PSI - Issue 68

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Yu.G. Matvienko et al. / Procedia Structural Integrity 68 (2025) 641–645 Matvienko, Pokrovskii / Structural Integrity Procedia 00 (2025) 000–000

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Table 3. The effect of biaxial tension on the failure stress

Criterion including SIF and the Т xx -stress

Criterion including SIF and Т xx - stress as well as Т zz -stress

σ x / σ y

K I , MPa m 1/2

Т xx , MPa -17,3 61,8 117,2

σ frac , MPa 85,3 73,2 61,9

K I , MPa m 1/2

Т xx , MPa

Т zz , MPa

σ frac , MPa 90,3 66,0 53,8

σ x / σ y

2 3 4

66,8 57,3 48,5

70,7 51,7 42,1

-18,4

-200,0 -145,5 -117,9

55,7

101,7

4. Conclusions The following conclusions can be drawn.

The fracture criterion, which is based on the maximum tangential stress taking into account the nonsingular T xx and T zz stresses characterizing two-dimensional constraint in the transverse ( Т xx ) and longitudinal ( Т zz ) directions along the crack front, has been proposed for three-dimensional solids. The maximum tangential stress is assumed to be equal to the local strength in the fracture process zone ahead of the crack tip. The Tresca–Saint-Venant criterion and the Huber–Mises plasticity criterion are employed to calculate the size of the fracture process zone and the local strength along the crack front. Comparison of the calculated values of failure stresses obtained on the basis of the proposed criterion with the results of experiments shows a good agreement. In contrast to Т хх - stresses, which are barely independent on the thickness, the nonsingular Т zz - stress significantly depends on the plate thickness that affects the failure stress. It was shown that the failure stress for the same plate under uniaxial tension is greater than the failure stress in the case of biaxial loading. The tensile stress in the transverse directions along the crack front leads to the constraint increase. As a result, the failure stress decreases. Acknowledgements The authors acknowledge the support of the Russian Science Foundation (project N 24-19-00117). References Gupta, M., Alderliesten, R. C., Benedictus, R. 2015. A review of T-stress and its effects in fracture mechanics. Engineering Fracture Mechanics 134, 218-241. Matvienko, Yu.G., 2020. The Effect of Crack-tip Constraint in Some Problems of Fracture Mechanics. Engineering Failure Analysis 110, Article 104413. Nakamura, N., Parks, D.M., 1992. Determination of elastic T-stress along three-dimensional crack fronts using an interaction integral. International Journal of Solids and Structures 29(13), 1597–1611. Orange, T.W., Sullivan, T.L., Calfo, F.D. 1971. Fracture of thin sections containing through and part through cracks, NASA TN D-6305. Pokrovskii, A.M., Matvienko, Yu.G., 2023a. A Fracture Criterion with Biaxial Constraints of Deformations along the Front of a Normal Rupture Crack. Journal of Machine Manufacture and Reliability 52(4), 320–328. Pokrovskii, A.M., Matvienko, Yu.G., 2023b. The Two-Parameter Fracture Criterion Taking into Account Two-Dimensional Deformation Constraints at the Front of a Mixed-Type Crack. Journal of Machine Manufacture and Reliability 52(6), 532–541. Williams, M.L., 1957. On the Stress Distribution at the Base of a Stationary Crack. Journal of Applied Mechanics 24, 109-114.