**2.1 Damage tolerance**

Over the years several fatigue design methodologies have developed trying to combine structural safety and low cost in the aircraft manufacturing and operation process. The first methodology was called safe-life. This approach consists of designing and manufacturing a safe aeronautical structure throughout its useful life. For this, one must consider, in the prototype tests, the most extreme situations of fatigue stresses, foreseen during operation. Such methodology results in factors that oversize the structural elements to prevent the possibility of failure. This approach leads to high project costs and is not able to guarantee safety if an unforeseen design failure occurs during its useful life.

Rationally, a new methodology was developed based on the concept of damage tolerance. In this methodology, it is assumed that the structure is capable of withstanding the actions for which it was designed until the detection of a fatigue crack or other defects during its operation. The aircraft is then checked, repaired, and put back into service until the end of its useful life. The concept of damage tolerance began from statistical analysis to control the spread of fatigue cracking and considering inspection intervals to maintain a low probability of complete failure [12]. Later, the damage tolerance has been applied in the use of aluminum alloys for aircraft structural applications [13, 14]. Thus, the fatigue damage analysis

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

considered some aspects of the design, predictions, and experiments associated with tolerance to damage to aircraft structures [15–17]. From this, it was noticed that the load cycles have a direct linear relationship with the logarithm of the crack size and that the largest formed cracks grow in an approximately exponential way, known as the "main crack" methodology [18], from small discontinuities (flaws and microcracks) inherent to the material, as soon as an aircraft enters service [19]. Currently, the concept of damage tolerance is applied to aircraft with composite structures [20–23], in the analysis of multiple cracks [24], and shape optimization design [25, 26]. Studies on tolerance to probabilistic damage are based on manufacturing components [27] and the dispersion of fatigue life from the distribution of initial defects [28]. Other works relate damage tolerance through computational methods, using XFEM [29, 30], BEM [31], and DBEM [32].
