PSI - Issue 81

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

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(1 ) = +[ − ]( 0 ⁄ ) 1 4 ) , (4) where B is the crack front length in the cruciform specimens, and 0 is the crack front length in the CT-1 specimen. Analysis of the experimental data indicated that, under conditions of small-scale yielding, biaxial loading has little effect on fracture toughness values. Under other conditions, however, the effect of biaxiality becomes significant, increasing as the relative crack length decreases. The reduction in fracture toughness under biaxial bending compared to uniaxial loading observed in small scale cruciform specimens is consistent with the results previously reported by Bass et al. (1999) for 100 mm-thick specimens and is associated with increased constraint along the crack front under biaxial bending for shallow cracks (a/W<0.2) (Fig. 5). One of the most widely cited modern universal parameters for characterizing constraint is based on the crack-tip opening displacement (CTOD) and is defined as the ratio of the opening displacement in a specimen or structural component δ to that in a standard reference specimen under plane-strain conditions δ ref at the same J-integral level, i.e., at the plane-strain fracture toughness, J re f (Xiao et al., 2023; Zheng et al., 2021). For experimental data obtained on materials of different classes, the authors proposed an empirical correlation to determine the fracture toughness J c in a structural component based on the known constraint parameter A d : = + 367.6[( − 1) + 0.983] 3.28 −374.16 ǡ (5) where A d is determined numerically ǣ = ⁄ . (6) Similarly, based on the parameter A d and using generalized data for materials of different classes, it is proposed to determine the reference temperature 0 : 0 = 0 − 170.3( −1), (7) where 0 ‹ s the reference temperature determined for CT-1 specimens in accordance with ASTM E1921 – 17a. In the present study, the parameter (5) was verified for predicting fracture toughness, which was determined experimentally for 15Kh2NMFAA steel using specimens with varying levels of constraint. The crack-tip opening displacement, , was calculated following the methodology of Xiao et al. (2023) and Zheng et al. (2021) (Fig. 6). To determine the parameter using equation (5), the relationship between δ and the J-integral was constructed (Fig.7). Analysis of the experimental data and numerical simulations showed that the δ - J relationship is linear, and that decreases with increasing constraint, i.e., the slope of the line in Fig. 7 decreases, as does the corresponding fracture toughness. For the SENB specimen with a short crack (a/W = 0.133), both the fracture toughness and the parameter were maximal. In contrast, biaxial bending of the CRSEN cruciform specimen with a short crack (a/W = 0.15) slightly increases the constraint and reduces the parameter.

CT-1 (reference spec) CRSEN (a/W=0,1...0,22) CRSEN old (a/W=0,15...0,23) CRSEN (a/W=0,3...0,38) SEN(B) (a/W=0,15...0,25)

400

300

200

100

K Jc , MPa m 0,5

-80 -60 -40 -20 0 20 40 60 80 0

T, 0

Fig. 5. Master Curve for 15Kh2NMFAA steel constructed using CT-1 specimens; fracture toughness values obtained under three-point bending (SEN(B)) and biaxial bending (CRSEN) converted to CT-1 equivalent values in accordance with ASTM E1921 – 17a (T 0ref =-12 0 C).

Fig. 6. Numerical determination of the crack-tip opening displacement.