PSI - Issue 42

Yuebao Lei et al. / Procedia Structural Integrity 42 (2022) 80–87 Author name / Structural Integrity Procedia 00 (2019) 000–000 (σ ��� ) � � �� = ( ��� ) ��� �1 − �� + ��� (17) where (σ ��� ) � � �� is the reference stress for loading conditions without shear stress, μ =0.5 for plates and ( ��� ) ��� represents the reference stress without bending stress σ 2b and can be evaluated using Eqn. (5), with c / W replaced by c / D , and the load ratios, λ , λ 1 , λ 2 and λ bt , in Eqns. (5) and (17) are defined as = � 6 � , � = �� � , � = �� � , �� = 2 3 �� ( ��� ) ��� (18) The reference stress of Eqn. (16) represents the global limit load of the model plate and is then used as a local limit load of the component/structure to define the R6 parameter L r (see Eqn. (14)) in J prediction for defect assessment. 7. Conclusions In order to extend the use of the local limit load model developed by Lei (2018) to more complex structures, the effects of bending stress parallel to the crack plane on the limit load and elastic-plastic J of plates containing semi elliptical surface cracks have been investigated using the finite element (FE) method. A reference stress estimation method for a plate containing a rectangular surface crack under combined biaxial membrane and biaxial bending stresses has been developed. Based on the results of the investigation, the newly-developed local limit load model has been updated to include the effect of bending stress parallel to the crack plane. The conclusions drawn from this investigation are as follows. 1. The elastic FE J results show that the bending stress parallel to the crack plane, as expected, does not affect the stress intensity factor (SIF). 2. The elastic-plastic FE J results show that the bending stress parallel to the crack plane does affect elastic-plastic J. The magnitude of the effect depends on the intensity and sign of the parallel bending stress. 3. A reference stress estimation method considering the bending stress parallel to the crack plane has been developed (see Section 5.2) and validated using FE J results. 4. The local limit load model has been updated to include the effect of bending stress parallel to the crack plane, based on the reference stress solution developed in this paper. Acknowledgements This paper is published by permission of EDF Energy Nuclear Generation Ltd. References ABAQUS, 2017. ABAQUS Version 2017 User ’ s Manual, Dassault Systèmes Simulia Corp.; Providence, RI, USA. Ainsworth, R. A., 1984. The assessment of defects in structures of strain hardening material, Engineering Fracture Mechanics 19, 633-642. Lei, Y., 2004. 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., 2018. A local limit load model for J prediction via the reference stress method, Structural Integrity Procedia 13, 571–577. Lei, Y., 2019a. J predictions for defective pipe elbows via the reference stress method, Transactions SMiRT-25 Division II, Charlotte, NC, USA, August 4-9. Lei, Y., 2019b. A local limit load model for structural integrity assessment of shell/plate components with defects, EDF Energy Report E/REP/BBGB/0234/GEN/19 Revision 000, EDF Energy Nuclear Generation Ltd., Gloucester, UK. Lei, Y. and Budden, P. J., 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. Madew, C., 2019. Finite element fracture analysis of cracked pipe branch connections to support the development of local limit load approach, Wood Report 208898-0008-1786-DA02-RPT-001 Issue 1. R6, 2019. Assessment of the Integrity of Structures Containing Defects, Revision 4, Amendment 12, EDF Energy Nuclear Generation Ltd., Gloucester, UK. Rozenblium, V. I., 1960. Plasticity conditions for thin shells, Journal of Applied Mathematics and Mechanics 24 Issue 2, 520-524. 87 8