PSI - Issue 68

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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employed from the paper published by Orange et. al. (1971). Table 1 presents the results of a comparison of the calculated and experimental failure stresses. In the case of the proposed fracture criterion, the average error is no more than 13%, which allows concluding that it is expedient to use the proposed approach for assessing the fracture toughness of structural elements. Table 1. Comparison of predicted and experimental failure stresses.

K I , MPa‧m 1/2

2W ,mm

2t, mm

2l , mm

Т xx , MPa

Т zz , MPa

σ exp , MPa

σ cal , MPa

δ, %

139.7 139.7 139.7 170.2 170.2 170.2

1.73 1.71 1.71 1.73 1.72 1.74

10.2 12.5 15.5 21.0 22.6 26.1

58.5 60.4 63.6 67.0 67.1 68.1

-472.9 -464.2 -444.3 -409.6 -408.7 -394.3

-282.1 -278.8 -269.8 -250.0 -252.6 -246.8

445.4 431.6 424.0 401.6 396.5 384.1

461.1 428.9 404.4 365.4 352.6 331.6

-3.53 0.626

4.62 9.01 11.1 13.7

To illustrate the possibilities of the proposed fracture criterion, the influence of the thickness on the failure stress is analyzed. The calculation was carried out for a square plate with a side of 200 mm and a crack with a length of 2 l = 140 mm. The fracture toughness is taken to be K Ic =65 MPa∙m ½ and the yield stress is 300 MPa. Table 2 shows the calculation results. In addition to the failure stress, the table shows the values of T- stresses. It can be seen, that with a decrease in the thickness of the plate the stresses Т хх and Т zz decrease due to the lesser constraint. As a result, the effective stress intensity factor also decreases, so the failure stress increases. There is negligible effect of the thickness on the failure stress in the case of including in the criterion only the Т хх -stress. At the case time, it should be also noted that, as it was expected, there is the effect of the thickness on the failure stress in the case of including Т хх - and Т zz - stresses into consideration.

Table 2. The effect of plate thickness on the fracture stress.

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

Criterion including SIF and the Т xx -stress

2t , мм

K I , MPa m 1/2

Т xx , MPa

σ frac , MPa 94,7 95,0 98,4 98,4

K I , MPa m 1/2

Т xx , MPa

Т zz , MPa

σ frac , MPa 125,8 119,7 109,9 101,6

10 20 40

74,1 74,4 77,1 77,0

-217,7 -212,8 -205,5 -207,0

98,5 93,7 86,1 79,6

-289,2 -268,0 -229,4 -213,8

-281,0 -245,7 -178,1 -107,3

100

To analyze the effect of loading biaxiality on the failure stress, a plate with the same dimensions and the mechanical properties of the material are considered. But, the plate thickness is assumed to be 10 mm. The plate is loaded along the y axis by stresses σ y = σ. Loading biaxiality σ x / σ y is assumed to be 2, 3 and 4. It should be noted that tensile stresses σ x do not affect the SIF value. The calculation results are presented in Table 3. This table shows that the values of Т- stresses increase with increasing the ratio between σ x and σ y . Moreover, Т хх stresses become positive if this ratio σ x / σ y >2. According to Table 2, the failure stress for the same plate under uniaxial tension is greater than the failure stress in the case of biaxial loading. Thus, the tensile stress in the transverse directions along the crack front leads to the constraint increase. As a result, the failure stress decreases.