*Advances in Fatigue and Fracture Testing and Modelling*

#### **Figure 19.**

*Estimated probability density functions for fatigue life for 3C criterion.*


#### **Table 7.**

*Mean values and standard deviation of number of cycles to 3C.*

#### **Figure 20.**

*Characteristic value for fatigue life (Nk) considering for 3C criterion.*

Position 1 presents a greater dispersion, which means a greater variation of the values of *N*3*<sup>c</sup>*. This is confirmed in **Table 7** by the highest coefficient of variation.

Considering the determination of the characteristic fatigue life (Nk), related to an α% probability that an *N* value would not be superior to Nk, **Figure 20** shows those characteristic values for that for α of 75% and 95%. Note the significantly higher values for position 1 rather than the other two positions for both α.

*A Probabilistic Approach in Fuselage Damage Analysis* via *Boundary Element Method DOI: http://dx.doi.org/10.5772/intechopen.98982*

**Figure 21.** *Failure probability for N3C for different λ values.*

Regarding *p <sup>f</sup>* as the failure probability of the structural element, *NG* <sup>&</sup>lt;<sup>0</sup> is the number of simulations in which a performance function for the number of cycles to failure for the #C compliance *GN*3*<sup>C</sup>* <0:

$$p\_f = \frac{N\_{G<0}}{N\_{total}} \tag{4}$$

$$\mathbf{G}\_{N\_{\mathcal{C}}} = \underbrace{\lambda \mu\_{N\_{\mathcal{C}}}}\_{\text{resistent}} - \underbrace{N\_{\mathcal{C}}}\_{\text{loading}} \tag{5}$$

$$\begin{array}{ll} \text{fatigue} & \text{fatigue} \\ & \text{life} \end{array}$$

In which *Ntotal* the total number of simulations, λ is like an inverse safety factor that scales an allowable (resistant) fatigue life, and *μ<sup>N</sup>*3*<sup>C</sup>* the loading average life. **Figure 21** shows the probability of failure of the three positions and different values of λ. It is noticed that the failure probability is greater for Position 3, followed by Position 2 and later from Position 1.
