PSI - Issue 77

R. Branco et al. / Procedia Structural Integrity 77 (2026) 376–381 Branco et al. / Structural Integrity Procedia 00 (2026) 000–000

379

4

50

95

B/T=1 (UT) B/T=1 (HT) B/T=2/3 (UT) B/T=2/3 (HT)

B/T=1 (UT) B/T=1 (HT) B/T=2/3 (UT) B/T=2/3 (HT)

40

85

20 Experimental angle, α 1 (°) 30

55 Experimental angle, β 1 (°) 65 75

10

(a)

(b)

0

45

0

10

20

30

40

50

45

55

65

75

85

95

Predicted angle, α 1 (°)

Predicted angle, β 1 (°)

Fig. 3. Numerically predicted versus experimentally measured: (a) crack initiation sites; and (b) early-stage crack growth paths of the first crack observed in the specimen subjected to combined bending-torsion loading for both the untreated and heat-treated conditions (UT: untreated; HT: heat-treated) in a few cases were caused by manufacturing defects located near one of the initiation sites, which accelerated the formation of the first crack relative to the second. Figure 3 compares the experimentally measured and numerically predicted crack initiation sites (Fig. 3(a)) and early-stage crack growth paths (Fig. 3(b)) of the first crack observed in the specimen subjected to combined bending torsion loading for both the untreated and heat-treated conditions. Numerical predictions were carried out from an uncracked geometry assuming that the crack initiates at the node with maximum value of the first principal stress and the early-stage crack growth direction is governed by the first principal direction at the initiation site (Branco, 2021). Overall, the proposed approach can capture the observed trends. Similar to the experimental observations, the predicted β angle increases with higher B/T ratios, while the α angle decreases as B/T increases. Regarding the crack initiation sites of the first crack analysed through the β 1 angle, see Fig. 3(a), some scatter can be observed, particularly under B/T=2/3, either for the untreated or heat-treated conditions. Nevertheless, most datapoints are within scatter bands of ±5º, which indicates a reasonable accuracy. The mean error was about 5º, while the standard deviation was about 4º. Branco et al. [6] reported a mean error of 6.1º in the β 1 angle for the same geometry subjected to the same loading scenarios fabricated from maraging. This value is close to the one obtained in this study. Concerning the early-stage crack growth directions of the first crack, see Fig. 3(b), numerical predictions were relatively close to the experimental α 1 angles, with almost all datapoints falling within the ±5º scatter bands. The mean error was about 4º, while the standard deviation was about 3º This suggests that the proposed approach can accurately estimate the early-stage crack growth path, which is fundamental to define the critical plane and the associated stress-strain state. The evolution of crack length ( a ) versus number of cycles ( N ), i.e., the so-called a - N curves, for different material conditions (untreated and heat-treated states) and loading scenarios is exhibited in Fig. 4. The effect of B/T ratio can be inferred by comparing the cases 1 and 3, both corresponding to the same material condition (heat-treated) and the same nominal stress amplitude ( σ a =28.9 MPa) but different B/T ratios. As shown in Fig. 4, lower B/T ratios result in shorter fatigue lives, which is explained by the higher shear stress level or, in other words, a higher equivalent von Mises stress amplitude ( σ a,vM ). It is clear from Fig. 4 that the slope of the a - N curves, fitted via exponential functions, is higher at the same crack length for lower B/T ratios, indicating faster fatigue crack growth. Moreover, crack initiation occurred earlier for B/T=2/3 compared to B/T=1. The effect of heat treatment can be assessed by comparing cases 2 and 3 of Fig. 4. These two tests were performed under the same B/T ratio (B/T=1) and the same loading scenario ( σₐ =28.9 MPa) but for two material states (untreated