PSI - Issue 57

Qingyang Wei et al. / Procedia Structural Integrity 57 (2024) 262–270 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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6

Fig. 6. Frequency-domain acceleration responses of node 1 with different crack depths, (a) x -direction; (b) y -direction; (c) z -direction.

4.2. Local strains responses

The stresses contained in the structures change while the loading varies. The existence of cracks inevitably changes the correlation of stresses on opposite sides of near cracks. The correlation of stress curves on opposite sides near a certain location reflects the physical continuity and further reflects the cracking status at this location. To quantitatively measure this correlation of stress variation, the correlation coefficient of stress curves (CCSC), belonging to the Pearson correlation coefficient, is defined as follows,

n

1    2 ( ( ) i i i n n i X X − =

)( X X Y Y − −

)

(1)

CCSC

=

2

(

)

Y Y −

i

1

1

i

i

=

=

where X and Y are stress curves on opposite sides of a detection position. X and Y , defined as 1 ( ) / n i i X X n = =  and 1 ( ) / n i i Y Y n = =  , are the average values of the stress curves. The value of the CCSC ranges from -1 to +1. The value +1 of the CCSC indicates a complete positive correlation and no crack existence. The greater the distance from +1, the higher the possibility of a crack.

Fig. 7. Layout of the excitation and measurement, (a) cracked; (b) uncracked.