Issue 59

C. Mallor et alii, Frattura ed Integrità Strutturale, 59 (2022) 359-373; DOI: 10.3221/IGF-ESIS.59.24

The idea for determining the periodicity of the non-destructive inspections (NDI) is depicted simply in Fig. 4. First, based on the conservative lifespan estimation, the residual lifetime (step 4) is delimited. This portion of lifetime is denoted as N def in Fig. 4 in reference to the lifetime for the definition of inspection intervals. Keeping in mind the considerations on the two-dimensional shape of the crack, and on its evolution due to fatigue loads, the N def covers the propagation from a min to a max (steps 1 and 3), being the minimum and the maximum crack sizes considered for the lower and the higher lifetime bounds, respectively, and it is calculated through the Eq (2).       def max min N N a N a (2) The usual assumption made is that a min corresponds to crack size a POD% that has certain probability of being detected by NDT, for instance the crack size a 95% which has a POD = 95%. Finally, the inspection interval T ins is determined by dividing N def by a number of times n times that takes account of the number of times that the crack can be detected before a failure could occur. This simple procedure is formulated in Eq (3).

N

def



T

(3)

ins

n

times

For example, the usual assumption considering n times equal to 2 or 3 [14], allows the crack to be observed at least twice or three times before it leads to catastrophic failure. This assumption is based on the fact that a crack could be missed at an inspection. It is, however, evident that even two or more inspections cannot ensure the crack detection.

Figure 4: Calculation of the periodicity of NDT inspections, i.e., inspection intervals of maintenance.

In particular, as it is not known exactly when crack growth is triggered by an accidental event, the component will always be subjected to inspection every T ins km, and depending on the inspection method used, the cumulative probability of detecting (CPOD) a crack in the axle or its complementary cumulative probability of failure (CPOF) or simply referred to as probability of failure ( P f ) can be computed as described in [22]. Summarizing, the CPOD of a crack growing according to an a-N curve, can be calculated based on the given number of inspections #i and the POD -a curve of the NDT method used. The easiest way to calculate the CPOD is to convert the POD of the individual inspections, #1 , #2 , #3 , … , designated with the sub-index #i , to probability of non-detection (POND) by the relationship POND( a #i ) = 1 − POD( a #i ) where a #i is the corresponding crack depth at the #i inspection. These PONDs, when multiplied give a cumulative probability of non detection in successive inspections (CPOND). Notice, that the individual POND decreases with increasing crack length. Finally, the CPOND is converted back to its complementary CPOD. In short, the cumulative probability of detection CPOD of a crack can be evaluated as in Eq (4).                  # # # # CPO 1 CPON 1 1 1 i i i i i i D D POND a POD a (4)

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