents methods to determine the parameters of the Basquin S-N curves formula written as follows: (N∙ 〖 ∆ S 〗 ^m=K_ ) Where: N: Number of cycles to failure ∆ S: Stress range Mean interfacial S- N curve (N∙ 〖 ∆ S 〗 ^m=K_50) Mean S-N curve means that the number of cycles corresponding to 50% of tests results are lower than the number of cycles given by the mean S-N curve. Design interfacial S- N curve (N∙ 〖 ∆ S 〗 ^m=K_P) based on lower tolerance limit. The design curve is associated to a specified probability of failure P and a confidence value (1-alpha).That means that there is a probability of (1-alpha) that a proportion of the number of specimens failing with lower number of cycles than the design S-N curve is lower than P. Alternatively, linearized design S-N curve is determined from two reference values on the tolerance limit curve defined below. The two reference points correspond to two values of number of cycles N=103 and N=107. They correspond to the bounds of the high cycles domain for steel welded details where the S-N curve is linear on a log-log scale with a single slope value [11]. The linearized design S-N curve based on those two reference values is included in the fatigue guidance NI611 next revision [12]. Moreover, for current steel marine structures, most of the damage induced by wave loadings occurs between N=103 and N=107 cycles. The linearized design curve is conservative versus the lower tolerance limit curve (second order polynomial inward curve). 5.1. Mean interfacial S-N Curve The aim of this part is to determine the parameters m and 50 of the mean S-N curve. Estimation of the regression parameters is performed considering: = = The base 10 logarithms are considered: = log 10 ( ) = log 10 ( ) Based on Erreur ! Source du renvoi introuvable. , the predicted values are: ̂ = 0 + 1 . With: b 0 = 17.15 and b 1 = -11.68 K: Coefficient of the S N curve m: inverse of S-N curve slope Based on [10], two S-N curves are determined.