PSI - Issue 13

Yuebao Lei / Procedia Structural Integrity 13 (2018) 571–577 Y Lei/ Structural Integrity Procedia 00 (2018) 000–000

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5. Discussion The local limit load model defined in Section 2 is a plate containing a rectangular surface crack circumscribing the real surface defect. The model has the same thickness as that of the component at the defect location and an adjustable width depending mainly on the half crack length. The width is also linked to the normalised crack depth in order to improve the conservatism for deep cracks in J prediction. The global limit load of this model plate is evaluated based on the uncracked-body elastic stresses locally at the crack location without considering the effect of the load types. Note that the reference stress is evaluated based on a solution without shear stress (Eqn. (3)) and the shear stress effect is approximately included in Eqn. (2). Therefore, this model is not suitable for shear stress dominated cases. The local limit load obtained from this model should not exceed the global limit load of the defective component if the global plastic collapse mechanism occurs at the crack section. Otherwise, the local limit load is not necessarily to be lower than the global limit load of the defective component. For plate cases, the through-thickness bending stress is applied to the model because it balances the applied bending moment. It is found that taking k = 1.5 in Eqn. (1) can significantly reduce the conservatism in J prediction for deep cracks. The validation results show that predictions for all cases are conservative but close to the FE results and using this model can lead to the best J predictions compared with other available local limit load definitions [Lei (2016)]. For cylinder cases, the through-thickness bending stress is treated as a primary stress and k = 1 is used in Eqn. (1) for both axial and circumferential cracks. The validation results show that predictions for all cases except for several cases with circumferential long and deep cracks under pressure are conservative but close to the FE results and using this model can lead to the best J predictions compared with other available local limit load definitions [Lei (2016)]. For some cases of cylinders with circumferential long and deep cracks under pressure, the predictions are slightly non conservative because the local limit load is higher than the corresponding global limit load. When the local limit load is capped by the global one, all predictions are conservative. For cracked elbows, the French RCC-MRx (2015) A16 method is used to estimate the local stresses. The through thickness bending stress is treated as secondary for circumferential cracks and primary for axial cracks. For all cases, k =1 is used in Eqn. (1). The validation results show that using the local limit load of this paper leads to conservative J predictions and very conservative results for bending moments. The validation results show that the local limit load values obtained from the local limit load model tend to approach the global limit load for defective plate and cylinders, especially for pressurised cylinders and, therefore, can significantly remove the conservatism of the Connors’ method. For elbow cases, the local limit load is close to the global limit load for pressure but very conservative for applied bending moments. Applying this method to more complex components, such as defective pipe branches, requires more validation. 6. Conclusions and future work A new local limit load model has been developed for shell/plate type components with surface cracks for determining the local limit load or local reference stress used to predict J via the reference stress J scheme for defective components. The model is a plate which contains a rectangular surface crack circumscribing the real surface defect and has the same thickness as the component at the crack location and is remotely loaded by the primary stresses of the component at the crack location obtained from elastic uncracked-body stress analysis. The global limit load of this model is used as the local limit load of the defective component. This model has been validated using some 3-D finite element (FE) J results for semi-elliptical cracks in plates, cylinders and elbows. The results show that when this local limit load is used in the reference stress J scheme, the predicted J values are reasonably conservative, compared with the FE values. Further validation will be carried out for more complex structures like cracked pipe branches.