PSI - Issue 42

Markus Winklberger et al. / Procedia Structural Integrity 42 (2022) 578–587 M. Winklberger et al. / Structural Integrity Procedia 00 (2019) 000–000

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1) Model-based crack identification

Baseline measurement of 2) Monitoring by EMI-measurements G M ( ω ) of pristine structure

Identification of crack sensitive freq. ranges by evaluation of σ 1 ( ω ) of pristine model

Periodic measurements of G M ( ω ) of monitored structure

Detailed FE analysis of G FE ( ω ) with high resolution in crack sensitive freq. ranges of pristine and cracked models to get T FE k

f M m , pristine

f M

m , c

f FE

f FE k , c

initialize T M i to get f M i , pristine

continue T M i to get f M

f FE

k , pristine

i , pristine

Interpolation of T FE k

i , c

and filtering out

T FE

FE

∆ f M

M i , c − f

M i , pristine

with quadratic trend

i , c = f

i ∈ T

k

λ FE i

∆ f M

i , c < 0

Estimation of crack length

a i , c =  ∆ f

M i , c /λ

FE i

Fig. 3. Method overview.

2.3. Method to estimate the crack lengths in aircraft lugs

The methodology to identify cracks in aircraft lugs with necked, straight and tapered shape is depicted in Fig. 3 and includes two main parts: 1) the model-based crack identification and 2) the monitoring of the structure by periodic EMI-measurements. The following paragraphs explain both parts of the methodology in detail.

2.3.1. Model-based crack identification The first part comprises an identification of crack sensitive resonance frequencies f FE i

and associated sensitivity

parameters λ FE

i . Crack sensitive resonance frequencies are found by using a validated numerical FE model of the

pristine structure and analyzing the mean major principal stress

N AAC  n = 1

1 N AAC

σ 1 ( ω ) =

σ 1 , n ( ω ) ,

(1)

where σ 1 , n ( ω ) is the major principal stress extracted from FEM results for specified angular frequencies ω = 2 π f and each node n ∈ N AAC (yellow nodes within the region of β in = 90 ◦ ± 10 ◦ and the full thickness of the lug, see Figure 2). Equation (1) is preferably evaluated in a wide frequency range and relatively rough frequency resolution to save computational time. In general, a fatigue crack initiates perpendicular to the major principal stress. Therefore, it is assumed that resonance frequencies with large σ 1 peaks are highly sensitive to initiating fatigue cracks in this region (Winklberger et al., 2021b). Subsequently, detailed FE analysis of the conductance G FE ( ω ) of a PWAS applied to pristine and cracked structures are performed in narrow frequency bands of 5 kHz with a high frequency resolution of 31 . 25 Hz around found crack sensitive resonance frequencies. The conductance G FE ( ω ) is calculated for each angular frequency ω = 2 π f by G FE ( ω ) = Re  I ( ω ) U ( ω )  = Re   j ω U ( ω )    N IMA  n = 1 ( Q n ) − j δε T 33 U ( ω ) t p A p      , (2)