PSI - Issue 38

Hamza Abbad El Andaloussi et al. / Procedia Structural Integrity 38 (2022) 238–250 247 Hamza Abbad El Andaloussi, Luc Mouton, Firas Sayed Ahmad, Xabier Errotabehere, Stéphanie Mahérault-Mougin, Stéphane Paboeuf/ Structural Integrity Procedia 00 (2021) 000 – 000 10 The parameters of the interfacial mean S-N curve are: • m = -11.68 • log 10 ( 50 ) = 17.15 Figure 7 presents the mean S-N curve:

Figure 7 Interfacial mean S-N curve for the studied bonded reinforcement

Then, these predicted values are used for the calculation of the lower tolerance limit values. The latter are the basis of the design interfacial S-N curve. 5.2. Design interfacial S-N Curve The aim of this part is to determine the parameters m and of the design S-N curve corresponding to a one sided tolerance limit at a failure probability value P and a confidence level (1- α). The design interfacial S-N curve is deduced from the mean interfacial S-N curve as follows: ̂ = ̂ − ̂. ( ,1− , ) . √1 + 1 + ( − ̅ ) ( − ̅ ) 2 With : • ̂ is the lower tolerance limit estimate; • is the factor for a one-sided tolerance limit for a normal distribution at a probability of failure P, a confidence of 1- α and γ degrees of freedom; • ̂ is the standard deviation of the regression results • n is the number of specimens considered for the statistical analysis For more information on these parameters please refer to Erreur ! Source du renvoi introuvable. §8.4. Table 4 presents the calculated values of these parameters: Table 4 Parameters of the calculation of the design S-N curve

̂ P γ n

Parameter

Value

0.46

2.50% 90.0% 2.509

1- α

23 25

The degrees of freedom (γ) is taken equal to n -p (p being the number of parameters of the regression line i.e. b 0 and b 1 ) i.e. 25-2=23.