PSI - Issue 81

V. Sidyachenko et al. / Procedia Structural Integrity 81 (2026) 123–128

127

Therefore, to analyze the effect of biaxial bending on the reference temperature T 0 and the parameter A d following the methodology proposed by Zheng et al. (2021), it is necessary to determine the reference temperature T 0 for CRSEN specimens based on the K Jc data (Fig. 5), taking into account the data validity criteria specified in ASTM E1921 – 17a. Subsequently, the parameter A d (5) should be evaluated numerically, and the averaged predicted reference temperature T 0p should be calculated using equation (6) and compared with the experimentally determined T 0 . For this analysis, the set of K Jc data obtained for CRSEN specimens with relative crack lengths a/W=0.1…0.22 was used, since, as noted above, the influence of biaxial bending on the K J characteristics is manifested specifically within this crack length range (Fig. 5). The value of T 0p estimated for CRSEN using equation (6) differs from the experimentally determined reference temperature obtained by the Master Curve approach by approximately -8 0 С (Table 1). Moreover, the prediction is non-conservative, although it remains within the experimental scatter band reported by Zheng et al. (2021).

Table 1. Experimentally determined reference temperature T 0 according to ASTM E1921 – 17a and theoretically predicted reference temperature T 0 p (6), and the constraint parameter (5) Specimen type a/W T test , 0 T 0 , 0 T 0p , 0 ∗ CT-1 0.5 +23 -12 - 1.0 CRSEN 0.1…0.22 +21 -29 -37 1.152 SEN(B) 0.1…0.25 +21 - -49 1.220

To characterize both in-plane and out-of-plane constraint, the stress triaxiality ratio ϭ m / ϭ i evaluated at a distance of 2J/ ϭ 0 from the crack front is also commonly used (Brocks and Schmit, 1995; Kim et al., 2016) (Fig. 8) = 1 + 2 + 3 3 , =√ 1 2 [( 1 − 2 ) 2 +( 2 − 3 ) 2 +( 3 − 1 ) 2 ] (8) Analysis of the data in Fig. 8 shows that the highest level of stress triaxiality is observed for the CT-1 specimen, while the lowest corresponds to the SENB specimen, due to differences in both in-plane and out-of-plane constraint, which are governed by the relative crack lengths and specimen dimensions. At the same time, the stress triaxiality parameter for the CRSEN specimen assumes intermediate values between those of the CT-1 and SENB specimens and, when approaching the free surface, exceeds the triaxiality level of the CT-1 specimen due to the presence of a stress concentrator in the form of an electro-discharge machined unloading slit.

100 120

2,5

CT-1, a/W=0.5 SENB, a/W=0.13 CRSEN, a/W=0.13

2,0

20 40 60 80

CT-1, a/W=0.5 CRSEN, a/W=0.13 SENB, a/W=0.13

1,5

 m  i

 J   m

1,0

0,5

0,0 0,2 0,4 0,6 0,8 1,0 0,0

0 1020304050 0

 B

J, kN/m

Fig. 7. Relationship between the average J-integral and the crack opening displacement averaged along the crack front for specimens with different levels of constraint.

Fig. 8. Distribution of stress triaxiality ratio over the crack front.

4. Conclusions Based on the analysis of the obtained experimental results, it was established that the transition to short cracks ( / < 0.2 ) in the three-point bending specimens reduces the level of deformation constraint compared to the CT-1 specimens, while the fracture toughness at test temperatures higher than 0 exceeds the upper bound of the Master Curve determined from the CT-1 specimens. In contrast, biaxial loading increases the deformation constraint relative to the three-point bending specimens and leads to a slight reduction in the fracture toughness values. To confirm this result, finite element modeling of the investigated specimens was performed. The numerical analysis demonstrated an intermediate level of both the stress triaxiality parameter and the constraint parameter for the cruciform specimen under biaxial bending, compared to the CT-1 specimen and the three-point bending specimen with a short crack.