PSI - Issue 54

Naveen Kumar Kanna et al. / Procedia Structural Integrity 54 (2024) 196–203 Author name / Structural Integrity Procedia 00 (2019) 000–000

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3.2. Calculation of crack size with the Johnson equation In order to calculate the crack length out of the measured potentials a calibration is necessary. This can be performed by using the crack length measured on the fracture surface. (Bär (2020)). The calibration is undertaken by plotting the relative crack depth a/t or the relative crack width c/w against the measured potential drop data and adopting the Johnson equation (Eqn. (4)) with a least square fit by using the half-distance of the potential probes y 0 as a free parameter. The result of this fitting procedure is shown in Fig. 8. = 2 ∙ � ℎ � ∙ 2 0 ∙ � ℎ � ∙ ℎ � ℎ � ∙ 2 0 ∙ � � ∙ 2 ℎ ∙ � �� � (4)

0.60

0.8

Johnson equation R 2 = 0.936 y 0 = 1.655

Johnson equation R 2 = 0.909 y 0 = 3.661

0.55

0.7

0.50

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0.45

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0.35

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0.30

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relative crack depth a/t

relative crack width c/w

0.25

0.1

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1.6

1.0

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mean Potential P mean

mean Potential P mean

Fig. 8. Least square fit by the Johnson equation. The fitted function overestimates the crack size in the short crack region and underestimates the crack size of longer cracks.

There is a good agreement of the Johnson equation with the measured potential data with an R 2 value of 0.93 and 0.91 for the relative crack depth and crack width, respectively. It is evident from the calibration curve that the Johnson equation overestimates the crack size for relatively short cracks (a/t<0.3) and underestimates the crack size for long cracks (a/t>0.5). Although the regression coefficient is within acceptable limits, the study of the growth of short cracks is practically impossible with the present fit due to the overestimation of the crack length in the lower range. 3.3. Calculation of crack size with the Tiedemann equation The calibration curve by employing the Tiedemann function (Eqn. (1)) with the least square fit establishes good agreement with the measured DCPD data as shown in Fig. 9, with an R 2 value of 0.95 and 0.9 for relative crack depth and crack width, respectively. These higher regression coefficients already depict a better agreement than the Johnson equation. In addition, the fitted Tiedemann equation shows a optical better agreement for both short and long cracks compared to the Johnson equation. Moreover, the Tiedemann function is mathematically simple and requires less computing effort to calculate the crack length.