PSI - Issue 66

Aditya Khanna et al. / Procedia Structural Integrity 66 (2024) 370–380 Author name / Structural Integrity Procedia 00 (2025) 000–000 shown in Figure 3b. Fortunately, the most significant variations in opening load ratio also occur at ⁄ <0.5 for both specimens. Evaluation of the residual SIF using the influence function method, Eq. (2) or the derivative ratio method, Eq. (4), requires estimation of strain gradients from noisy experimental data. The incremental polynomial fit method described in ASTM E647 is utilised to fit a parabola to 2 +1 data points and evaluate the derivative at the central point by analytically differentiating the parabolic fit. In the present work, =3 is selected, i.e. a sliding window of 7 data points is used to evaluate the parabolic fit of the residual strain data. The influence function and derivative ratio methods provide nearly identical results, which is expected since the two methods are mathematically equivalent (Smudde et al, 2023). The estimated distribution of the residual SIF along the crack path for 0.25< ⁄ <0.54 is shown in Figure 4 for both crack path orientations. In general, the residual SIF for crack growth transverse to the weld deposition direction is more tensile than the residual SIF for crack growth longitudinal to the weld deposition direction. The order of magnitude of the residual SIF remains relatively constant over a wide range of crack lengths and roughly one order of magnitude smaller than the maximum applied SIF. Due to the K-increasing nature of the fatigue tests performed in the present study, it is expected that the effect of the residual SIF on the stress ratio would be most pronounced during the initial stages of the fatigue crack growth test, i.e., when the ratio ⁄ is small. 377 8

S1L S2T

S1L S2T

20 40

0.0

-80 -60 -40 -20 0

-100.0

-200.0

(

(

-300.0

Eq. (9) satisfied

-400.0

-120 -100

-500.0

0.2 0.3 0.4 0.5 0.6 0.7

0.25 0.3 0.35 0.4 0.45 0.5 0.55

(a)

(b)

Fig. 3. Residual back-face strain values obtained by extrapolating the linear part of the load-strain curve to zero load. (a) At large crack lengths, the remaining ligament size becomes smaller than the empirical limit given by Eq. (9), which corresponds to a rapid increase in the residual back face strain, (b) shows the zoomed-in data at small crack lengths at which crack tip plasticity has insignificant effect on the residual back-face strain.

6

4

2

0

(MPa√m)

S1L S2T

-2

-4

0.25

0.3

0.35

0.4

0.45

0.5

Fig. 4. Residual stress intensity factor obtained using the open crack compliance methods. Eqs. (2) and (5) yield nearly identical results.