by the minimum flaw size,predicting fracture strength and fracture criteria.

stress intensity factor, K = Yσ√(πa).σ is the applied stress, 'a' is the crack length, and Y is a dimensionless geometry correction factor.

Ashutosh Kumar Yadav

Thanks for your answer. Using minimum flaw size to establish fracture criteria is indeed practical. To clarify further, does this 'minimum flaw size' typically represent: (1) actual material defects (e.g., crystalline imperfections or manufacturing flaws), or (2) an equivalent crack length for fracture strength prediction? Additionally, is there a reliable standard or empirical rule to determine this parameter in engineering applications?"

Aleksandr G. Sulamanidze

Thank you for your answer.​​

Regarding using SED to evaluate crack initiation and fracture strength in crack-free structures, is the critical region size easy to determine? I'm still inclined to consider both energy and K-based criteria comprehensively.

There are two overarching implications from the our study. A-First, comparison of experiment and modeling establishes that the KTada solution for the pinned SEN(T) geometry loses high accuracy only for specific combinations of specimen geometry, material stiffness, and applied loading. Potential error in KTada was suggested by others due to changing boundary condition and loading eccentricity during crack growth, but the effects were not quantified in those studies . The current study demonstrates that the reduction of applied K compared to KTada arises from a complex non-linear geometry influence, and defines regimes of alloy stiffness, load, and untracked ligament size where these errors become significant. This finding contrasts with the stated broad accuracy of KTada 0.05 < a/W < 0.95 . However, these prior studies did not capture non-linear geometry effects. For example, the experimental validation by Sanford and Kirk utilized very low K loading , while modeling of Joyce and others used geometrically linear finite element approaches , which inherently neglect such effects. Called for by others , it is necessary to develop a new K solution that can be broadly employed for pinned SEN(T) samples of different alloy stiffness and loading configuration by accounting for the influence of non-linear geometry change. It were shown to be effective for developing straight-forward K solutions that accurately capture complex dependencies; such approaches can be leveraged for the pinned SEN(T). Moreover, geometrically non-linear FE modeling should be employed to assess the extent to which boundary conditions changes affect accepted K solutions for other bending-based specimens such as the C(T) and eccentrically loaded single edge notch tension (ESE(T)) geometries employed in fatigue and EAC studies . The second implication of our study is that there are clear combinations of material stiffness, specimen geometry, and loading that result in true K values that agree within 5% or better with KTada. So, example, the non-linear finite element simulations show that KTada is within 5% of the calculated K value up to a/W = 0.6 for a realistic pinned SEN(T) specimen configuration (H/W = 29) loaded to Kmax = 17 MPa/m for Al alloys . For stiffer steels, this critical a/W is 0.75 for this K level and 0.6 for higher K of 30 MPa/m. Nickel-based superalloys will likely align with this regime of validity established for steel, while Ti alloys will be intermediate to steel and Al alloys. This assessment is affirmed by the extensive fatigue crack growth data sets summarized. The second implication of our study is that there are clear combinations of material stiffness, specimen geometry, and loading that result in true K values that agree within 5% or better with KTada. So, example, the non-linear finite element simulations show that KTada is within 5% of the calculated K value up to a/W = 0.6 for a realistic pinned SEN(T) specimen configuration (H/W = 29) loaded to Kmax = 17 MPa/m for Al alloys . For stiffer steels, this critical a/W is 0.75 for this K level and 0.6 for higher K of 30 MPa/m. Nickel-based superalloys will likely align with this regime of validity established for steel, while Ti alloys will be intermediate to steel and Al alloys. This assessment is affirmed by the extensive fatigue crack growth data sets summarized

Aleksandr G. Sulamanidze

Thank you for the references. I'm currently exploring how to ​​incorporate these factors into the fracture criteria​​.

Paul Olaru

Thank you, Prof. Olaru.

I've read the introduction you recommended from "On the validity of the Tada stress intensity factor solution for the single edge notch tension specimen with pinned ends" (Engineering Fracture Mechanics, Volume 301, 2024, 110037).

This paper provides insights into both the limitations of the KTada solution under nonlinear geometric effects and its precise range of validity across different materials and loading conditions. Perhaps my theoretical K-solution could follow this approach to develop calibration methods for real metallic materials.