PSI - Issue 42

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Yuebao Lei et al. / Procedia Structural Integrity 42 (2022) 80–87

Author name / Structural Integrity Procedia 00 (2019) 000–000

bending stress parallel to the crack plane are applied at the right-hand side surface of the plate defined by x= W as a linearly distributed load. To avoid the effect of local plastic deformation on the loading, elastic properties are assigned to the elements in the first layer at the top of the plate for cases with small cracks. Loading cases for each crack depth analysed are ( � ) ± �� , ( � ) ± �� , ( � + � ) ± �� and ( � + � + �� ) ± �� . All loads are applied proportionally during the analyses. J is evaluated using the ABAQUS in-built “contour integral” function on 15 contours for each crack tip location and 11 locations along the crack front. Very good path independent results are obtained except for the values on the first contour. J values presented in this report are the values obtained on the second contour, which represent the maximum value on the 2 nd to 15 th contours for each crack tip location, in general. 4. FE J results The FE elastic J results show that, as expected, both the membrane and bending stresses parallel to the crack plane have no effect on elastic J and, therefore, the stress intensity factor (SIF). It is observed from the FE elastic-plastic J results that the applied membrane and bending stresses parallel to the crack plane affect the location for the maximum elastic-plastic J . In this paper, the presented elastic-plastic J values are those taken from the location with the maximum J value at a high load level along the crack front. These values are then normalised by the maximum elastic J value at the deepest point or at the surface point for the same loading levels. Note that the location for maximum elastic-plastic J may be different from that for the maximum elastic J . This treatment is consistent with R6 (2019) fracture assessment method where the elastic-plastic J for a surface crack is predicted from the maximum elastic J at the deepest or surface point, which is judged to be the maximum value along the crack front. The normalised FE J results for selected cases are plotted in Figs. 2(a)-4(a) against ( �� ) � � ⁄ , where the reference stress ( �� ) � is evaluated using Eqn. (5) without considering the effect of σ 2b . Figure 2(a) is for applied membrane stress σ m with/without σ 2b ( a / t =0.2), Fig. 3(a) is for applied bending stress σ b with/without σ 2b ( a / t =0.5) and Fig. 4(a) is for applied combined biaxial membrane stress ( σ m and σ 2m ) and bending stress σ b (λ=0.25 and λ 1 =0.5) with/without σ 2b ( a / t =0.8). In each figure, a curve representing the R6 Option 2 failure assessment curve (FAC) based reference stress J prediction (see Eqn. (13) in Section 5.3 below) is plotted, indicted by “Prediction”, for comparison with the FE results. For a given reference stress value, the reference stress prediction is conservative when the FE data are located under the “Prediction” curve and the limit load solution used to evaluate the reference stress can result in a conservative assessment result when it is used to define L r in an assessment using the R6 failure assessment diagram (FAD) method. From Figs. 2(a)-4(a), the bending stress parallel to the crack plane does affect elastic-plastic J and the magnitude of the effect depends on the intensity and sign (+/-) of the parallel bending stress. It is also seen from the figures that

Prediction FE, NPBS=0

FE, NPBS=1.08 FE, NPBS=2.25 FE, NPBS=-1.08 FE, NPBS=-2.25 NPBS = �� ⁄

J / J e

a/c=0.6 a/t=0.2

0.5

1.5

2.5

0.5

1.5

2.5

(  ref ) 0 /  y

 ref /  y

(a) ( σ ref ) 0 based on Eqn. (5), ignoring σ 2b (b) σ ref based on Eqn. (11) considering σ 2b Fig. 2 Comparison of normalised FE J for applied membrane stress σ m with/without σ 2b with the reference stress predictions without/with considering the effect of σ 2b in σ ref estimation ( a / c =0.6, a / t =0.2)

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