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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Results can be found in Figure. 8. A logarithmic scale has been used so that the distribution of elastic J around the crack front can be plotted together. For the shallow crack (a/t=0.2, Figure. 8 (a)), elastic J increases in a monotonic manner from the surface point to the deepest point for all bending cases, hence the maximum elastic J was found at the deepest point. For the deep crack (a/t=0.8), such a trend only exists for the pure tension case ( = 0.0). For the moderate bending cases ( = 0.2, 0.5, Figure. 8 (b)), the maximum elastic J is located between surface and deepest points. J values at the surface point increase steadily with the increase of membrane and through thickness bending stress. Only at large bending ratios ( = 1.0, 2.0), does the maximum elastic J move to the surface point. From the above two observations, it can be concluded that the J/J el ratio will be overestimated if maximum J el were taken from either the surface or deepest point for the case of a high aspect ratio crack at deep depth, unless there is no through thickness bending or the bending stress is not large. 5. Conclusions Limit loads for plates containing surface cracks under combined tensile loading perpendicular to the crack face, positive cross-thickness bending (crack opening moment) and membrane stress parallel to the crack face, are validated through FEA based J . The limit loads for cracked plates in this paper were characterized by the relationship of J/J el vs L r , compared with R6 options 1, 2 and 3 FACs. Conclusions can be drawn as the following: 1. FE results have been presented in the form of J/J el vs. L r = σ ref σ y ⁄ (i.e. R6 option 3 FACs) together with R6 option 1 & 2 FACs, where the global limit load solution from Lei and Budden (2015) is used for the reference stress calculation. FE results shows R6 option 1 & 2 FACs are generally conservative for assessment of cracked plates under combined plate end tension and bending load with additional stress parallel to crack plane. However, for a high aspect ratio crack at deep depth (a/c=0.2, a/t=0.8), R6 option 1 & 2 FACs may be non-conservative if maximum elastic J, J el , are taken from either the deepest or the surface point. This is because maximum elastic J, J el , occurs between the surface and the deepest point for such a crack at deep depth. 2. For shallow cracks with aspect ratio a/c=0.2, the location of maximum elastic J, J el , depends on the normalised crack depth (a/t) and through thickness bending ratio,  . For deep crack (a/t=0.8) and at moderate through thickness bending ratio (  =0.2, 0.5), the maximum elastic J, J el , is located between the surface and the deepest point. Goodall, I. W. and Webster, G.A., 2001. Theoretical Determination of Reference Stress for Partially Penetrating Flaws in Plates. International Journal of Pressure Vessels and Piping 78, 687 – 695. Lei, Y., 2004a. J-integral and Limit Load Analysis of Semi-elliptical Surface Cracks in Plates under Tension. International Journal of Pressure Vessels and Piping 81, 21-30. Lei, Y., 2004b. J-integral and Limit Load Analysis of Semi-elliptical Surface Cracks in Plates under Bending. International Journal of Pressure Vessels and Piping 81, 31-41. Lei, Y., 2004c. J-integral and Limit Load Analysis of Semi-elliptical Surface Cracks in Plates under Tension and Bending. International Journal of Pressure Vessels and Piping 81, 43-56. Lei, Y. and Budden, P., 2015. Global Limit Load Solutions for Plates with Surface Cracks under Combined Biaxial Forces and Cross-thickness Bending. International Journal of Pressure Vessels and Piping 132/133, 10-26. Lei, Y., 2020. Modification to a Local Limit Load Model to Include the Effect of Bending Stress Parallel to the Crack Plane. E/REP/BBGB/0240/GEN/20 Revision 000. R6, Assessment of the Integrity of Structures Containing Defects, Revision 4, Amendment 12, EDF Energy Nuclear Generation Ltd, 2019. References