PSI - Issue 45

James Martin Hughes et al. / Procedia Structural Integrity 45 (2023) 44–51 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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3. Closure Measurements and Crack Growth Rate 3.1. Closure Measurements using Piezoelectric Sensor

Crack closure was identified using the modified ASTM method, which has been presented in a number of prior publications (see Song and Chung, 2010; Wallbrink et al., 2023) and will not be repeated here. It is assumed that the reader is familiar with the associated terminology. As found in previous work by Wallbrink et al. (2023), a 15% span and 5% shift (as a percentage of the cycle load range) was used to calculate the compliance offset curves from the sensor measurements. A threshold opening value of 2% compliance offset plus the mean open crack compliance offset was used. This differs from the ASTM recommendation of 2% compliance offset, but reduces errors due to hysteresis. It is worth nothing that changes in the span, shift, and crack opening threshold criteria will impact the closure loads calculated. The values used in this study are based on our previous work as stated which demonstrated enhanced crack closure detection. The opening load ratio (calculated using Eq. 2) as a function of both crack length ratio and stage of fatigue life is presented in Fig. 2. The opening load for each stress ratio at each crack length was calculated as the mean value of the 100 cycles within the load block (except for R = 0.5, which contained more cycles), and the error presented is the standard deviation. As the pre-cracking procedure imparts some low level plasticity ahead of the crack tip, crack closure is observed even at the beginning of the main load sequence. At this very early stage of fatigue damage the wake of plasticity is not well established, leading to low closure levels across all stress ratios. During the middle stages of fatigue life the accumulation of fatigue damage is associated with an increase in crack closure levels and subsequently a decrease in the opening load ratio. This change is most apparent for lower stress ratios, which provides a logical explanation for the stress ratio effect. For cycles with a stress ratio above R = 0.3, the closure load appears very similar. The results of this analysis show that almost all cycles exhibited non-negligible level of crack closure, which retards crack growth. Upon the establishment of the plastic wake, the opening load ratio reaches a minimum value at approximately 50% fatigue life (corresponding to a/W = 0.28). As predicted by the crack closure theory, lower stress ratio cycles experience greater crack closure effects, reducing the SIF range by a larger amount. The closure levels decrease steadily towards the end of the fatigue life as the crack grows larger due to changes in the wake of plasticity for large cracks. The opening load values presented here are used in Sec. 3.2 to collapse the fatigue crack growth rate curve into a single master curve.

1

1

b)

a)

0.9

0.9

0.8

0.8

R = 0.5 R = 0.4 R = 0.3 R = 0.2 R = 0.1 R = 0

R = 0.5 R = 0.4 R = 0.3 R = 0.2 R = 0.1 R = 0

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0.7

Opening Load Ratio, U

Opening Load Ratio, U

0.6

0.6

0.2

0.3

0.4

0.5

0.6

0

20

40

60

80

100

Percentage of Fatigue Life

Crack Length Ratio, a/W

Fig. 2. Opening load ratio for different stress ratios plotted against a) percentage fatigue life, and b) crack length. Black arrows indicate locations at which crack growth rate measurements were taken.

3.2. Fatigue Crack Growth Rate The growth rate of the fatigue crack was evaluated at eight crack lengths using images taken with an optical microscope. Figure 3 shows a typical image of the fracture surface mid-way through the fatigue life, where three load sequences can be identified. Measurement of the crack progression per load block is aided by the R = 0.5 load block