PSI - Issue 45

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

48

5

marker bands which separate the lower stress ratio content. It is clear from the figure that there is greater crack growth during the lower stress ratio loading blocks, which is expected due to the increased SIF range. The crack growth rate per cycle was determined by measuring the crack growth in each of the load blocks using the scale provided. To reduce the statistical error, several measurements were taken at various locations across the load block band, and the average value and standard deviation recorded.

Load Sequence

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

Fig. 3. Optical microscope image of the fracture surface for / = . . The striations related to each of the load blocks have been marked and used to calculate the crack growth rate of each load block.

1E-06

1E-06

b)

a)

1E-07

1E-07

R = 0.5 R = 0.4 R = 0.3 R = 0.2 R = 0.1 R = 0 Line of Best Fit

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

1E-08

1E-08

da/dN (m/cyc)

da/dN (m/cyc)

R 2 = 0.94 SSE

resid = 0.61 12 15

1E-09

1E-09

3

6

9

12 15

3

6

9

Δ K (MPa.m 0.5 )

Δ K eff (MPa.m

0.5 )

Fig. 4. Fatigue crack growth rate against the stress intensity factor range for a) raw data, and b) corrected for opening using piezoelectric gauge measurements.

The fatigue crack growth rate curve as a function of the applied SIF is presented in Fig. 4a. A similar tendency to that shown in Fig. 14 of White et al. (2018) is observed. The crack growth rate for lower stress ratio cycles is smaller compared to higher stress ratio cycles with the same SIF. As mentioned in the introduction, it is expected that the stress ratio effect is the result of crack closure, and when corrections for closure are applied the dependence on stress ratio will vanish. These corrections, based on the piezoelectric measurements presented in Sec. 3.1, are applied in Fig. 4b, which shows the crack growth rate curve against the effective SIF. The raw SIF range is modified using the opening load ratio, U (see Eq. 2), in Fig. 2 and the crack length at the point of measurement. The effect of crack closure, particularly in the lower stress ratio cycles, causes a significant reduction in the SIF range, which collapses the individual stress ratio growth rate curves into a single master curve. Qualitatively, the collapsing procedure using the measured crack opening loads is very successful, and the dependence on stress ratio is almost completely removed. Quantitatively, the line of best fit (see Fig. 4b) has a high R 2 value and low residual error. The ability to reconcile the crack growth rate curve into a single master curve for a variable amplitude loading sequence provides strong evidence of the crack closure phenomenon.