Issue 78

A. Zakharov et alii, Fracture and Structural Integrity, 78 (2026) 260-274; DOI: 10.3221/IGF-ESIS.78,16

Loading biaxiality and crack tip curvature effects on plastic stress intensity factor behaviour at small-scale and extensive plasticity

Aleksandr Zakharov, Valery Shlyannikov Institute of Power Engineering and Advanced Technologies, FRC Kazan Scientific Center, Russian Academy of Sciences, Russia

alex.zakharov88@mail.ru, http://orcid.org/0000-0003-3568-1427 shlyannikov@mail.ru, http://orcid.org/0000-0003-2468-9300

Citation: Zakharov, A., Shlyannikov, V., Loading biaxiality and crack tip curvature effects on plastic stress intensity factor behaviour at small-scale and extensive plasticity, Fracture and Structural Integrity, 78 (2026) 260-274.

A BSTRACT . An elastic–plastic finite element analysis (FEA) was performed for a Mode I plane-strain center-cracked plate (CCP) made of a titanium alloy and subjected to biaxial tension/compression loading. Two crack-tip configurations were considered: a mathematical notch (MN) and a finite radius of curvature (FRC). In the present study, both the J-integral and the plastic stress intensity factor (plastic SIF) were employed to characterize the elastic–plastic stress fields near the crack tip. The distributions of the J-integral and the plastic SIF were evaluated as functions of loading biaxiality and applied stress level. The analysis covered a biaxial stress ratio range extending from equibiaxial tension–compression to equibiaxial tension and included both small-scale yielding (SSY) and extensive plasticity conditions. The results reveal a pronounced coupling between loading biaxiality and crack-tip configuration effects on the fracture parameters. Opposite trends in the variation of the J-integral and the plastic SIF with respect to the biaxial stress ratio and crack-tip geometry were observed. In addition, a comparative assessment of SSY and extensive plasticity regimes was carried out for both crack-tip configurations. It was found that under extensive plasticity conditions the plastic SIF becomes dependent on the crack tip radius of curvature, whereas under SSY conditions it remains essentially independent of crack-tip geometry. K EYWORDS . Biaxial loading, J-integral, Crack tip geometry, Plastic stress intensity factor.

Received: 16.06.2026 Accepted: 01.09.2026 Published: 07.09.2026 Issue: 10.2026

Copyright: © 2026 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

I NTRODUCTION he initiation of crack growth is controlled by the local stress-strain fields around the crack tip. These near-tip fields are strongly dependent on the local crack-tip shape. Typically for FEA, the crack tip may be idealized in two distinct ways: as a mathematical notch (MN) with zero root radius, or as a crack root with a finite radius of curvature (FRC). T

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