PSI - Issue 42

Shiwen Wang et al. / Procedia Structural Integrity 42 (2022) 441–448 Shiwen Wang, Paul A Shard , Antony M Hurst and Yuebao Lei / Structural Integrity Procedia 00 (2019) 000 – 000

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Therefore, FACs in the form of equation (5, 6) are used to present all results in this paper. For the above equations, J e and J are values of the J-integral from the elastic and elastic-plastic FE analyses respectively, at a load corresponding to L r = σ ref σ y ⁄ . The value of L r can be determined from the limit load solutions as those considered in this paper. In addition, the results in the form of assessment points are also compared to R6 Option 1 and Option 2 FACs to demonstrate whether the analysis results give a conservative J estimation in the case of both the Option 1 and Option 2 FACs. For the Option 1 FAC, the reference stress J estimation, it can be represented as the following: = 1+0.5( ) 2 (0.3+0.7 (−0.6( ) 6 )) 2 for option 1 (9) For option 2 FAC, the reference stress J estimation scheme (Lei, 2020) predicts the total J from the elastic J, J e , using the reference stress, σ ref , and corresponding reference strain, ε ref , via the following relationship: = + 2 2 for option 2 (10) The reference stress and strain relationship in Equation (10) follows a uniaxial true stress-true strain curve of the material. For the Ramberg-Osgood type stress-strain relationship, this can be expressed as equation (3). Combining equations (10) and (3), J prediction using the R6 Option 2 failure assessment curves (FACs) can be expressed as: = 1 + ( ) −1 ( 0 ) −1 + 1 2 ( ) 2 (1+ ( ) −1 ( 0 ) −1 ) for option 2 (11) 3. FE Results J/J el vs. Lei and Budden L r Solution In this section, FE results are presented in the form of J/J el vs L r defined by the Lei and Budden limit load solution (Lei and Budden, 2015). The FE J values have been evaluated on 15 contours for each crack tip location and 11 locations along the crack front. Good path-independent results were found, except for the values on the first contour. The maximum difference between J values obtained on any contour except that on the first contour and the average of all values obtained on the 2 nd to 15 th contours is less than 5%. J values presented in this section, in general, represent the maximum value on the 2 nd to 15 th contours for each crack tip location. It should be noted that presented elastic-plastic (or total) J values are taken from the location with the maximum J value along the crack front. These values are then normalized by the maximum elastic J value between the deepest point and 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 the R6 fracture assessment method (R6, 2019) where the elastic-plastic J for a surface crack is predicted from the elastic J which is judged to be the maximum value along the crack front (in engineering practice, it is normally the maximum elastic J at the deepest and surface points because the elastic J at other crack front locations are not always available). The obtained elastic-plastic J in the R6 assessment is assumed to be the maximum value along the crack front, which controls possible crack initiation. The L r solutions are based on Section 2.3. R6 option 1 and option 2 FACs in the form of J/J el vs. L r are presented, including L r factored by 80% and 90% from the original L r values in order to assess the margins of R6 option 1 and 2 FACs. 3.1. J/J el vs L r for tension (  = 1.0), without and with lateral stress (   =0, ±0.5, ±1.0) Results of J/J el vs L r for 9 crack sizes (a/c=0.2, 0.6, 0.8, a/t=0.2, 0.5, 0.8), 2 plastic materials properties (n=5, 10), and 5 in-plane stress ratios (   = 0.0, ±0.5, ±1.0) with cross thickness bending (  = 1.0) are presented in Figure 2 to Fig. 6. The R6 option 1 curve is found to be bounding for all cases and all loads, except high aspect ratio cracks at deep crack depth (a/c=0.2, and a/t=0.8). The R6 option 1 is not conservative for L r at moderate value between