Issue 78

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

Figure 9: The plastic SIF distributions for both small-scale yielding (Kssy) and extensive plasticity (Kp) as a function of the crack tip configuration. It should be noted that the numerical results for the plastic SIF in both the SSY and extensive plasticity regimes correspond to a cracked plate approximating an infinite-size cracked body. Nevertheless, for real structural components or test specimens subjected to complex stress states, where the plastic zone size is no longer negligible compared to the crack length the difference between the SSY and extensive plasticity predictions could be even more pronounced than observed here.

C ONCLUSIONS

A

n elastic–plastic finite element analysis of an infinite center-cracked plate subjected to biaxial loading was performed to investigate the behaviour of crack-tip fracture parameters under varying loading conditions and crack-tip geometries. Based on the numerical results, the coupled effects of stress biaxiality and applied stress level on the J integral and the plastic stress intensity factor were quantified. The J-integral exhibits noticeable variations within the normalized distance range 3 < r σ ₀ /J < 12, and its distribution is strongly influenced by the crack-tip configuration. In contrast, the plastic SIF remains nearly constant over the same range of normalized distances, indicating greater stability as a descriptor of the near-tip elastic–plastic stress field. The results demonstrate that the J-integral is highly sensitive to both crack-tip geometry and stress biaxiality. By comparison, the plastic SIF exhibits greater robustness with respect to crack-tip location and provides a more consistent characterization of the crack-tip field under varying loading conditions. For applied stress levels σ / σ ₀ ≤ 0.15, the J-integral is practically insensitive to the biaxiality ratio. However, at higher stress levels ( σ / σ ₀ > 0.15), the influence of remote stress biaxiality becomes significant. For the FRC crack-tip model, the J-integral decreases with increasing biaxiality ratio, whereas the opposite trend is observed for the MN configuration. The plastic SIF exhibits pronounced sensitivity to biaxial loading and decreases monotonically as the biaxiality ratio increases from equibiaxial tension–compression ( η = − 1) to equibiaxial tension ( η = +1), irrespective of crack-tip geometry. A comparison of small-scale yielding and extensive plasticity conditions indicates that the plastic SIF provides a more stable and informative characterization of the near crack-tip elastic–plastic stress field than the J-integral when variations in crack tip distance and crack-tip geometry are considered. Nevertheless, under extensive plasticity conditions, the plastic SIF becomes sensitive to the finite crack-tip radius of curvature. While the plastic SIF is essentially independent of crack-tip geometry under small-scale yielding conditions, substantial differences between the MN and FRC configurations are observed in the extensive plasticity regime. These findings highlight the necessity of accounting for finite crack-tip geometry when applying the plastic SIF approach to fracture analysis involving large-scale plastic deformation.

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